Copyright: copyright (c) SoftTech 1995 - 1996


Tutorial Contents

At first, if you are new to bridge, there will seem to be a lot to learn. However, the ten informative sections, which make up the tutorial, should be an interesting guide:

Basic concepts

Overview

Step by step

Scoring

Basic card play

Basic bidding

Improving your game

Exercises

Appendix

Glossary

Copyright


Basic concepts

The first idea is that Bridge is played by four people. They play in pairs and normally sit at a small square table, the two members of each team sitting opposite each other.

The game is played with a standard pack of cards. Most people are familiar with the standard pack and the idea of a suit. In bridge the suits are very important and there are four of them as follows: ♠ spades, ♥ hearts, ♦ diamonds, ♣ clubs. The suits are ranked in order of importance. The ranking is as follows (the highest ranked first): spades, hearts, diamonds and clubs. The two higher-ranking suits, spades and hearts, are known as major suits; while the lower-ranking, diamonds and clubs are known as minor suits. You probably know that there are a total of 52 cards in the standard pack giving thirteen cards in each suit. In each suit there are the following cards (the highest value first): ace, king, queen, jack, ten, nine, eight, seven, six, five, four, three and two. Any ace, king, queen, jack or ten is called an honour. The fact that the cards are ordered is as important as the fact that the suits are ordered.

1.	How to start Bridge Assistant

It is a good idea to start Bridge Assistant now. There are a number of ways to do this from Windows; the easiest way is to double-click the Bridge Assistant icon:

The first thing you will see is the main program window. Enlarge it - if necessary - so that you can see all the parts of the program. You should see the table in the middle of the screen. Around the table you can see the four places. It is a convention in bridge that the four players are referred to by their compass position at the table. The player at the bottom is South, opposite is North, to the left West and to the right East (opposite West). You are South; at the bottom of the screen, to the right, you should see that it says South on the Status Line.

2.	Bridge with real players

When bridge is being played by real players (not on computers) there are a number of things to be done before play can begin. It is necessary to decide who is going to play with whom and who is going to sit where.

If it has not already been agreed who will play with whom the players will spread a shuffled pack of cards face down on the table. Each player will then choose a card. The players that choose the two highest cards will play with each other in a partnership against the other two players. The player with the highest card also decides where to sit and is the dealer.

The player on the dealer's left shuffles the pack which the dealer then passes to the player to the right to cut. Once this is done everything is ready and the dealer distributes the cards. Each player receives a hand of thirteen cards. The cards are distributed face down on the table and each player then picks up the cards, taking care to make sure that no other player sees them, and usually sorts them.

3.	Bridge Assistant Tutorial

When playing Bridge Assistant there is obviously no need to determine partners. You can, however, decide where you are going to sit at the table.

3.1	Changing position

Select Position from the Options Menu. This displays a sub-menu. One item will be checked indicating your current Position (if you are have not changed any program settings it will be South). If you wish to change this for example to East click on this item. The Status Line will change to indicate your new position; don't forget to change it back to South for the remainder of the tutorial.

3.2	Quick start

With Bridge Assistant you can select the dealer, shuffle and deal very quickly; also you don't have to sort the cards. To see immediately how this is done with Bridge Assistant go to:

Quick start.

New Ideas

Suit

Major

Minor

Honour

Hand

Shuffle

Deal

Sort


Suit
Suit (Basic concepts)

Each card in a standard pack falls into one four groups determined by which one of the following symbols is on the card: ♠ spades, ♥ hearts, ♦ diamonds, ♣ clubs. The order of the symbols in the list is the order in which the suits are ranked in bridge.


Major
Major (Basic concepts)

Bridge suits are ranked in order of importance; spades, hearts, diamonds and clubs. The two higher ranked suits are called major suits and the two lower ranked suits are called minor suits.

Spades and hearts are therefore major suits. Major suits are worth more points than minor suits points during the scoring.


Minor
Minor (Basic concepts)

Bridge suits are ranked in order of importance; spades, hearts, diamonds and clubs. The two lower ranked suits are called minor suits and the two higher ranked suits are called major suits.

Diamonds and clubs are therefore minor suits. Minor suits are worth less points than major suits points during the scoring.


Honour
Honour (Basic concepts)

Bridge cards have different values. In a given suit the ace will beat the king and the three is stronger than the two. The top five cards in each suit are known as honours.

Under certain circumstances having all four or five honours in a certain suit or all four aces will score points.


Hand
Hand (Basic concepts)

In Bridge each player has an initial hand of thirteen cards to play with. The cards are randomly dealt to each player.


Shuffle
Shuffle (Basic concepts)

In Bridge each player is given thirteen cards to play with. These cards have to be randomly selected. This is achieved by shuffling the pack. Not shuffling the pack properly will probably result in badly distributed hands.

The player to the left of the dealer usually shuffles the pack before passing it to the dealer to deal.


Deal
Deal (Basic concepts)

The dealer distributes the cards by starting with the player on the dealer's left and then giving out the cards one by one in a clockwise direction until there are none left. As a check the last card should be given to the dealer and each player should have thirteen cards.

As an additional point, it is normal for the pack to be cut before it is dealt. This is done by the player on the dealer's right.


Sort
Sort (Basic concepts)

Most bridge players sort out their cards as soon as they pick them up from the table. Usually players sort their cards by suit and in order of value. This makes it easy to identify how strong your hand is, what good cards you have and which suits are your best.


Overview

The idea of this section is to put all the basic bridge concepts in one place for easy reference. It is broken down into ten basic ideas covering scoring, bidding and playing. If you find it complex remember that there is a step by step tutorial in the next section where you can see how the ideas in this section are actually applied.

1.	Bridge is a competitive game

The first idea is that Bridge is a competitive game that is played for points. The competition in bridge revolves around a sequence of deals known as a rubber. Each side tries to win each deal and eventually the rubber. Winning the rubber scores a large points' bonus in addition to the points picked up along the way. For some people this is sufficient but others add the element of gambling. The way this works is that at the end of a session the number of points each side has scored is added up and the difference is calculated; the amount won or lost is then found using the formula: X amount for every 100 points.

2.	Trick and premium points

The second idea is that in bridge there are two types of points to be scored. The first type are trick points and are written below the line which runs across the middle of the traditional bridge scorecard. The second type are premium points that are written above the middle line of the scorecard.

3.	Games and part-scores

The third idea is that a rubber is won by the first side to make game twice. A partnership wins a game by being the first side to score 100 or more trick points. It is important to understand that only trick points count towards game. Once one side has scored game, a line is drawn under the trick points scored so far and another game begins with both sides attempting once again to be the first to accumulate 100 trick points. A score below the line that is not sufficient to make game is called a part-score.

4.	Contracts

The fourth idea is that to score points a player must bid and make a  contract or alternatively prevent a contract being made after the opposition has bid it. There are different levels of contract and more points are scored the higher the contract. But high contracts are harder to make - they require the partnership to have better cards. This is where the skill is in bridge; it lies in judging carefully the maximum contract that a partnership is likely to make without knowing how the other cards have been dealt. Similarly it is necessary to be able to judge when the opposition is unlikely to be able to make the contract they have bid. Only the side that wins the contract can score trick points, although both sides can score premium points; in particular, if the contract is defeated the winning side will score penalty points, which are one type of premium point. It is possible to make game by bidding and making a single contract but there are also some contracts that are too low to make game in one deal, these are known as part-scores. A player can make game by making a sequence of part-scores that eventually total 100 trick points or more. However, there is a risk that if the opponents score game before this happens then the part-score will have been wasted because the old part-score does not count towards the new game.

5.	Auctions

The fifth idea is that the contract is determined by an auction. How the auction works is that each player says what the contract should be (starting with the dealer). The bidding then passes in turn clockwise giving each player the chance to bid. Bids, like suits and cards, are ranked and each subsequent bidder must make a higher bid than the previous highest bidder - this pushes the final contract up. A player does not have to bid and to do this says 'pass' or 'nobid'. After all players have had a chance to bid and there have been three passes in a row the auction is complete and the contract is the highest bid made. The partnership that won the auction will then attempt to make it while the other side will defend and attempt to make the contract fail.

6.	Calls and bids

The sixth idea is that of the call. A call is when a player says something like: 'one club', 'four diamonds', 'pass', or 'seven notrumps'. A call can also be a bid; these are the calls with a number ranging from one to seven followed by one of the suits ranging from clubs to spades or the denomination notrumps; the calls that are not bids are 'pass', 'nobid', 'double' and redouble. Each subsequent bid must be higher than any previous one and the ranking is that if there is a higher level then that bid is higher. If two bids are at the same level then the bid with the higher ranking suit is the higher bid. And that notrumps is higher than any suit. Therefore, 'two diamonds' is higher than 'one spade', 'one heart' is higher than 'one club' and 'three notrumps' is higher than 'three hearts'. The highest possible bid is 'seven notrumps'. The calls 'pass' and 'nobid' are interchangeable and are used to indicate that a player does not want to bid, 'double' indicates that the player believes that the opposition has bid too high and raises the stakes in the scoring and 'redouble' raises the stake even further if the side that has been doubled believes that the contract will be made after all.

7.	Declarers and defenders

The seventh idea is that the players have different roles during the phase of the game when the cards are being played. The side that wins the contract attempts to make it while the other side tries their best to defeat the contract. A very important concept is that only one player plays the cards for the side that won the auction and is trying to make their contract. The one that plays the cards is known as declarer and the other member of this partnership that does nothing is known as dummy. An opponent is known as a defender. The player that becomes declarer is the member of the partnership that first bid the denomination of the final contract. Dummy's cards are in fact placed face up on the table so that all the players can see them. But this is only done after the first card is played. This means that all the players can see dummy's cards and that the declarer, for example, knows exactly what 26 cards the partnership actually has; remember that declarer only saw 13 cards (one hand) during the auction.

8.	Plays and tricks

The eighth idea is that of the play. Each player is dealt thirteen cards. The cards are played one trick after another until thirteen tricks have been played. What happens is that one player beginning with the player to the left of the declarer places a card face up on the table. The next player (in a clockwise direction) then plays a card and this continues until all four have played and there are four cards on the table. One of the players will have won the trick. The player that wins then gathers up the cards on the table and plays another card (the first of the new trick) to which each of the other players follows; this continues until all the cards have been played. Therefore, it should be clear that in each deal there are thirteen tricks to be made. It is possible for one side to make all thirteen tricks and the other to make none, but this is very rare. More frequently things will be more even; however, one side will always make more tricks than the other and the contract will always be either made or lost - there cannot be a draw. It is the attempt to guess how many tricks will be made from just looking at your own cards and hearing the bidding that requires a large amount of skill.

9.	Trumps

The ninth idea is that of the trump suit. When tricks are played the card that wins is usually the highest card in the suit that is led (that is the first card played in the particular trick). However, the contract may be a trump contract in which case it is possible to win a trick by playing a trump. In that case the card that wins will be the trump or if more than one trump is played the highest card played in the trump suit. Note, however, that if a player has a card of the same suit as that led he must play it. Therefore the opportunities for trumping are not as large as would appear at first sight. This links to the bidding and explains why a player would make a bid such as 'one spade'. The player does this to make spades trumps. This is done when the player has a lot of spades (for example, a very good situation would be one where the player has four spades and his partner also has four). By making the trump suit one in which the declarer's side has more cards than the opposition the declarer hopes to trump some of the opposition's tricks which would otherwise have won if there had been no trumps. If the contract is notrumps then there are no trumps and the card that wins is then always the highest in the suit led.

10.	Bidding systems

The tenth idea is that bridge can be a very subtle and complex game. If you already know something about bridge you may have heard that experts bid using extremely complex bidding systems. This is true but a beginner should concentrate on learning a natural bidding system, that is one where the bids made indicate the contract that the player thinks is feasible, the alternative is that the bids do not indicate the suit the player wishes to be trumps but some other feature of the hand such as strength or shape. Once the basics of a natural bidding system are understood the next stage is to grasp the idea of a convention. Conventions are bids used in a specific context to determine specific information about partner's hand. For example if an opening bid is 'one notrump' there is a convention known as the Stayman convention in which the partner replies 'two clubs'; this does not indicate that partner wants clubs to be trumps but the idea is to find out if the opener has four cards in a major suit. As you can imagine things can get quite complicated. There is also subtlety and complexity in the play of the cards. The point is that, as declarer say, you do not know how the cards you cannot see are placed. If you look at your hand and cannot make the contract immediately then you must begin to make assumptions or even guess where the cards are placed. There are also a number of techniques that have been invented to extract extra tricks when the cards have been determined to be distributed in highly specific ways. Some of these techniques are peculiar and some rare that players can play for a lifetime and never come across them, in a way therefore they are only theory.

This section has attempted to cover the most important bridge concepts in one place. Many of the concepts introduced here are explained again elsewhere in other contexts.

New Ideas

Rubber

Points

Trick points

Premium points

Game

Part-score

Contract

Auction

Call

Bid

Denomination

Declarer

Dummy

Defender

Play

Trick

Trump

Convention


Rubber
Rubber (Overview)

Bridge is played as a sequence of deals. The dealer deals the cards then the players bid and when the auction is complete play the cards. A rubber starts with the first deal and ends when either side has made two games.

The rubber is the complete unit of bridge scoring and when the rubber is complete the scoring starts again from zero. Also if the partners have not already been determined they will be determined again for the start of the next rubber.


Points
Points (Overview)

Bridge revolves around scoring points of which there are two types: trick points and premium points.

Only trick points count towards winning game. However, all points count towards the final score.


Game
Game (Overview)

Bridge is played as a sequence of deals. In each deal a player can make game by scoring 100 trick points. A player can also complete a game by bringing the total trick points scored to 100 by a sequence of deals.


Part-score
Part-score (Overview)

Bridge is played as a sequence of deals. In each deal a player can make game by scoring 100 trick points. A part-score is a score below the line that is not sufficient to make game.

That is a player has a part-score if in the current game he has scored 20,

30, 40, 50, 60, 70, 80 or 90 trick points.


Contract
Contract (Overview)

A contract is what one side is trying to achieve; for example, if the highest bid made is 'four spades' then that side must make ten tricks to succeed and score the points. If the contract is 'one notrump' then 7 tricks must be made to win and if the contract is 'seven clubs' then thirteen tricks must be made.

The method for calculating the number of tricks required is simple. It is the level of the contract (e.g. three diamonds has a level of three) added to six. Therefore, to make a contract of three diamonds 3 + 6 = 9 tricks have to be made.


Auction
Auction (Overview)

The auction is the process that is used to determine what the contract will be. It takes the form of a sequence of calls with the highest bid being the final contract.


Call
Call (Overview)

Calls are made by the players during the auction. They can be either a bid, pass (or nobid), double or redouble.


Bid
Bid (Overview)

Bids are part of the auction. Particular bids either attempt to fix the contract or supply information about the hand to partner. Bids take the form of calls like 'one club', 'four hearts' and 'seven notrumps'.


Denomination
Denomination (Overview)

When a bid is made it can either name a suit or notrumps which together with a number between one and seven makes up the bid. The choice from the five possible: clubs, diamonds, hearts, spades and notrumps is called the denomination of the bid.


Declarer
Declarer (Overview)

The player that makes the highest bid wins the auction and determines what the contract will be. However, the declarer is not necessarily the player that made the highest bid - the bid that won the contract. The declarer is the player that was the first to have bid the contract suit in the partnership that won the auction.


Dummy
Dummy (Overview)

The partner of the declarer. The word is also used to refer to declarer's partner's cards once they are spread on the table.


Defender
Defender (Overview)

A defender is either of the opponents of the declarer.


Play
Play (Overview)

Players make plays by taking a card from their hand and placing it face up on the table. This occurs during the stage of the game that follows the auction which is known as the play.


Trick
Trick (Overview)

Tricks are the units by which progress towards making a contract is measured. The cards are played as thirteen separate tricks one after another. Each trick is one by one player and the total number won by each side determines the outcome of the contract.


Trump
Trump (Overview)

When tricks are played the card that wins is usually the highest card in the suit that is led (that is the first card played in the particular trick). However if the denomination of the contract is a suit it is possible to win a trick by playing a card of the contract suit; these cards are called trumps. When a trump is played it wins the trick unless another higher trump is played by another player. However, if a player has a card of the same suit as that led he must play it - that is he must follow suit - which means that the opportunity for trumping is not as great as it seems.


Convention
Convention (Overview)

A convention is a bid which has a meaning other than the natural one. That is the bid does not suggest playing in the denomination of the bid but conveys other information to the player's partner. An example is the Blackwood convention which conveys the fact that a player is interested in a slam and needs to know how many aces partner has.


Trick points
Trick Points (Overview)

Trick points are one of two types of point in Bridge. Trick Points can only be scored by winning an auction and then making the resulting contract. The number of points actually scored for making a particular contract varies with the particular contract, but on the whole the higher the level of the contract the more points are scored.

If more than 100 trick points are scored, the player makes game, otherwise he makes a part-score and has to attempt to reach the total of 100 points on future deals - before the opponents do so and wipe out the part-score already made.


Premium points
Premium Points (Overview)

Premium points are one of two types of point in Bridge. Unlike Trick Points, which can only be scored by winning an auction and then making the resulting contract, Premium points can be scored in a number of ways.

By winning the rubber - score for either 2-0 or 2-1.

By making a doubled or redoubled contract - score for doubled or redoubled.

By making a slam contract - score for small or grand slam.

By making more tricks than required - score for number of overtricks.

By Having 4 or 5 honours in the trump suit or 4 aces in notrumps - honours.

By defeating a contract - score for number of undertricks.


Step by step

This section of the tutorial will be a step by step walk through Bridge Assistant. It will introduce you to the program and show you what the most important commands are. At this stage you should have started Bridge Assistant and got past the introductory screen and resized the window so that you can see everything.

The aim here is for you to play through a deal and see what happens. At any point if you get lost the tutorial can be restarted from the beginning. Remember that you are in the South position.

1.	Choosing the dealer

If you have read the sections before this you may guess that the first step is to select which player is going to be the dealer. There are four players in bridge and the other three, including your partner, will be played by the computer. The dealer can be any of the four players and is chosen at random.

Select the First Dealer option from the Bridge menu. Alternatively use the Dealer button in the Toolbar:  click on it. The program will randomly select the dealer. Note that on the second panel in the Status Line the player that is the dealer will be indicated. This will be either South, West, North or East. Also note that on the first panel of the Status Line a '1' is now displayed. The indicates that this is the first deal of the rubber.

2.	Dealing the hands

The next step is for the dealer to deal the shuffled pack of cards. One advantage with computers is that no one has to shuffle the pack. The computer does this automatically every time the program deals.

Select the Deal option from the Bridge menu. Alternatively use the Deal button in the Toolbar:  click on it. You should see that the program has dealt. As you are playing South the cards in the south position are displayed. The other cards are hidden.

Because the deal is random it is impossible for the tutorial to use the hand that has just been dealt. Therefore at this stage you should open the existing hand deal1.brg. In this deal South is the dealer as indicated in the second panel in the Status Line. Note that when a hand is opened the player that is dealer is restored along with the distribution of the cards.

3.	Making bids

The next stage is to decide which bid you would like to make. You make the first bid because you dealt. 1 Notrump is a reasonable bid to make on this hand (using the Standard American Bidding System). Identify the Bids Palette that is visible on the right of the screen window and labelled Bids. Press the [image] button in the bids palette. Now look at the Auction Box that is on the left and labelled Auction. You should see the bid you have just made directly under South.

4.	Completing the auction

Once the first player has bid it is the turn of the player to his left to bid. In this case since the dealer is South the second position to bid is West. West is being played by the program so the computer will bid for this hand. The program is waiting for you to tell it to bid; press the [image] button in the Toolbar. Once again you can see the bid displayed in the Auction Box, this time below West. West bids 'pass', it is now your partner's, North's, turn to bid. Press the bid button again; this time North will bid. North bids 'three notrumps' and it is East's turn to bid. Press the bid button and East will bid. East passes; as you can see there has been a complete round of bidding and once again it is your turn to bid. It would be simpler if the program would bid by itself without waiting for a button to be pressed each time. Go to the Bridge Menu, select the Auto Option and click on Bid; the program will now bid automatically when necessary without waiting for you to press a button.

Now you have to make another decision about what to bid. Pass is the correct bid in this situation. Press the [image] button in the bids palette. You expect the opposition to also pass meaning that your partner's bid of 3NT will win the auction and be the contract. Auto bid is on so bidding will continue automatically after your bid. West now bids, note that this is the last bid (the third pass in sequence) so with West's last bid the contract is complete. Look once again at the Status Line, in the third panel it is indicated what the contract is and who the declarer is: '3 Notrumps - South'. So you are the declarer, this agrees with the rule above that says which member of the partnership becomes declarer when the contract is won.

The contract of 3NT means that South and North have set themselves the target of making 9 tricks. If they make this contract they will score at least 100 points. East and West have to make 5 tricks to stop the contract being made.

5.	Playing cards

Now that the auction is complete the play starts, to start the play choose the Play option from the Bridge menu, alternatively click the Play button in the Toolbar: . West will play a card - the opening lead; in this case the ♣Q is played.

Once the opening lead is played dummy's cards are displayed - the program does this for you automatically. You now have to decide which card to play from dummy. Click on the card in the dummy that you wish to play - try the ♣6. The card will be moved to the table and then it is East's turn to play. Click again on the play button - east plays the ♣2. Now it is South's turn to play. As stated above the aim is to win tricks, so far the best card played is West's ♣Q; therefore to win you must play a higher card, play the ♣K.

The contract is notrumps so the card that wins is the highest card in the suit that was led. In this case clubs was the suit led and the highest card played was the ♣K which was played by South. Therefore South has won the trick; the first trick has been made towards the target of nine. Look at the fourth panel in the Status Line, you should see '1/0' this indicates that North and South (in this case you and your partner) have made 1 trick and that East and West (the opposition) have scored 0. It would be simpler if the program would play by itself when necessary. Similar to setting auto bid; go to the Bridge Menu, select the Auto Option and click on Play; the program will now play automatically when necessary without waiting for you to press a button.

There are twelve more tricks to be played. The table below shows the play for all thirteen tricks. In the table each trick is on a separate row, numbered 1 to 13. One of the cards is between two angled brackets '<>'; this indicates the first card played in any trick. As you can see the brackets are always in the same column as the hand that won the previous trick. The card that won the trick is also indicated by square brackets '[]'. West the next player after the declarer, South, in a clockwise direction plays the very first card.

To make it absolutely clear how this works the play for all thirteen tricks is explained again step by step below:

Trick 1: West played ♣Q, North played ♣6, East played ♣2, and South played ♣K; South won the trick. Score: 1/0; South to lead.

Trick 2: Click ♦Q in your hand, West plays ♦3; click ♦7 in dummy, and East plays ♦6; South wins the trick. Score: 2/0; South to lead.

Trick 3: Click ♦2 in your hand, West plays ♦5; click ♦J in dummy, and East plays ♦10; North wins the trick. Score: 3/0; North to lead.

Trick 4: Click ♦Α in dummy, East plays ♥4, click ♦4 in your hand, and West plays ♦8; North wins the trick. Score: 4/0; North to lead. (Note the discard).

Trick 5: Click ♦Κ in dummy, East plays ♠8, click ♦9 in your hand, and West plays ♣4; North wins the trick. Score: 5/0; North to lead.

Trick 6: Click ♥5 in dummy, East plays ♥9, click ♥K in your hand, and West plays ♥2; South wins the trick. Score: 6/0; South to lead.

Trick 7: Click ♥Α in your hand, West plays ♥3, click ♥8 in dummy, and East plays ♥J; South wins the trick. Score: 7/0; South to lead.

Trick 8: Click ♣5 in your hand, West plays ♣10, click ♣A in dummy, and East plays ♣3; North wins the trick. Score: 8/0; North to lead.

Trick 9: Click ♠5 in dummy, East plays ♠Κ, click ♠Α in your hand, and West plays ♠2; South wins the trick. Score: 9/0; South to lead.

Trick 10: Click ♠4 in your hand, West plays ♠Q, click ♠6 in dummy, and East plays ♠9; West wins the trick. Score: 9/1; West to lead.

Trick 11: West plays ♥7, click ♥10 in dummy, East plays ♥Q, and click ♥6 in your hand; East wins. Score: 9/2; East to lead.

Trick 12: East plays ♣7, click ♣9 in your hand, West plays ♣J, and click ♣8 in dummy; West wins. Score: 9/3; West to lead.

Trick 13: West plays ♠3, click ♠10 in dummy, East plays ♠J, and click ♠7 in your hand; East wins. Score: 9/4; Contract made.

6.	Updating the score

The next stage is to update the score. But first of all the Scorecard has to be displayed. Go to the View Menu and select the Score Card Option. The Scorecard will now be displayed. The Scorecard Box is labelled Scorecard and is displayed on the left. The box has two columns one labelled 'We' and the other 'They'. Any points that your side scores will go in the 'We' column and the points scored by the other side in the 'They' column.

Now that the Scorecard is visible you can score for the last deal - the contract of 3NT which was made by the NS partnership. To score the deal choose the Score Option from the Bridge menu, alternatively click the score button in the Toolbar: . The program has now scored the last deal.

You should see that the program has written 100 on the 'We' side below the line drawn halfway down across the middle of the Scorecard. The program has then drawn a new line beneath the 100. Also along the bottom the program has calculated the totals that indicate that North and South are winning at this stage and have scored a total of 100 points to their opponents 0 points. Bridge scoring is actually quite complicated; but what has happened here is that by making a contract of 3NT you have made scored 100 points and made the first game.

7.	Continuing the rubber

Once the auction is complete, the play finished and the score card updated it is time to assess the situation. If the rubber is finished, that is, on the last deal, a partnership won its second game then everything starts again from the beginning. If the rubber has not finished then it is time for the next player to deal. The deal moves round the table in the clockwise direction. Therefore since South dealt the last hand it is now West's turn to be dealer.

It would be simpler if the program would rotate the deal by itself when necessary. Similar to setting auto bid; go to the Bridge Menu, select the Auto Option and click on Rotate; the program will now rotate the deal automatically when necessary and you will not have to change the dealer yourself. To change the dealer manually choose the Next Dealer Option from the Bridge menu, alternatively click the change dealer button in the Toolbar: . The program has now rotated the dealer clockwise. The Status Line will change to indicate the new dealer. Note that in the first panel of the Status Line a '2' is displayed, this indicates that this is the second deal in the Rubber.

Select the Deal option from the Bridge menu. Alternatively use the Deal button in the Toolbar:  click on it. You should see that the program has dealt; and also that because the dealer has changed from South to West that it is now West's turn to open the bidding - this is indicated in the Auction Box where the first player to bid is always on the left. Once again the tutorial cannot use a randomly dealt hand; open the existing hand deal2.brg.

West is the dealer and therefore makes the opening bid. Since West has to make the first bid you could simply click on the bid button to start. Alternatively, in the same way as setting auto bid; go to the Bridge Menu, select the Auto Options and click on Open; the program will now open automatically when necessary without waiting for you to press a button. In either case West bids first and passes. North passes and then East. It is now your turn to bid; the correct bid is 1♥. West passes again. This time North does not pass but bids 2♦, East passes again. It is now your second bid, bid 2♥. West passes. North bids 4♥, the next three bids are all passes and complete the auction. The outcome is that you are declarer again; the final contract of 4 hearts means you must make 10 tricks and that hearts are trumps.

Now you must play the cards. The play of the cards is indicated in the table below. West has to play the first card. You could simply click on the play button to get things started. Alternatively, in the same way as setting auto bid; go to the Bridge Menu, select the Auto Options and click on Lead; the program will now lead automatically when necessary without waiting for you to press a button. There are thirteen tricks to be played in all; for either North or South you must click on the card to play it, the East and West cards will be played automatically (if auto play is on).

The play will not be repeated again as it was for the first deal above. Instead what is most interesting about each trick will be discussed.

1:	The club lead is won by the highest card.

2:	Declarer deliberately leads a low club with the intention of winning by trumping it. His plan works East and West follow with clubs.

3:	Declarer leads a diamond from dummy. This will also be trumped.

4:	Declarer plays another low club. Notice how all the low cards are being trumped. South is getting rid of the 'losers' in his hand.

5:	Declarer leads a trump, a heart, from dummy. He is now playing out his winning trumps.

6:	Declarer leads a diamond which is trumped. The reason is to create a situation where the lead can come from declarer's, South's, hand.

7:	Declarer leads a winning heart. Trumps will be played until the defenders no longer have any. This is called drawing trumps. It prevents the opponents trumping unexpectedly

8:	South finishes drawing trumps. Note that low diamonds have been discarded from dummy.

9:	Declarer plays his winning club and discards another diamond in dummy.

10:	Declarer now plays a low spade although clearly the defenders will win this trick. West wins.

11:	West plays the diamond ace which declarer wins by trumping. North and South have now made ten tricks so the contract is secure.

12:	Declarer leads a spade, East wins.

13.	East then plays the last trick and wins with the only remaining club.

The next stage is to update the score. Make sure the Scorecard is visible. Press the score button and the program will now score for the second deal. Observe the score. Another 120 points have been added to the 'We' column and a second line has been drawn beneath this; this means that you have scored another 120 trick points and have made the second game. Also note that 700 points have been added to the 'We' column above the middle line. This is the bonus, in premium points, for winning the rubber 2-0. The final score for the rubber is therefore N/S 920 points E/W 0 points. The rubber is now complete and a box appears to confirm this, when you are ready press OK. This will clear everything and prepare for a new rubber. On the fifth panel in the Status Line a running total now appears, this now shows $920. You have won 920 electronic dollars congratulations!

8.	Finishing the game

Once the rubber is complete everything starts from the beginning. Go to section 1 above, choosing the dealer. Select the First Dealer option from the Bridge menu or click the button in the Toolbar: . Continue as before. The game continues as a sequence of rubbers with the score accumulating in the Status Line.

This step by step account of how to use Bridge Assistant has not really explained the strategies behind bridge. For this you must see the next section.

Related Ideas

Opening an existing hand

Making a bid

Viewing the auction

Discarding a card

Viewing the score


Opening existing hands (Step by step)

Select the Open option from the File menu. Alternatively use the Open button in the Toolbar:  click on it. You should see the file open Dialog box appear. Select the file you want to open. (The files for the tutorial are called deal1.brg, deal2.brg, etc.) Press OK.

You should see the hand displayed in the same way as when you dealt.


Making a bid (Step by step)

Bids are made using the Bids Palette which is shown below. To make the bid simply press the button corresponding to the bid you wish to make.

P: Pass	N: Nobid

D: Double	R: Redouble


Viewing the auction (Step by step)

The entire auction is displayed in the auction box. The bids are recorded here as they are made.


Discarding a card (Step by step)

Players have to play a card of the same suit as that led. However, sometimes a player does not have a card of the same suit. When this happens the player can play any card from the hand.

If the contract is a trump contract the player can choose to play a trump. This card will then win unless another player has also run out of cards in the suit that was led and can therefore play a higher trump.

If the player does not have a trump, or chooses not to play one then the card played can never win and is known as a discard.


Viewing the score (Step by step)

The score is displayed in the Scorecard Box. The scores are recorded here as they are made.


Bridge scoring

This section of the tutorial deals with the subject of bridge scoring in detail. How are points scored? Which contracts make the most points? What does all this imply about strategy? You may have expected the auction and play to be discussed first; however, putting the score first does have the advantage of setting the goal so that you know clearly why you are doing various things.

In the overview section above some of the basic concepts have already been discussed. Here more details will be given and new ideas will be explained. The fundamental idea is that there are two types of points to be scored in bridge:

trick points and premium points; and that on the traditional scorecard trick points are written below the middle line on the card and premium points above that line. Only declarer can score trick points on any deal while premium points can be scored by either or both sides. An additional important factor in calculating the points scored is the concept of the double.

1.	Trick points

Trick points are scored by declarer when the contract that was bid is made; so how many trick points does declarer score? This depends on three factors: (1) the denomination of the contract, (2) the level of the contract, and (3) was the contract undoubled or was there a double or redouble .

So how does it work. For every trick over six bid and made declarer scores a number of points:

Clubs:	20 points.

Diamonds:	20 points.

Hearts:	30 points.

Spades:	30 points.

Notrumps:	30 points (First trick 40 points).

Here are a few examples for undoubled contracts bid and made.

1♣	20 points.

3♥	90 points.

5♦	100 points.

4♠	120 points.

2NT	70 points.

The score can be represented in a table. Each row represents a given level of contract while each column represents a given denomination.

If a contract is doubled the trick points are simply doubled. If the contract is redoubled the points scored is four times the value in the table. Here are some more examples:

2♥	doubled	120 points.

7♦	undoubled	140 points.

2♣	doubled	80 points.

7NT	redoubled	880 points.

1♠	redoubled 	120 points.

3NT	undoubled	100 points.

2.	Premium points

Either or both sides in any deal can score premium points. Premium points can also be scored in more than one way, to be specific there are six ways to score this type of point. A very important concept that appears often is that of vulnerability; this concept must be fully grasped to understand bridge scoring properly. It is also important to appreciate the scoring potential of the slam

2.1	By winning the rubber

By winning the rubber a player scores a large number of premium points. The points scored depend on whether the rubber is won 2-0 or 2-1. The two cases score as follows:

2-0	700 points.

2-1	500 points.

Sometimes the rubber is not fully concluded. In that case the score might be either 0-0, 1-0 or 1-1. In two of these cases the scores are level, therefore neither side scores any points; in the third case (1-0) the side that is ahead scores. Another case is where one side has the only PART SCORE in an uncompleted game, that side also scores points as below.

1-0	300 points.

part-score	100 points.

2.2	By making a doubled or redoubled contract

There are two cases here depending on whether the contract has been doubled or redoubled. Declarer not only scores twice or four times the number of trick points but also gets 50 or 100 points for the "insult".

Doubled	50 points.

Redoubled	100 points.

2.3	By making a slam contract

By bidding and making a slam contract a large number of points can be scored; this reflects the difficulty of making 12 or 13 tricks. The number of points scored depends on whether the slam is a small slam or grand slam, and also on whether declarer is vulnerable or not (that is has already made game in the current rubber). The following table gives the scoring:

2.4	By making more tricks than required - overtricks

If declarer bids a contract and actually makes more tricks than required then each extra trick scored is known as an overtrick. It is important to remember that such tricks do not score trick points and therefore do not count towards making game. The number of points scored depends on whether the contract was doubled, on whether declarer was vulnerable and if the contract was undoubled on the denomination of the contract. The following table gives the score for each overtrick:

The table refers to trick values. These depend on the denomination and are the same as those scored by declarer as trick points for each trick above six made. That is:

Clubs:	20 points.

Diamonds:	20 points.

Hearts:	30 points.

Spades:	30 points.

Notrumps:	30 points

2.5	By Having honours

A player can score points for having certain cards - honours if the correct contract is arrived at. There are three situations where this can occur:

Four Trump honours	100

Five Trump honours	150

Four Aces in a notrump contract	150

All the cards must be in one hand. Either side can score but it would be quite unusual for it not to be declarer or his partner. Sometimes players, by agreement, choose not to score honours.

2.6	By defeating a contract - undertricks

If declarer bids a contract and fails to score the necessary number of tricks then the opponents score points. Tricks short of making the contract are known as undertricks. The number of points scored depends on whether declarer is vulnerable, the contract is doubled and on how many tricks declarer failed by.

The scores are given in the table below. Where there are two figures in a box for example, '200/300', the first is for the case where declarer is not vulnerable and the second for the case where declarer is vulnerable. Fourth and subsequent tricks score the same points.

Defenders can therefore score very highly by defeating declarer's contract. To give the most extreme example. A player is vulnerable and bids seven diamonds which is then doubled and redoubled; declarer makes no tricks. The defenders would score 7600 points. This has probably never happened in the history of bridge; however, there is the basic lesson which is that penalty points can be very profitable.

3.	Strategy

This section aims to give you a feel for what you are trying to do and how it all fits in with the figures for scoring given (in great depth) in the previous two sections.

To summarise the above it is clear that some of the ways of scoring points are either minor for example points for honours, and overtricks and undertricks when the contract is undoubled; or dependant on the opposition making bad decisions for example points for making doubled contracts; or depend on good luck for example defeating a soundly bid contract and earning a large penalty bonus.

Given the above clearly you must focus on the best way to score significant amounts of points by your own efforts. There are two. Firstly to bid and make contracts with the intention of winning two games and hence the rubber before the opponents do. Secondly to bid slams whenever it is likely that they can be made. Achieving these goals earns hundreds not tens of points. And since hands strong enough to make slams are relatively rare your focus must be on winning the rubber and scoring the premium points for this. To win the rubber you must win two games so the focus is really on bidding and making game. While doing this there is always the possibility that your contracts will be defeated but your goal should be to ensure that (1) the contract is not so bad that it will fail by many tricks (2) that the opponents do not feel they can double it (3) that you are more cautious when you are vulnerable.

Although the two methods are important for scoring points you should always remember that a very large point score is possible for defeating contracts. As already mentioned you should try to avoid this by careful bidding. However, the opponents may not be so careful and so you should always be on the look out for badly bid contracts especially when the opponents are vulnerable. When you think you have found such a contract you should double and if you defeat it by many tricks you could gain premium points in one deal equal to that made by winning a rubber or making a slam. But to repeat, significant penalty points can usually only be scored with at least some help from the opposing side. Although a certain number of contracts are destined to fail simply due to bad luck these will usually fail by one or two tricks at the most and are not really worth doubling especially part-scores.

If you examine the score table and remember that to make game 100 trick points are needed you will notice that to reach game in different denominations the contracts must be at different levels. See the following list:

5♣	100 points.

5♦	100 points.

4♥	120 points.

4♠	120 points.

3NT	100 points.

What this implies is that these particular contracts play a very important role in bridge. Although you can make lower contracts in each denomination, by doing so you will only make a part-score with the constant risk that the opponents will score game before you do and thereby wipe out your part-score. The 3NT contract makes game with only nine tricks, however the major suit game contracts are of at least equal importance because the presence of trumps can compensate for the fact that ten tricks are required. This brings us to the most basic strategy in bridge bidding that is:

Bid game if you have a 50-50 chance of making the required number of tricks. Otherwise bid the lowest part-score the opponents will allow you to play in. Bid a small slam if you have a 50-50 chance of making 12 tricks. Bid a grand slam if you have a 75-25 chance of making 13 tricks.

There are exceptions to every rule but the above is absolutely fundamental and bearing it in mind will explain many things in bridge. You may ask how you can know what the odds of making a particular number of tricks are, which denomination should be considered, and how it is even possible to guess since the number of tricks that can be made depends on the cards in both hands and not just those you can see in your own hand after the deal. The answer is simple and is that you must make inferences about partner's hand from the bidding and assess the combined trick winning potential of the two hands from this. More about trick winning can be found in the section that follows on playing the cards in bridge and more about how bids describe a hand in the section on bidding.

So to conclude this section: in bridge the main struggle between the two sides revolves around the attempt to win the rubber and score the premium points for doing this. Both sides where possible will try to bid game but failing this will bid part-scores and try to make game on subsequent deals before the opponents can. Slams should be bid where it is likely that they can be made and the additional premium points scored.

New Ideas

Double

Redouble

Vulnerability

Slam

Overtrick

Undertrick


Slam
Slam (Scoring)

The strategy in bridge can roughly be described as bidding the highest contract you think you can make. If your hand is very strong and you infer from the bidding that your partner also has a strong hand then you may bid 6 or 7 of a suit or notrumps. These contracts are known as slams.

To make a slam contract you will then have to make 12 or all 13 tricks. This is not an easy feat.

A 6 level contract is known as a small slam and a 7 level contract as a grand slam. They are quite rare. It is important to know that there is a large bonus in premium points for making slams. For example, if you make a grand slam when you are vulnerable you will score 1500 extra points.


Vulnerable
Vulnerable (Scoring)

A side that has won one game towards winning the rubber is described as vulnerable. This term comes from the fact that the premium points scored are now increased. For example, if a vulnerable partnership bids a contract and that contract is doubled and is defeated by three tricks, that is there are three undertricks, then the opponents will score 800 points. This is a large score. As a comparison if the partnership is not vulnerable then the score would be 500.

This means that players have to be more careful when they are vulnerable. That is their bidding should be more cautious.

Both sides can be vulnerable if the current score in the rubber is 1-1 (both sides have made one game).


Double
Double (Scoring)

A player can double any contract bid by the other side. This is done when the player thinks that the opponents will not make the contract. By doing this the stakes are considerably raised.

If the contract is actually made then the number of points declarer scores will also be increased. Therefore doubling has to be carefully judged.

It is also possible to redouble. This is done when a contract has been doubled and the side that bid it thinks that, on the contrary, they can make it. The stakes are raised even further by redoubles.


Redouble
Redouble (Scoring)

A player can redouble any contract that the other side has doubled. This is done when the player thinks that the contract will be made notwithstanding the opponents' double. By doing this the stakes are raised even higher.

If the contract actually fails then the number of points the defenders score will also be increased. Therefore redoubling has to be carefully judged.


Overtrick
Overtrick (Scoring)

An overtrick is an extra trick made by declarer beyond the minimum number required to make the contract.


Undertrick
Undertrick (Scoring)

An undertrick is each trick that was not made by declarer but which was required to make the contract.


Basic card play

Although it may seem a better idea to introduce the auction next, in keeping with the fact that the section on scoring was discussed first the play will now be described; this is justified by the fact that the bidding is really only a preliminary to the play. This will give you a feel of how a variety of different types of hands play and therefore what contracts they are suitable for.

In the play of cards things must be considered in two entirely separate ways for the declarer and the defenders things are also quite different depending on whether it is a trump or notrumps contract. Other factors that can affect how the contract is played are whether or not it is a slam and whether either side is vulnerable.

Topics

Playing introduction

Playing basics

Playing no trumps

Playing trumps


Playing Introduction

A very important point that all beginners should be aware of is that the play of the cards, especially for declarer, is not done on a trick by trick basis. It is important to plan the entire play as soon as dummy appears. How this planning works will be discussed below. What can be said is that it involves choosing the best strategy based on various probabilities for the distribution of the missing cards; choosing good strategies will win in the long term but interestingly on specific hands a bad strategy can sometimes win.

There are a number of very obvious things in bridge that can have profound consequences so for the benefit of the beginner here they are:

1.	Someone has every card

There are four suits and thirteen cards in each suit. All the cards are dealt so every card is somewhere. If you do not have a particular card then one of the other players has it. If dummy does not have it (after the opening lead) and you are declarer then one of the defenders has it.

2.	There are thirteen cards in each suit

If you are declarer and have four cards in a suit and dummy has four cards in the suit then the defenders have five between them in that suit. That is as soon you see dummy you know how many cards the other two players have in the suit. You can deduce nothing from this fact about how they are divided between the two players; one may have all five, one may have four and the other one or they may be split 3-2.

3.	Suit are more likely to be split evenly

If there are a number of cards missing in a suit then it might be very important whether or not one defender has a lot of them or whether both defenders have roughly equal amounts. It is always most likely that a defender has close to half the missing number of cards. For example, if six cards are missing it is most likely that a given defender has three rather than four (or two) and if five cards are missing two (or three) rather than four.

4.	Discards place the remaining cards of a suit.

If a player discards a card then it means that if there are cards missing in that suit - that is cards of that suit have not already been played and they are not in yours or dummy's hand - then the other player has them. This means that you can sometimes definitely identify who has certain cards; with other techniques it is possible to draw inferences which are almost as strong.


Playing basics

Although there are significant differences between the play of a notrumps and a trump contract there are some basic principles which both have in common. These are concerned with the techniques used to ensure that the maximum number of tricks is obtained from any suit. The differences are concerned with the handling of trump cards.

1.	How to win tricks

This section will deal with playing tricks in a general way. Tricks can really only be won in three ways. All of these different ways play an important role. This is because the aim is to make the contract and the final trick that achieves the required total is as important as all the earlier ones.

1.1	With high cards

The most basic fact about playing is that high cards tend to win tricks. Look again at the playing of the cards in the first deal of the tutorial. What you can see from this is that of the thirteen total tricks four are won by aces, three are won by kings, three by Queens and three by Jacks.

The conclusion that can be drawn is that, especially in notrumps, high cards will win tricks.

1.2	With trumps

Consider also the playing of the cards in the second deal of the tutorial. In this case three tricks are won by aces, two are won by kings, one by a queen, two each by jacks and tens and three by non-honours. In this case all the non-honours that win tricks are trumps. And in all cases they either beat an opponent's honour or prevented an honour being played to win the trick.

The conclusion that can be drawn is that in trump contracts low trump cards can win tricks.

1.3	With low cards

But sometimes even in a notrump contract low cards can win tricks. See the playing of the cards in the hand deal3.brg. What you can see from this is that of the thirteen total tricks four are won by aces, four are won by kings, one each by a queen and jack and three by small cards. The small cards manage to win because they are in a suit of which, in that particular deal, North and South had nine cards. After three tricks had been played in that suit which were all won by high cards the opponents had no cards left in the suit and therefore what remained won when the suit was led again.

The conclusion that can be drawn is that in notrump contracts, but sometimes also in trump contracts, low cards (that in the case of trump contracts are not trumps) can win tricks if the partnership has many cards of that suit.

2.	Establishing high cards

High cards tend to win tricks but only if they are not beaten by an even higher card. This is why aces are so valuable, when played (especially in a notrump contract) they are very likely to win the trick; and if the ace and king are together then two tricks are almost certain. Look at the following diagram showing a suit in the North and South hands.

The ace and king will make a trick but will the jack win a trick? This will depend entirely on whether when the ace and king are played by North on the first two tricks in this suit the queen is played by one of the defenders. The defenders can see the ace and king in dummy and will hardly play the queen voluntarily since they know it will beaten. So it will only be played if the defenders have to do so in order to play a card of the suit led - this is called 'being forced to follow suit'. If the queen does appear then when the jack is led it will win a trick.

A very important tactic in bridge is to force the opponents to play their high cards when you play your winning honours, this will mean that they will not win tricks in their own right and lower cards you hold in your hand may be promoted to being the highest unplayed card in a suit.

In other words the best use for an ace is to win the opponents' king.

3.	Winning without the top card

What is the problem? Consider an isolated bridge trick:

For example the diagram above shows the last trick of a notrumps contract. The card that wins is the highest in the suit that is led. And if all the players have a card of the same suit then it does not matter who makes the opening lead the holder of the highest card will win the trick. This example demonstrates this; whoever leads East will win the trick with the spade king. But in other cases it does matter who leads.

Consider the following two examples that show the last two cards of a deal. The difference is that the East and West cards are exchanged.

There are two tricks at stake and it should be obvious that the ace will win one of them. The question is therefore whether the king or the queen will win the second trick. If the ace wins the first trick and the king is played then clearly the queen will win the second trick; but there is a more subtle situation which is when the king is not played on the first round because it would be captured by the ace and the queen wins the first trick. What happens depends on who leads the first card and what card is played when players have a significant choice to make.

Diagram a:

First of all consider diagram a. Suppose South leads with the intention of playing the king from dummy. West can either play the ace or the queen. Either way the king will win a trick. If West leads he can either lead the ace or queen once again the king wins a trick. If East leads then on West once again will have to choose between playing the ace and the queen and North's king will win a trick. But suppose North leads then he can either lead the king that will lose to the ace or lead the two that will lose to the queen; and then West will play the ace and drop the king making two tricks. What has been shown is that who leads can decide who makes a given trick. Note that in three of the four cases above declarer made a trick and the defenders also made one, while in the remaining case the defenders made two tricks.

Diagram b:

Now consider diagram b. Suppose South leads with the intention of playing the king from dummy, West will capture the king with the ace and then win the second trick with the queen. If West leads then the situation will be almost identical and the defenders will make two tricks. If East leads then North's king will make one trick. And if North leads then he can either lead the king that will lose to the ace or lead the two that will lose to the queen; and then West will play the ace and drop the king making two tricks. Once again who leads decides who makes a given trick. Note that in three of the four cases above declarer made no tricks and the defenders made two, while in the remaining case declarer made one trick and the defenders also made one.

What factors decided the outcomes? The key factor was whether the hand with the king, in this case North, got to play a card after the hand with the ace. Whenever this happened, the king won the trick. In one case the ace was in the East hand and therefore since the play moves clockwise the decision whether or not to play the king would always have to be made before East has to decide whether to play the ace - with one exception which is when East led. What follows from this is that if you are trying to win a trick with a high card and the opponents have a higher card the most important factor is which hand has the missing card. If it is before your card then with a lead from three of four positions, you will win the trick. If it is after your card, then you will only win with a lead from one position.

The opponent that has missing high cards is determined by chance. But if you are trying, for example, to win a trick with a high card in the type of situation described above then you have a 50-50 chance of making the trick everything else being equal. Now suppose declarer has the lead in the situation above and had the opportunity to decide which hand to lead from in the positions in the two diagrams. Clearly leading from dummy would not win a trick in either case (a) or (b). Whereas leading from South would win a trick in case a but lose in b. One is certain defeat and the other a 50-50 chance. The choice is clear:

A very important principle of card play in bridge is to lead towards high cards and to avoid leading away from them. This will win extra tricks when the opposing cards are favourably placed.

In other words opponents can be presented with a difficult choice of what card to play before you have to play your card.

4.	The famous finesse

Anyone learning bridge will very quickly hear about the technique called the finesse. So what is it? At one level it is simply a case of obeying the rule above and leading towards high cards. But it often also combines an element of establishing high cards. Consider the following suit:

South is declarer and is attempting to win as many tricks as possible from the spade suit. South could simply play the ace and hope that the king would fall and that the queen and jack would be established. This is a long shot - one of the defenders would have to have the king alone. This would be a 6-1 split and is rare; or alternatively declarer may be satisfied with two tricks in which case playing the queen or the jack will allow the defenders to win a trick but set up a winner. But declarer could arrange (if possible) to lead a low card from the South hand and play the queen from dummy. In this case West, seeing the ace in dummy, will play low and the queen will win. Now declarer plays the ace from the dummy and the king has to be played by West with the result that the jack is now a winner.

However, when declarer began to play this suit the layout of the cards was not known. Consider the following possibility:

In this case the queen simply loses to East's king. The finesse fails. The jack is still promoted to a winner and North and South will make two tricks in this suit. Another possibility is the following:

In this case the queen wins and the finesse succeeds but when the ace is played the king does not fall. Therefore the strategy does not achieve the desired goal of making three tricks. The jack is not established as a winner. And the final example:

In this case the queen loses to the king. But what is interesting here is that if declarer has pursued the strategy of playing the ace then three tricks would have been made. However, the odds for playing the queen are far better than those for playing the ace. The point is that bad play can sometimes be rewarded!

A very important technique in bridge is the finesse. It is an attempt to win a trick with a card lower than the opponents' highest. It is often combined with an attempt to establish more winners by making it more likely that a high honour will fall.

5.	Percentage plays

Two techniques have been described for winning additional tricks; establishing high cards by dropping the opponents' winners and leading towards high cards to exploit the favourable placing of the opponents' cards. But consider the following situation:

After the king is played and wins the first trick a low card is led from dummy to which East plays low South has a choice. The possibilities are to either attempt to drop the queen or to assume that the queen is favourably placed with East and to finesse it. Which choice is correct? Or more importantly how should such a choice be made? Everything being equal; that is if there is no indication as to who has the queen (from the bidding not the opponents' body language)! The problem is solved by stating that the odds favour playing for the drop. See the appendix for the details. Therefore in this position you should play the ace.

If you looked at how the odds were calculated you can see it was complex and involved the use of a probability table. You may ask if you have to do this every time. The answer is that you have to learn to remember the various combinations of cards and what to do in each case. It should become easier with practice.

In card play choices often have to be between different plays. The principle that works is to choose the play with the highest chance of success. Sometimes the play with the lower odds will would have won but by following this strategy a player will win in the long run

Of course players do not usually work all this out when playing but tend to remember common card combinations. It can help, however, to understand why a particular play is recommended with a given combination of cards.

6.	Safety plays

You have now seen a variety of techniques for making tricks. However, one important factor has not been mentioned which is the importance of the order in which you play your cards. Consider the following:

After noting that East and West have four spaded between them you could simply say that it is likely that they will all fall on the first three tricks so you will simply go ahead and play the ace, king and queen. But the chance of the spade suit breaking 4-0 is 10% and if this happens the jack will win the fourth trick. Since your aim is to maximise the odds of winning, a skilful player will see if even this 90% chance can be increased - perhaps to 100%.

The solution comes from observing that you will know if there has been a 4-0 break after the first trick is played. You have two choices to either win the first trick with the ace or with the king (or queen). If you win with the king and a 4-0 break shows up then you can finesse the jack in either of the opponents' hands. However, if you win with the ace you can only finesse if East turns out to have four cards. Therefore the first strategy wins five tricks 100% of the time and the second 95%. The choice is clear, win the first trick with the king in the South hand. This takes care of a rare distribution without any additional risk. Once again practice is needed to learn the card combinations and what the plays are.

In card play the order in which winning cards are played can be important. The possibility of bad distributions should always be considered.


Card Play Deal1.brg (Playing basics)


Card Play Deal2.brg (Playing basics)


Card Play Deal3.brg (Playing basics)


Playing no trumps

1.	Count the winners

On any deal, if you are declarer, the player on your left makes the opening lead. Once this occurs your partner will place his cards, the dummy, on the table. At this point whether it is a trump or notrump contract, you must assess the situation. For a notrump contract this assessment consists in counting the winners.

1.1	Counting winners in deal1.brg

Look at the club suit you have an ace in your own hand and the king is in dummy this means that you will definitely win two tricks in this suit. Look at the diamond suit, here you have the ace, king, queen and jack this means that you will make four tricks in diamonds. Look at the heart suit you have the ace and king, two tricks. And look at the spade suit here you just have the ace, one trick. Adding up the winners gives 2+4+2+1 = 9. To make 3 notrumps you need nine tricks and because a club was led and you can win the first trick you can deduce that the contract will be made before you have even played a card.

1.2	How to count winners

The way to count winners is as follows. The maximum number of tricks you can win in a suit is equal to the maximum number of cards that either your hand or dummy has in that suit. For example consider the following hand. The contract is 3NT, Declarer is South and the opening lead is ♠Q. In clubs there is the potential to win four tricks however since you do not have the ace count zero winners; in diamonds you have the potential to win three tricks and you have the ace, king and queen so count three winners; in hearts the potential is four tricks you have the ace but not the king count one winner and in spades the potential is two tricks you have the ace and king count two winners. This gives the 0+3+1+2 = 6.

Unlike the case above you do not already have the required number of winners in this case you need three more tricks to make the contract. Where will these additional tricks come from? This is the next step; understanding the potential of various suits to make extra tricks. In diamonds for example there is no potential to win any more tricks while in hearts it is clear that once the defenders have played their king you will make two more tricks. Similarly once the ace of clubs is played either the king or queen will win a trick. In spades there is little chance of finding another trick.

1.3	Additional winners - opening lead

In bridge there are always subtleties. For example consider the following hand. The contract is 3NT, Declarer is South and the ♥6 is led. There are six winners. But the king of hearts is in your hand. It now becomes a winner because it will either win this trick or if East has the ace and plays it the king will become the highest unplayed heart. Therefore in situations like this you must upgrade your count to take into account the opening lead.

1.4	Additional winners - low cards

Sometimes it is clear that low cards will win tricks. For example consider the following hand. The contract is 3NT, Declarer is South and the ♠Q is led. There are six winners. Now suppose that instead of the ♣6 in the South hand you had the ♣J. But East and West only have four clubs between them. This means that since you have the top four honours that you can play out all their cards. When you do this there will still be two clubs in the North hand and they will both be winners. This would give a total of nine winners: two spades, one heart and six clubs.

1.5	Lost winners - no entry

There is another potential problem. For example consider the following deal. The contract is 1NT, Declarer is South and the ♣K is led. There are apparently six winners: one club and 5 spades; but look closely at the spade suit. Although there are five potential winners and you and dummy have the five top cards in the suit after the ace and king are played from the South hand and it is time for the queen to win a trick there is no way to lead a spade for the queen to win a trick. You cannot lead a spade from South because there are none left and there is no way to get to the North hand to lead the queen of spades itself. This is known as not having an entry. Therefore the queen, jack and ten are not winners and you only have three winners.

1.6	Opponents' winners

Your opponents will not allow you to have things all your own way and will try to win tricks of their own. They will also make the opening lead so with skill or luck they may make enough tricks to defeat your contract.

Consider the hand, the contract is 3NT, South is declarer and the ♥Α is led. You have nine winners and are maybe thinking that you will make the contract. But West has the ♥AKQJT in hearts and will win the first five tricks. Therefore, your contract will actually go down. If West was for some reason (it would be a very bad lead) to lead something other than a heart then you would make your winners and the contract. In other words there is a kind of race to make tricks and you have to be aware that your opponents have winners of their own and may get the chance to play them before you can play yours.

2.	Finding extra tricks

Once the opening lead has been made and you have counted your certain winners the next step is to check how many extra tricks you will need to make and decide where they are going to come from. The possibilities for making extra tricks in different types of hand are almost infinite. But below there are some basic principles.

2.1	Example

For example consider the following hand. The contract is 3NT, Declarer is South and the ♠Q is led. There are six winners. Therefore to make your contract you must make three more tricks.

2.2	How to find extra tricks

The place to start is by assessing each of the four suits for its potential to make extra tricks. However, with experience it will become clear on the one hand that certain suits with certain combinations of cards are unlikely to produce extra tricks and on the other that extra tricks tend to come from the longest and strongest suit. Once again consider the following hand.

There are two winners in the spade suit (from a possible total of three), but it is highly unlikely that the ♠6 will win a trick, so forget spades for extra tricks. There is one winner in the heart suit (from a possible total of three) and there is also another honour, the jack. Can the jack win a trick? The king and queen are missing and if either is in the West hand it is likely that the jack will not win a trick. There is about a 25% chance that the jack could win a trick - not very good; and three extra tricks are needed. There are no winners in the diamond suit (from a possible total of five) once again there are honours, but higher honours are missing and whether the king will win will depend on who has the ace. If West has it then the ace is well placed to capture the king; there is a 50% chance of winning a trick with the diamond king. There are three winners in the club suit (from a possible total of six) and because declarer and dummy have the majority of the cards there is the possibility that low cards could win. There are four clubs in the East and West hands and so it is likely that when the top three honours are played East's and West's clubs will be exhausted. Then the club suit will provide three more winners. This is the number required to make the contract; so in this deal declarer must look to the club suit for his extra tricks.

3.	Discovering dangers

The next stage is to assess your options. There may be only one way of making the additional tricks or there may be several. In the latter case the decision you will have to make is which method is the best; and best means is most likely to succeed given that you do not know how the cards are actually distributed. In fact whenever there are potential tricks, which are not winners, there is always a danger to be found and assessed.

3.1	Bad break

Once again consider the hand, with the same declarer, contract and opening lead. There are six winners and the club suit has been identified as a source of additional tricks. To repeat the low club tricks are potential winners because when you get the lead you cannot guarantee that you will win them immediately. But in this case what declarer intends to do is to play the AKQ of clubs and hope that on the three tricks all the opponents' clubs will be played leaving the three remaining clubs in dummy as winners. But a danger lurks which is that one opponent will have all four clubs. If that happens then the club jack will possibly win a trick which will mean that clubs will not provide three additional tricks and another trick will have to be found elsewhere - possibly in diamonds.

So the danger in this case is of a 4-0 split in the club suit. A 2-2 split or a 3-1 split is no problem.

3.2	Badly placed high cards

Consider the hand; the contract is 3NT. There are six winners and the heart suit is an obvious source of potential tricks. The finesse is obvious and if it works would bring in three extra tricks; but a danger lurks which is that East has the king. If that happens then the heart suit will only produce two additional tricks and another trick will have to be found elsewhere - possibly in clubs.

So the danger in this case is of East having a specific card, the heart king, if West has it the contract is easily made.

3.3	No stoppers in a suit

Consider the hand; the contract is 3NT, South is the declarer and the ♠J is led. You have eight winners and the club suit appears to give the potential to make at least one more. However, there is a problem which is that you have no stoppers in the heart suit, the top four cards are missing and if the opponents get the lead they will play them. In other words the opponents have five winners when they get the lead.

So the danger in this case was that the opponents have sufficient winners to defeat the contract as soon as they get the lead. Therefore, they cannot be allowed to get the lead before you have made nine tricks.

3.4	No entries

Consider the hand; the contract is 3NT, South is the declarer and the ♥Q is led. You appear to have nine winners: five clubs, one diamond, two hearts and a spade. Also you can win the first trick; but suppose you win the first trick with the ace and then begin to win your club tricks. After you have won the first three you will not be able to play the jack in dummy; you do not have a low card to lead towards it and you cannot get to dummy to lead it from dummy. This illustrates a fundamental point, that to win a trick you need both the winner and the opportunity to play it. In this case the problem is solved by winning the first trick with the king in the South hand, the heart ace then serves as an entry to dummy to play the winning clubs after the top three honours have been played and won.

So the danger is in this case was leaving winning cards in a hand with no entries. The solution was to preserve an entry so that the winners could be made later.

3.5	The opponents' develop extra tricks first

If the opponents cannot immediately defeat your contract they will try to find extra tricks of their own. You goal is to make it as difficult as possible for them to develop extra tricks in their chosen suit. Consider the following hand; the contract is 3NT, South is the declarer and the lead is ♦10. A quick count reveals that declarer has eight winners and a very good chance to get another in one of the other suits. But the defenders will be trying to score tricks of their own. They will quickly see the club king in dummy, West will wonder whether East has the ace and given the chance will lead a club. The defenders could easily develop a number of low card winners in the club suit and this would defeat the contract. Declarer has to be aware that the opponents have a suit they can play and must counter their plans.

So the danger is in this case is that the defenders have a suit in which they can develop winners.

4.	The final plan

So for any hand you should (1) count the winners (both for your side and the opposition), (2) If you are short of the required total, decide where the extras tricks are going to come from and (3) check where the dangers are. Once this is done you are ready to begin play. But first you should plan the play out in advance so that you won't be surprised by what happens. This section deals with this planning by working through a number of examples.

4.1	Example one

Once again consider the hand; contract 3NT, South declarer, ♠Q led.

(a) Count winners:	8.

(b) Extra tricks:	From clubs

(c) Dangers:	4-0 club break,

Few entries to the North hand.

(d) Plan:	Play:- spade ace or king and win the first trick.

Play:- club ace.

Check?- 4-0 split.

No:- contract is made. End.

Yes:- 4-0 finesse West's JT twice. End.

Yes:- 0-4 serious problems (5%).

Play:- low club allow East to win.

At this stage you realise that the contract depends on chance. East has many choices of what to lead.

The success or failure of the contract was out of your hands if the particular bad break occurred; however, you would have reduced the risk to below 5%. Note that the spade entry to North is not vital and has to be balanced against the advantages of having a choice of when to win a spade return.

4.2	Example two

Consider the hand; the contract is 3NT, South is the declarer and the ♠J is led.

(a) Count winners:	8.

(b) Extra tricks:	From clubs by forcing out the ace,

an extra spade from a 3-3 split.

(c) Dangers:	Heart suit is wide open (4 or 5 tricks).

(d) Plan:	Play:- spade king and win the first trick.

Play:- five diamond winners.

Play:- spade ace.

Play:- spade queen

Check?- 3-3 split or all opponents' spades gone.

Yes:- contract is made. End.

No:- serious problems (64%).

At this stage you know that the contract will almost certainly fail. You can lead a club and hope for the best.

Note how by playing your diamonds before spades you gave the defenders the opportunity to make a bad discard. Spades had to be used for the extra trick since if the opponents got the lead there was the risk that they could take at least five winners immediately.

4.3	Example three

Consider the hand; the contract is 3NT, South is the declarer and the ♦10 is led.

(a) Count winners:	8.

(b) Extra tricks:	From spades by finessing the queen.

From hearts by finessing the king.

(c) Dangers:	Club king exposed to a lead from West.

(d) Plan:	Play:- win the opening lead in the South hand.

Play:- queen of hearts and finesse. End

The plan here was to seek the extra tricks in hearts rather than spades. This was because if the heart finesse lost East would be on lead whereas if the spade finesse lost West would be on lead. You did not want to give West the opportunity to lead a club through your king. This plan has a 100% chance of success.

5.	Exercises

Test your play.


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Card Play (Playing notrumps)


Basic bidding

If you are working through this tutorial in order you will just have read the section on play. You would have got some idea of what combination of cards is needed to play in particular contracts. However, you can go through this section before the section on play if you prefer. This section will explain how to go about reaching the right contract.

Topics

Introduction

Basics

Uncontested auctions

Contested auctions

Slams

Conventions


Bidding introduction

The bidding is the stage of the game of bridge that sets the target which one side tries to make and the other side tries to defeat. Bidding also sets the target at various levels; either high or low. And since the number of points scored will depend on the contract, the side with the better cards will in general try to bid as high as possible to score as many points as they can.

Simply put what bidding does is to say in advance how many tricks you think you can make. The actual sequence of bids enables you to judge the strength of your partner's hand and your assessment of the combined hands then allows you to judge the level you can safely play at.

Look at the hand. As you can see this hand contains no Ace, King, Queen or Jack. It is a very weak hand. The next hand is stronger, it contains an Ace, a King, a Queen and Jack. It is an average hand - to see this imagine the honours being divided evenly between the players - each player having one of each honour. It is important to realise that on average your hand will be like this. And more subtly that the more hands are like this the more likely they are to occur. That is you are more likely to have a hand containing an Ace, King, Queen, and two Jacks than you are a hand with an Ace, King. Queen and four Jacks. Now consider the hand. This hand contains an Ace, two Kings, four Queens and two Jacks. It is a strong hand. As such it is rarer than the average hand mentioned above. A player would definitely open the bidding with this hand.

Look again at the hands in this section as you can see they are of many different types. Note that in some cases a hand has many cards of one suit this defines a property of a hand known as the shape. Hands with shape can be very powerful especially if the long suit ends up being the trump suit. What will tend to happen is that the low cards of a long suit will win simply because the opponents have run out of cards in that suit. Also because there are 'extra' cards in one suit there will be corresponding shortages in other suits. If these suits are led and there are no longer any cards of that suit left to play then a trump can be played and the trick won. These considerations lead to the following basic principle of bidding in bridge:

The two factors that determine the strength of a hand are firstly the number of high cards it contains and secondly its shape. A player must take both into account when calculating a hand's strength.

But the question still remains about how to judge how many tricks the combined hands can make without being able to see your partner's cards. Recall the section How to win tricks which analysed what type of card tends to win tricks. Suppose that all four players have average hands (one ace, one king etc.), it is intuitively obvious that both sides should make six tricks with the thirteenth being determined by luck. Now suppose an average honour (a king say) is transferred from one hand to another then it should follow that this hand would win one more trick and the other one less. This is the underlying idea behind most systems of bridge bidding. However hands are usually described in terms of points, the points being calculated by assigning a range of values to honours.

So at the end of this section you should have understood the basic reasoning in bridge bidding that goes like this. "I have an average, above average or below average number of honours, therefore my hand is likely to make X number of tricks. I don't know how many honours my partner has but I could suppose that the ones I don't have are split evenly among the other players. This means that my partner is likely to make Y tricks. This means that the total number of tricks the hands will make is likely to be Z tricks. I will therefore not bid beyond this level and expect my partner to keep the bidding low without the expected strength".

This line of reasoning will help you determine the level you can play at but it does not help with determining which denomination you should play in. Recall the section on bridge scoring strategies which discussed the tactics that result from the rules of bridge scoring. There it was stated that your fundamental aim is to reach game - slams are rare and are of secondary consideration - but to stop in a part-score if it becomes clear from the bidding that you do not have the strength required. In the various denominations you must bid at certain levels for game: 3NT, 4♠, 4♥, 5♦ and 5♣ are the minimal game contracts in each denomination. From the previous discussion it is clear that you need more strength (honours) to make higher contracts therefore 3NT is a very important contract because it makes game with the fewest number of tricks.

It would seem that your strategy is simple: bid notrumps. But in evaluating a hand's strength shape also counts. And finding that you and your partner have eight cards between you in a suit (known as a fit) can be worth at least an extra trick. This means that where there is a major suit fit the major game is a better contract than notrumps. Here is an example of a hand that demonstrates how this works. Suppose the hand is played in 3NT the opponents are very likely to lead hearts after which the suit will be wide open. But in a spade contract you would be able to trump the opponents' hearts and thereby maintain control of the suit while you developed your winners in other suits. Therefore sound bidding strategy is to try to identify a major suit fit and to bid game in that suit if the combined hands have sufficient strength.

But what happens if there is no major suit fit? It is then a sound strategy to aim for game in notrumps. However, there is a condition which is that the hands must be balanced or have stoppers in every suit; a balanced hand is one with at least two cards in every suit (the hand with the 5-4-2-2 shape is marginal). And if there is no major suit fit and the hand is unbalanced? This would imply that there is strength in the minor suits; the strategy is then to consider how risky it would be to play in a notrumps game or a minor suit game, and if the odds are too low to play in a minor suit part-score. To summarise the strategy:

Look to see if there is a major suit fit, if so investigate the major suit game. Failing this evaluate the possibility of playing in notrumps and check if your distribution and stoppers are sufficient. If both of these fail consider the minor suit game. If the hand is without sufficient strength stop in an appropriate part-score, but also be on the look out for strong hands that could make a slam.


Bidding Basics

As you have seen what is needed is a way to judge hands, and answer the question how strong is this hand? Also what is required is a way to judge what partner's bid says about the strength of the hand and finally a method to judge how many tricks the combined hands will make. In the introduction to bidding the idea was that a rough idea of strength could be obtained by counting honours; but some honours are better than others and hands can have many different combinations of honours. What is therefore needed is a system that take all this into effect and simply returns a number that says: this is how strong a given hand is.

1.	The High Card Point system

The high card point system is a method for evaluating the strength of hands that is very widely used by bridge players; in fact it is a tried and tested system that has been in existence for a very long time. What the player does is to calculate a value for his hand based on the table below. That is for every ace in his hand he counts four points, for every King he counts 3 points, for every Queen two points and for every Jack 1 point. The total gives the number of high card points (HCP) in his hand.

Consider the hand. This hand has no aces, kings, queens or jacks and therefore no high card points. The hand has 1 Ace, 1 King, 1 Queen and 1 Jack. It therefore has 4+3+2+1 = 10 HCP. In the complete pack there are 4 Aces, 4 Kings, 4 Queens and 4 Jacks therefore the total number of points is Aces (4 * 4) = 16, Kings (4 * 3) = 12, Queens (4 * 2), = 8 and Jacks (4 * 1) = 4; this gives a total 16 + 12 + 8 + 4= 40. Therefore this average hand has 10 HCP which is one quarter of the total - this should not be surprising. And the third hand with an ace (1 * 4), two kings (2 * 3), three queens (3 * 2) and four jacks (4 * 1) has a total of 4 + 6 + 6 + 4 = 20 HCP. This hand is therefore twice as strong in HCP as the average hand; as an aside a hand with 10 HCP occurs more than tens times as frequently as a hand with 20 HCP.

So the first thing a player does as soon as the cards are dealt is to count the number of points. For experienced bridge players this is instantaneous process; that is they can calculate the number of HCP in a hand probably just by looking at it. For other people it takes practice.

As an exercise you can look some bridge hands dealt by Bridge Assistant and practice calculating the number of high card points.

2.	Problems with the HCP system

The High Card Point system is fairly good but it does have some problems. One problem is that it does not take into account distribution. Another is that it does not say what to do with your points. Except that if you and your partner have 26 HCP total in your two hands then all things being equal you are likely to be able to make game. Note that it does not say what happens if you have 25 HCP and whether you should play the game in a suit contract or in notrumps.

In the referenced section an extension to the High Card Point system called the Decision Points system is described. It addresses some of these problems.

3.	The Standard American system

With any technique for evaluating hands it should be clear that there are only a limited number of possible bids to handle every biddable hand. What is therefore needed is a system for assigning particular bids (and sequences of bids) to various types of hand. It is important that both players should understand what every bid made at the table means, because if there is a misunderstanding it can easily result in a disaster and the loss of points. Note that the rules of bridge also state that the opposition must be able to understand the bids (bidding systems are not secret!), this is so that they can use the information to help their defensive play.

Bridge Assistant uses the Standard American bidding system; this is the most popular system world-wide. Another widely used system is the ACOL system. Where they differ is in how they handle 1 Notrump bids and also that Standard American uses the double raise to signify strength where as ACOL uses it as a limit bid; these concepts will be explained later.

It is important to stress that both systems are natural bidding systems. This basically means that when a bid is made and a suit called there is some relationship to the strength of the suit; in bidding systems that are not natural a bid of one club, for example, may have no relation at all to the club suit. There are many other bidding systems some of them highly complex. This complexity usually means that they can only be used by partnerships that play together frequently; the question of which bidding system is the 'best' is a subject of frequent discussion and is very hard to resolve.


Bidding uncontested auctions

One type of auction is the uncontested auction. This is where the first side to open bids the entire auction by themselves and the opponents do not interfere; this is either because they have weak hands or cannot bid a suit at a safe level. About half of all of auctions are uncontested. Contested auctions are more complicated but they are also handled using the principles that will be explained in this section.

1.	Some basic principles

Before you begin to read this section it is a good idea to make sure you understand how to make bids using Bridge Assistant. In this section you will often be asked to make the program bid; a convenient way is to use the bid button in the Toolbar: . On other occasions when it is your turn to bid you will be asked to let the program give you a hint: use the hint button to do this: .

1.1	Some opening bids

[ Open the hand deal4.brg ]

[ Turn on hints using: Options → Allow Hints ]

[ Turn off auto bidding using: Bridge → Auto → Bid ]

[ Choose the hint command: Bridge → Hint ]

As you can see the program has bid 1 spade. It is easy to see why this is the bid for this type of hand in the Standard American bidding system. The hand is strong, 17 HCP, much stronger than the 10 HCP average hand described above. The hand also contains a strong spade suit. It is most likely that a player will have three cards in a suit but here there are five spades. Notice also that the suit contains three honours: the ace, the king and the ten. So this is an 'obvious' bid.

[ Open the hand deal1.brg using: File → Open ]

[ Choose the hint command: Bridge → Hint ]

As you can see the program has bid 1 notrump this time. It is obvious that the hand does not contain a particularly strong suit. In fact all the suits are fairly similar. 1NT indicates that the hand is balanced, that is the hand has one of the following shapes: 4-3-3-3, 4-4-3-2 or 5-3-3-2. A player in a notrumps contract does not want to risk the opponents establishing a long suit which they can use to win a stream of tricks with low cards. This is a real risk when bidding notrumps and a player should be as sure as possible that the opponents cannot 'run' a long suit. Players can either check using the bidding that they have 'stoppers' in every suit or bid notrumps only with balanced hands as a way of preventing disaster.

[ Open the hand deal5.brg using: File → Open ]

[ Choose the hint command: Bridge → Hint ]

The program has bid 2♠ for this hand. As you can see this is a strong hand. The hand is especially strong because it has a large number of spades. It is stronger than deal4.brg, although it has the same number of HCP, due to the long suit. But why has the program bid 2♠ instead of 1♠ as with deal4.brg. After all both hands are stronger than average; and since there is a continuous range of possible hand strengths where is the cut-off point between 1♠ and 2♠. The answer to this question is that a player should bid 2♠ when afraid that his partner will pass and thereby miss an almost certain chance to make game.

1.2	Bids at the one level

The bids 1 club, 1 diamond, 1 heart and 1 spade will be referred to by the common form 1X. This is because these bids in natural bidding systems are made inter-changeably depending on which suit is the strongest. Note that this does not include the 1 notrump bid which will be referred to by the short form 1N.

1X bids are the bids on which the Standard American system is built. If a hand is biddable then the first bid the player should consider is a bid of one of a suit (1X). The next question is which suit; the answer is the longest suit. You may ask about two suits having the same length and  what to do in this situation. This problem will be dealt with below.

1.3	Looking ahead

Every time you make a bid you have to be aware of what your partners responses could be and what you will do after each response. It is possible that your partner can make a bid which will leave you with no suitable reply. Consider the following example:

[ Open the hand deal6.brg using: File → Open ]

[ Choose the hint command: Bridge → Hint ]

As you can see the hand is fairly weak but still suitable for an opening bid. Your longest suit is spades. But what happens if you bid 1♠ and your partner bids 2♦. You will not have a good bid to make in this position. Therefore you must be aware that you can be embarrassed by partner's reply and plan for this possibility. With the hand shown the player has to be flexible and bid 1♣. This is one exception to the advice to bid the longest suit. But note that there is a reason for the exception which is that after a plausible bid by your partner you would not have had a suitable bid.

1.4	Bidding notrumps

Since all hands can, in theory, be opened by 1X bids what is the purpose of the 1 notrump opening bid?

The purpose is to show a balanced hand - that is one without a six card suit or a singleton. Partner will therefore immediately know that if a game is to be played it will most likely be played in 3 Notrumps. So for hands to be opened 1NT they have to be balanced. Another property such hands must have is that they must have between 16 and 18 HCP. This is for the Standard American system and these limits are quite strict. This is one area where bidding systems vary widely; ACOL for example uses 1NT for balanced hands in the range 12 - 14 HCP; other systems use the range 15-17 HCP.

There is a reason for the narrow band of HCP values allowed for the bid. It is this. Partner will be trying to judge whether the two hands combined have sufficient strength to play in 3NT. If partner has 9 HCP there is no problem; if however partner has 8 HCP then the two hands combined point score could be anywhere in the range 24-26 HCP. This means that partner cannot immediately jump to 3NT but must bid 2NT and if you do not have minimum 16 HCP hand then you can raise to 3NT. For this reason the range of points must be narrow. If partner has 7 HCP then he knows that game is only possible if you are maximum and therefore will not bid 2NT. Therefore, to repeat, the range of values for a bid of 1 Notrump is 3 HCP: 16 HCP, 17 HCP and 18 HCP.

2.	The opener's bid

This section covers the range of opening bids available to a player using the Standard American system. The fundamental principle is that with 13 HCP you should always open the bidding. Another way of saying this is that you should pass with an average hand but bid when you have additional values approximately equal to an extra king.

On some hands you will need to take into account the shape of the hand. On other hands you will have very good intermediate cards such as tens and nines. And on others a bad feature like a singleton king which is very likely to fall under the opponents ace and therefore is not really worth three points. The high card point system as described so far does not really consider all this. However if you wish to have a single value that tells you how strong the hand is and takes these factors into account you can modify the points count according to the following table. It is really a matter of personal choice and you can choose to make these modifications to the system or not.  Usually HCP is used for points but where the figures have been adjusted for shape SCP will be used to make this clear when necessary.

2.1	1X bids

1X bids are the basis of the entire bidding system. The basic principle is that with 13 HCP a hand can be opened with a 1X bid. If your hand has additional features you may have another bid available but this is where to start. The hands in the following list are therefore suitable for an opening bid; they are however minimum. In the list below some types of hand have less than 13 HCP. In each case there are additional features: a five card suit, a six card suit, two tens or a combination of the these features that makes the hand biddable - note that using the modifications to the HCP system described above these hands have 13 points. However hands (7) and (8) do not, these hands are marginal; they are the borderline cases where there can be flexibility:

1.	13 HCP [♠ A54 ♥ Q62 ♦ QJ83 ♣ A54 ] Bid 1♦.

2.	14 HCP [♠ QJ954 ♥ K7 ♦ ΑQJ ♣ 976 ] Bid 1♠.

3.	12 HCP [♠ A3 ♥ KQJ42 ♦ 84 ♣ Q732 ] Bid 1♥.

4.	11 HCP [♠ AK543 ♥ Α9843 ♦ 2 ♣ 64 ] Bid 1♠.

5.	10 HCP [♠ AKJT43 ♥ 72 ♦ 8 ♣ QJT4 ] Bid 1♠.

6.	12 HCP [♠ A987 ♥ QJ43 ♦ 6 ♣ AJ86 ] Bid 1♠.

7.	13 HCP [♠ AQ43 ♥ J85 ♦ QJ ♣ K532 ] Bid 1♣.

8.	13 HCP [♠ AKQ765 ♥ 92 ♦ 2 ♣ J964 ] Bid 1♠.

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2.2	1N bids

The previous section gave the rule for basic 1X bids. But you should also consider whether your hand is suitable for notrumps. The basic principle is that with 16 - 18 HCP and a balanced hand you should bid 1NT. The following are plausible contenders for a 1NT bid:

9.	16 HCP [♠ AJ43 ♥ QJ2 ♦ K4 ♣ KQ64 ] Bid 1NT.

10.	18 HCP [♠ K8 ♥ AQ9 ♦ KQJ ♣ QJ872 ] Bid 1NT.

11.	15 HCP [♠ QT8 ♥ A3 ♦ KQJ63 ♣ QJT ] Bid 1NT.

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2.3	2C bids

The next bid to consider is the bid of 2♣. This bid is reserved for very strong hands and is not really a natural bid, that is it does not mean you wish to play in clubs. The principle here is that with 23 or more HCP bid 2♣ and also consider the bid with fewer HCP and an unbalanced hand. The following are valid types of hand for this bid:

12.	23 HCP [♠ QJ83 ♥ AK3 ♦ KJ2 ♣ AKQ ] Bid 2♣.

13.	21 HCP [♠ AKJ732 ♥ A ♦ K65 ♣ AQ5 ] Bid 2♣.

14.	19 HCP [♠  ♥ KQJ92 ♦ KQJ975 ♣ AK ] Bid 2♣.

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2.4	2X bids

The next bid to consider are the 2X bids these bids do not include the bid of 2♣. These bids are reserved for very strong hands which are not strong enough to be opened 2♣. The principle here is that with 21 - 22 HCP bid 2X with a five card suit and with fewer HCP bid 2X if your hand looks as if it could make eight tricks on its own. The following are the valid types of hand for this bid.

15.	21 HCP [♠ A4 ♥ AKJ53 ♦ AKQ ♣ 943 ] Bid 2♥.

16.	16 HCP [♠ AKQ6543 ♥ 54 ♦ K4 ♣ A2 ] Bid 2♠.

17.	19 HCP [♠ A3 ♥ A ♦ KQJT5 ♣ AJ543 ] Bid 2♦.

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2.5	2N bids

The previous section gave the rule for 2X bids. But you should also consider whether your hand is suitable for notrumps. The rule here is that with 21 - 22 HCP and a balanced hand you should bid 2NT. The following are plausible contenders for a 2NT bid:

18.	21HCP [♠ KQ98 ♥ QJ8 ♦ A3 ♣ AKQ ] Bid 2NT.

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2.6	3X bids

The next bid to consider are the 3X bids. Note that these bids are not used for strong hands but for hands that have long suits with at least three honours which are not strong enough to be opened with a 1X bid. The principle here is that with 7 - 9 HCP a seven card suit with three honours bid 3X with a seven playing tricks if vulnerable and six playing tricks if not vulnerable. The number of playing tricks is the number of tricks the hand will probably make if played with the long suit as trumps. This type of bid is known as a pre-emptive bid because the primary aim is to shut the opponents out of the bidding when they may actually have the better cards.

19.	7 HCP [♠ QJT7532 ♥ T5 ♦ A ♣ 985 ] Bid 3♠ (not Vul).

20.	7 HCP [♠ QJT7532 ♥ T5 ♦ A ♣ 985 ] Bid Pass (Vul).

21.	9 HCP [♠ A6 ♥ 762 ♦ KQT9654 ♣ 6 ] Bid 3♦.

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2.7	4X bids

The 4X bids are very similar to the 3X bids. The principle here is that with 7 - 9 HCP a seven card suit with three honours bid 4X with a eight playing tricks if vulnerable and seven playing tricks if not vulnerable. Once again he number of playing tricks is the number of tricks the hand will probably make if played with the long suit as trumps.

22.	7 HCP [♠ 52 ♥ KQJ7432 ♦ 9 ♣ K85 ] Bid 4♥ (not Vul).

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2.8	Unusual  and rare bids

There are a some other bids but these are unusual or quite rare. One bid is 3NT. This is used for hands with a solid minor suit and about 12 HCP. Solid means that the suit contains the AKQ - this is vital. Another is the 5X bid. This applies only to minor suits and is used for hands with 7 - 9 HCP a very long suit with three honours with nine playing tricks if vulnerable and eight playing tricks if not vulnerable.

23.	8 HCP   [♠ A ♥ 8 ♦ KJT987532 ♣ 74 ] Bid 5♦.

24.	11 HCP [♠ Q42 ♥ 65 ♦ 3 ♣ AKQ9432 ] 3NT.

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When you make a suit bid the suit you choose should be biddable; it should either have five or more cards or if it has four cards some additional strength, that is any two honours or at least a queen if it only has one honour. However, sometimes any four card suit has to be bid when the rules call for a one level bid, whether  biddable according to the definition above or not.

The next problem is which suit to choose when you have decided to make correct  a 1X bid and you have more than one biddable suit. The answer is the longest suit.

25.	12 HCP [♠ AQ42 ♥ 65 ♦ 75 ♣ AQ942 ] Bid 1♣.

As always there are a few exceptions to the rule. These are all cases where you may have difficulty finding a good rebid because your hand is fairly weak if you simply bid the longest suit:

26.	13 HCP  [♠ Q65 ♥ 8 ♦ AKQ9 ♣ Q8742 ] Bid 1♦.

27.	11 HCP  [♠ AQ965 ♥ Q98432 ♦ K3 ♣  ] Bid 1♠.

28.	13 HCP  [♠ A843 ♥ QT8 ♦ K72 ♣ AT4 ] Bid 1♣.

The next problem is how to handle the situation when you have two biddable suits and a 6-6 or 5-5 pattern. The solution is to bid the higher ranking suit with the intention of bidding the second suit when (if) the bidding comes round to you again.

28.	11 HCP [♠ JT432 ♥ T9 ♦ J ♣ AKQ73 ] Bid 1♠.

Once again there is an exception:

29.	12 HCP [♠ 97653 ♥ J4 ♦ A ♣ AQJT3 ] Bid 1♣.

A similar problem occurs when your longest suit is four cards but there are is more than one biddable suit. With a 4-4-3-2 shape you should bid the first biddable suit next in rank below the doubleton (the suit below clubs for this purpose is spades). With a 4-4-4-1 shape apply the following rule based on the position of the singleton: spade bid 1♥, heart bid 1♦, diamond bid 1♣, and club bid 1♥.

3.	How auctions develop

For every bid a player makes there is usually a range of replies that partner can make (including to pass) and after the reply a range of bids that the first player can make in response. The situation can be imagined as a tree with branches representing the different choices that can be made at each stage. In this analogy the leaf at the end of a branch can be seen as the final bid that ends the auction. The point of the analogy being that just as a tree has very many leaves so in bridge the number of possible auctions is enormous.

So the problem is this. In the previous section there were eight sub-sections each devoted to one types of bid. Imagine that for each of these types of bid there are eight possible replies that would mean that this section would have 64 sections. And that the section that follows 512. This would be impossible to remember and would not be very practical.

3.1	HCP and game

The sections that follow will therefore be summaries but based on a very important idea. If the combined hands have 26 HCP then the odds are in favour of making game in notrumps with balanced hands or stoppers in all the suits, or of making game in a major suit with a fit. After the opener's bid responder should begin to narrow down his partner's range and this is a process that continues with both players until the auction is complete. For example, if 1NT was bid then responder knows that opener's hand contains 16 - 18 HCP; now if responder's hand contains 9 HCP then the range of the combined hands is 25 - 27 HCP. With a balanced and no four card major suits 3NT could now be bid. Note how the responder has narrowed down the range of the strength of the combined hands to three points! There is a similar idea to the one above for slams.  If the combined hands have 34 HCP and the opponents cannot make two quick tricks then there is a 50-50 chance of making a small slam. The corresponding number points for a grand slam is 37. It should be noted that weaker hands can often make suit slams but there has to be a good fit and shape so that the trumps can be used.

3.2	Types of responses to 1X bids

As 1X bids (1♣, 1♦, 1♥, 1♠) are the most common opening bids so a player has to understand that the response depends on the type of hand the responder holds. The most common situations that occur are as follows.

(1) The responder has a weak hand in which case the usual bid is Pass. (2) The responder has four cards in the suit that was opened. This means that there is a 'fit' and it is very likely that the two hands will play well together. The responder has to indicate that a fit has been found so that players will be aware of the situation. (3) There is no fit but responder has a good suit which can be bid. (4) Responder has a balanced hand with no fit for the opener's suit

There are other situation, they are rarer (and are not dealt with in the tutorial for beginners) the most important of which is the jump shift which is used when the responding hand has 19 HCP or more. This is, of course, a very rare occurrence.

3.3	The fit

If opener bids a suit (1X) and you have four cards in that suit that you already know that you have a fit. This is what you are looking for. Eight cards in a suit means that the partnership has the clear majority of cards in that suit and that if the 5 outstanding cards are split fairly evenly between the opponents then one opponent will have three cards and the other two. These are favourable circumstances for using trumps to win tricks. There are other types of fit other than the 4-4 type; for example 5-3 and 6-2 and these are equally good when trying to find fits.

The question is what to do next. The first thing to do is to consider which suit was bid, if it is spades or hearts (a major suit) then you should at this stage already be aiming to reach game in 4 Spades or 4 Hearts. If it is clubs or diamond then game in clubs or diamonds (that is 5 Clubs or 5 Diamonds) is still remote and therefore you should consider very carefully how or if you can reach 3NT and make game there.

3.4	Interpreting Responses

This section deals with the vital question which is the problem of interpreting partner's bids. This is again one of those details that is often ignored; you cannot see partner's hand and therefore because there may be a range of possible scenarios which led to the bid you have no way of telling which one it was and have to assume a range of possibilities that includes all the possible hands that could have led to the particular bid.

For example partner bids 4♠ a response to an opening bid of 1♠. This means that responder has assumed that the opener has 13 points and has 7 points in his own hand but also a five card spade suit and a short suit (singleton or void). This is an aggressive bid aimed at shutting out the opponents. All the HCP needed to make game in 4♠ may not be there but they may be and the opponents would have to be very brave to double such a contract.

What this example shows is that the responder's bid can give definite information about the hand and this information must in turn be used by opener. And that whenever partner makes a bid a player must make an active mental effort to interpret it and not just focus on the player's own bids.

3.5	Types of responses to 1N bids

Responses to 1NT are very simple in a system that uses natural bids. The responder will usually raise notrumps using the level to which he raises the bid to indicate the strength of the hand. A raise to 2NT would indicate 8 HCP and a balanced hand, a raise to 3NT would indicate 9-14 HCP and raise to 4NT 15-16 HCP with balanced hands. A bid of 2X would indicate a weak hand 0-6 HCP and the fear that 1NT could be defeated and at least five cards in the bid suit. A bid of 3X would indicate 9 HCP or more and a five card suit.

Some of these replies would invite further actions. After some, for example, a bid of 3NT in response to 1NT the response is always to Pass. The trick is to evaluate the minimum strength of partner's hand from the reply add this to the strength of your own hand and bid game if possible but if the bid indicates weakness to keep the level of the final contract as low as possible. So if partner bids 2X after 1NT by you a Pass is almost obligatory. However, a suit bid at the three level (3X) indicate strength you can see 25 points already and if there is a fit in a major suit then game is almost certain either in the suit or in notrumps.

4.	The responder's bid

The responder's bid is the reply to the opener's first bid and must be looked at from two points of view. (1) From the point of view of the responder looking at the cards in the hand and trying to make a decision about what to bid and (2) from the point of the opener trying to guess what the bid means and what cards partner is likely to hold.

Looking at the problem from responder's point of view the problem of finding a bid breaks down to two primary groups (1) Responses to suit bids and (2) responses to notrump bids. Responses to suit bids are handled in two entirely different ways depending on whether or not a fit has been found. Responses to notrump bids depend on whether or not responder has a balanced hand. But the precise response given depends on the strength, in HCP, of responder's hand.

On some hands you will need to take into account the fact that you and your partner have a fit. As with shape for the opener if you wish to have a single value that tells you how strong the hand is and takes this factor into account you can modify the points count according to the following table. Once again it is a matter of personal choice. Usually HCP is used for points but where the figures have been adjusted for fit and shape FSP will be used to make this clear when necessary.

4.1.	Responses to 1X bids with a fit

If you are considering playing the contract in the suit that partner bid (the level at which you intend to play does not matter) then this tutorial assumes you adjust your points using the table above. That is the values have been recalculated to take into account the fit and extra values for short suits.

Once you have recalculated your points what you should do depends primarily on how strong your hand is and secondarily on the suit that partner bid. The basics of the reply to partner's bid are as follows:

4.1.1	0-6	FSP	Pass.

4.1.2	7-10	FSP	Single Raise.

4.1.3	11-13	FSP	Delayed Raise.

4.1.4	10-12	FSP	Triple Raise (major suit, 5 cards, singleton or void).

4.1.5	14+	FSP	Double Raise.

Examining each of these in turns will be helpful as it shows the consideration that go into making bids:

4.1.1	Pass. This is the bid made on weak hands. They should be passed at the first opportunity so that the contract is kept as low as possible. Note the danger; assume that partner has 14 FSP then the total number of FSP in the two hands could be as low as 20 even if responder's hand has 6 FSP. This suggests that the partnership will make only seven tricks. It is therefore a good idea to leave the bidding at the 1 level.

4.1.2	Single Raise. This represents a weak hand but note that the two hands almost certainly have 22 FSP. This may be slightly weak to be at the two level if  partner is absolutely minimal but the slight risk can be accepted to show the fit. The problem arises if opener has a 4-3-3-3 shape, a way round it is for opener to subtract one SCP before making a suit bid with this shape. It should be clear that the minimum FSP in opener's hand would now be 15 after a fit is shown and that this would mean that the partnership is guaranteed 22 FSP and raise is safer.

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4.1.3	Triple Raise. This is only used for major suits and is done to shut out the opponents giving them no opportunity to contest the auction at low levels. Although the opponents will know that the bid may not be entirely sound they would be unwise to double as they have no idea how strong opener's hand is except that the opposing partnership will have a lot of trumps and short suits.

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4.1.4	Delayed Raise. This is an interesting part of the Standard American system. It can cause problems in that it does not immediately inform partner that a fit has been found. Some players have therefore replaced it with the double raise and use other bids to show a strong hand. The idea of the delayed raise is to bid another suit in reply then show support on the next bid.

4.1.5	Double Raise. This is used to show a strong hand and support for opener's suit. It is forcing to game. This applies to major suits and minor suits. Therefore the player will have to take care with minor suit openings to make sure that the strength for game is there before a double raise is made. After a double raise a player should consider whether a slam is possible.

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4.2	Responses to 1X bids, no fit, suit to show

If opener bids a suit and partner does not have 4 cards in that the suit the player has two choices (1) to bid a new suit showing cards of his own (2) to bid notrumps showing that he cannot support partners suit and suggesting that the contract should be played in notrumps. As always in bridge there is another possible alternative which is to support partner with only three cards in the suit.

The idea is therefore to look at your hand and decide whether you have a suit worth bidding. What you should then do depends on the strength of your hand.

4.2.1	0-5	HCP	Pass.

4.2.2	6-18	HCP	New suit.

4.2.3	6-9	HCP	New suit at the 1 Level.

4.2.4	19+	HCP	Jump Bid.

4.2.1	Pass. Again this bid shows a weak hand with which you do not want to risk going any higher. The Pass is the correct response even if you are very weak in partner's suit. The idea is that if you are going to lose a lot of tricks then the opposition have good cards and could make a good contract of their own in any case.

4.4.2	A  new suit. This bid is 'forcing' . That is the opener will have to bid again. This means that you will get another chance to bid. The bid can be either at the one or two level depending on the suit.

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4.2.3	One in a new suit. This bid is also 'forcing'. The bid is essentially used in the same way previous way except that because your hand is weak you cannot bid at the two level.

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4.2.4	Jump bid. These bids take the bidding to the two or three level. Assuming that opener has 13 HCP then it is obvious that the two hands combined have enough points for game and that the main question is whether or not a slam is possible.

Just as with opening bids there may be a problem with choosing suits. The rule is to bid the longest suit first. To every rule in bridge there are exceptions. One exception is that if the hand does not have 10 HCP and the shorter suit of the two can be bid at the one level then bid that suit. Another problem is that there may be two suits with the same length. The answer in this case is to bid the higher ranking first if the suits are 6-6 or 5-5 and the cheapest first if they are 4-4. The reason is that if you have two long suits you will wish to bid the second suit on the next round, giving partner an easy choice between the two suits. Whereas if you have 4-4 in the two suits you are already planning for a possible notrump contract.

4.3	Responses to 1X bids, no fit, no suit to show

If opener bids a suit and there is no fit and if the responder is unable to show a suit of his own the alternatives are as follows.

1.	0-5	HCP	Pass.

2.	6-9	HCP	1NT.

3.	10	HCP	1NT 4-3-3-3 shape.

4.	10-12	HCP	Bid in a new.

5.	13-15	HCP	2NT.

6.	16-18	HCP	3NT 4-3-3-3 shape.

7.	19+	HCP	Jump Bid.

Looking at the above list of alternative it should be clear that you should try to show a 4 card suit especially if it is a major before considering notrumps. Also that to bid notrumps you should have a balanced hand.

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4.4	Responses to 1N bids

After an opening bid of 1NT the response is dictated by one main factor and that is whether the hand is likely to end up being played in trumps or notrumps. Depending on this factor what the player should then bid will depend on the strength of the hand. A hand is likely to play well in notrumps if it is balanced and to play well in a trump suit if it is unbalanced; but in this case there will have to be a fit and a major suit provides a much better chance of game.

4.4.1	Balanced hand.

4.4.2	Unbalanced hand with a long suit.

4.4.3	Unbalanced hand with no long suit.

4.4.1	Balanced hand. The possibilities are listed below, since the opener is known to have 16-18 HCP the range of the partnerships total points is also given.

a.	0-7	HCP	Pass	16-25	HCP.

b.	8	HCP	2NT	24-26	HCP.

c.	9-15	HCP	3NT	25-33	HCP.

d.	16-17	HCP	4NT	32-35	HCP.

e.	18-19	HCP	6NT	34-37	HCP.

f.	20	HCP	5NT	36-38	HCP.

g.	21+	HCP	7NT	37+	HCP.

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4.4.2	Unbalanced hand with long suit. With an unbalanced hand responder should bid the long suit (that is a suit with more than six cards). Except if the suit is a minor and there are enough points for game in which case game in Notrumps should be bid.

a.	0-7	HCP	Bid 2X.

b.	8-14	HCP	Bid 4X if the long suit is a major.

c.	8-14	HCP	Bid 3NT if the long suit is a minor.

d.	15	HCP	Bid 3X.

It should be added here that there is a very common convention called the Stayman convention uses the 2♣ response after an opening bid of 1NT to begin a sequence that tries to find a 4-4 major suit fit. If is being used the 2♣ bid cannot be used in (a) above.

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4.4.3	Unbalanced hand with no long suit.

a.	0-6	HCP	Pass with no five card suit.

b.	0-6	HCP	2X with a five card suit.

c.	7-8	HCP	2♣ with four card major.

d.	7-8	HCP	2NT with no four card majors

e.	9+	HCP	3X with a five card suit

f.	9+	HCP	2♣ with four card major.

g.	9+	HCP	3NT with no four card majors.

Note here the 2♣ bids. This is problem typical in bridge which is that there are not enough natural bids to show even common hands. If 2♠ is used to show a weak hand with 0-6 HCP and long spades, and 3♠ used to show a hand with 9+ HCP and five spades, then how are hands with 7-8 HCP or 9+ HCP and four spades to be bid. This is why there are so many conventions in bridge; the Stayman convention for example using the 2♣ response to a 1NT opening bid is designed to find a major suit fit after a 1NT opening and would handle these situation quite well.

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5.	The opener's rebid

After the opener's first bid and responder's reply opener has to make a second bid. There are a large number of possibilities because there were many possibilities for opener's first bid and for each opening bid several possible replies depending on the strength of responder's hand. Some of the possibilities are listed below to show how complex the situation has become. The suggests that a way is needed to cut through the complexity without memorising a vast number of rules.

The symbol 1X is used to represent the natural bid of a suit at the one level and the symbol 1Y is used to represent a bid of a suit different from the suit already bid at the given level. For example the sequence 1X-1Y could be 1♣ followed by 1♦ or 1♦-1♠.

1.1	1X - 2X	Suit bid, then single raise

1.2	1X - 3X	Suit bid, then double raise

1.3	1X - 4X	Suit bid, then triple raise

2.1	1X - 1Y	Suit bid, then new suit at one level

2.2	1X - 2Y	Suit bid, then new suit at two level

2.3	1X - 2Y(J)	Suit bid, then a jump bid

2.4	1X - 3Y(J)	Suit bid, then a jump bid

3.1	1X - 1N	Suit bid, then 1 Notrump

3.2	1X - 2N	Suit bid, then 2 Notrumps

3.3	1X - 3N	Suit bid, then 3 Notrumps

4.1	1N - 2N	1 Notrump, then 2 Notrumps

4.2	1N - 3N	1 Notrump, then 3 Notrumps

4.3	1N - 2X	1 Notrump, then new suit at two level

4.4	1N - 3X	1 Notrump, then new suit at three level

The list above does not cover all the possible combinations, some are missing for example 1N-4N. If you have a very good memory you will be able to remember what to do in each situation depending on what cards you have. But what is happening is that at each stage each player has a number of choices of what to bid (for the purposes of this example say four); then on the first bid opener has 4 rules, for the reply responder has to remember 16 rules to handle all the possibilities and on opener's second bid there will be 64 different situations. You will not be surprised that the number of possibilities for responder's second bid is very large. Perhaps not 256 because for some combinations of hands the bidding will have already terminated for example the sequence 1N-3N; and for others there are no choices other than Pass, for example 1N-2N-3N.

This helps to explain why adding conventions makes the bridge bidding so much harder to learn. Because for each special bid added the number of possibilities at a level increases.

This is the main point of the Decision Points system; to give the memory a way of working systematically through a large number of possible bids.

So having explained why things are now starting to get complicated it is time for the actual rules. But for some hands you will need to take account of the fact that you and your partner have a fit. Opener should modify the points count using the same table as responder did. Once again it is a matter of personal choice. The acronym FSP is used where necessary to make it clear that the HCP have been adjusted for fit and shape.

5.1	1X bids raised

Throughout this section a distinction will be made between major suit opening bids and minor suit bids. This is because with the former the primary aim is to get to game in the suit whereas with the latter the primary aim is to get to 3NT if possible. Reaching five clubs or five diamonds is a possibility but a remote one.

5.1.1	Single raise. This is the type of situation in which FSP are very  useful. Opener can have a wide range of FSP but responder's hand has been narrowed down to a range of approximately 4 points 7 - 10 FSP. This is a case where what opener will be thinking is completely different depending on whether the suit under consideration is a major or a minor suit. The problem is that if a minor suit has been bid then the minor suit game is unlikely and opener will have to consider bidding in notrumps and trying to reach 3NT with sufficient values.

After a single raise in a major opener should bid game if the combined hands have 28 FSP. But how does he know this? Simply by taking the minimum number of FSP that his partner has shown which is seven and adding it to the number of FSP in opener's own hand. This means that opener is looking for 21 FSP to bid game immediately; there will be a 50-50 chance of making the contract if partner has a minimum hand, if partner has additional values then playing the hand will be very easy! With fewer than 21 FSP opener has the possibility of bidding 3 Hearts/Spades and inviting partner to bid 4 with a stronger hand containing 9 FSP. Obviously to do this opener will need 19 FSP to give a total of 28 FSP.

If the opening suit is a minor then opener should consider his hand. As always game in a minor suit at the five level is remote and risky. So opener must assess his hand for play in notrumps. And with the following ranges of HCP do the following:

1.	0-16 	HCP	Pass

2.	17+	HCP	Make a trial bid

3.	19+	HCP	Bid 3NT with a balanced hand

A trial bid is a bid a new suit showing a three card suit. Responder uses this information to check whether 3NT would be a safe contract. Note that points for fit and shortage do not count so the trial bid serves the purpose of notifying partner that the contract may not be played in the agreed suit and therefore to use the correct point count. Note that it will always be safe for partner to bid 3 of the first suit after a trial bid.

In some unusual cases opener may find that a slam looks likely after a single raise if partner's hand turns out to be maximum. This is unusual and may indicate that the hand was originally underbid.

5.1.2	Double Raise. This bid shows a strong hand. Opener should immediately calculate the total FSP in both the hands to see if there is a possibility that the hands have a total of 34 FSP. If that is found to be the case then he should check for aces and bid a slam. If not opener should bid game in a major suit or try for notrumps if the opening suit was a minor. Opener does not know responder's precise strength so if responder is stronger than minimum there may still be the possibility of a slam. How opener goes about finding this out has to be left for the section on slam bidding.

5.1.3	Triple Raise. This response to this bid is almost always Pass. But the FSP point count allow a slam to be considered if opener can see a total of 34 points in the combined hands. This is another reminder that responder - in fact both players - must always be careful not to make bids with weaker hands than partner expects.

<Responses>

5.2	1X bids followed by a reply in a new suit

This is a very common situation: responder does not have a fit and shows his own suit. To describe the situations that arise is quite complex but the following ideas form the basis for analysis:

1.	Raise partner's suit.

2.	Bid a new suit.

3.	Rebid the first suit.

4.	Bid Notrumps.

5.	Jump in a new suit.

5.2.1	Single raise. If Opener has four cards in partner's suit then the obvious reply is to show the fit. Once again the major/minor distinction appears. If the responder has bid a major suit then Opener has a range of bids to show support depending on the strength of the hand. If the sequence was say 1 Club - 1 Spade he can show support by bidding 2 Spades, 3 Spades or 4 Spades. At this point the list of possible ranges of values for the points could be given and the response in each case but for the beginner it is sufficient to say that the responses follow from the attempt to verify whether the combined hands have 26 HCP for game or perhaps even 33 HCP for the slam.

<More>

5.3	1X bids followed by a notrump reply

There are three possible notrump responses to an opening bid of one of a suit and they each indicate the strength and shape of the hand.

5.3.1	1X - 1N. This indicate a hand with 7 - 10 HCP. With a balanced hand opener should raise to 2NT with 16 HCP, and to 3NT with 18 HCP. If you find these bids risky you can always shade up slightly by a point. This again demonstrates one of the advantages of a points system which is that it allows each player (or partnership) to access risk precisely and bid according to personal taste.

With an unbalanced hand you can rebid you original suit. If the suit is a major you can jump either to 3X or 4X depending on whether you can see 24 HCP or 26 HCP - note that you need a strong suit because your partner does not absolutely guarantee a balanced hand. The last major alternative is to bid a new suit; the strength of the hand will determine whether you should bid a suit that is higher-ranking than the first suit that you bid.

5.3.2	1X - 2N. This bid is made when responder's hand is balanced with 13-15 HCP. The opener either bids game in notrumps or in a major. A bid in a new suit at the three level is an attempt to reach a slam.

5.3.3	1X - 3N. This bid is made when responder has a balanced hand and 16-18 HCP. It can be assumed that the hand has 4-3-3-3 shape. Opener should bid a major suit game or make a slam try.

<Responses>

5.4	1N bids raised

This is a simple case. Opener simply adds the HCP that responder has shown to the points in his own hand and bids accordingly. For example if the points total is 25 opener simply bids game in notrumps, 3NT.

<Responses>

5.5	1N bids  followed by a reply in a new suit

If the suit bid is at the two level then the best idea is to Pass. If it is a major suit at the three level bid 4 with three cards otherwise bid 3NT. The same applies to a minor suit bid. Partner must have a reason for looking for a minor suit fit, either a very strong hand or one that is unbalanced. Let partner know that the fit is there.

<Responses>

6.	The responder's rebid

This is the last bid that can be described exhaustively with rules. As mentioned when describing opener's rebid the number of possibilities for bids further into the auction are very large. For example the case where bidding begins with one of a suit followed by a new suit at the one level the following are just some of the possibilities.

1.1	1X - 1Y - 2X	Suit bid, new suit, then single rebid.

1.2	1X - 1Y - 3X	Suit bid, new suit, then jump rebid.

1.3	1X - 1Y - 4X	Suit bid, new suit, then game rebid.

2.1	1X - 1Y - 2Y	Suit bid, new suit, single raise.

2.2	1X - 1Y - 3Y	Suit bid, new suit, double raise.

2.3	1X - 1Y - 4Y	Suit bid, new suit, then game raise.

3.1	1X - 1Y - 1N	Suit bid, new suit, then notrump.

3.2	1X - 1Y - 2N	Suit bid, new suit, then notrump at two level.

3.3	1X - 1Y - 3N	Suit bid, new suit, then notrump at three level.

4.1	1X - 1Y - 1Z 	Suit bid, new suit, another new suit at the one level.

4.2	1X - 1Y - 2Z	Suit bid, new suit, another new suit at the two level.

4.3	1X - 1Y - 2ZJ	Suit bid, new suit, then a jump to the two level.

4.4	1X - 1Y - 3ZJ	Suit bid, new suit, then a jump to the three level.

And this is not the complete scheme; it deals with one type of opening bid and one type of reply and is not even exhaustive with respect to opener's rebid. There is the whole range of slam invitation bids. And in a full bridge system there would be any number of conventional bids that could be used. And note that for the bids 1X - 2Y - ?? the rules although similar are sufficiently different to mean that they would have to be described separately.

The question thereby arises of how to cut through this complexity. The only real way to do this is to always keep in mind the basic principles. To repeat: the primary goal is to find a 4-4 or 5-3 major suit fit and with 26 HCP to play in 4 Hearts or 4 Spades. Failing this the next best idea is to play in 3 NT with all suits stopped and 25 HCP. Playing in 5 Clubs or 5 Diamonds requires 30 HCP (almost a slam) and is a remote possibility. In fact it is almost impossible to reach 5 in a minor without at some stage considering and rejecting the possibility of a slam. The player also has to be prepared to stop as soon as it becomes clear that game cannot be reached and keep the contract in a safe part-score. The player must also be constantly aware that either player may have additional values and that partner may not be aware of this and that this could mean that a slam is possible.

The problem is therefor to classify the large number of possible combinations of bids into a few basic cases and then to describe how these should be handled. The  Decision Points system also gives a few interesting pointers.

6.1	1X bids raised followed by another raise or notrumps

This is the first of the typical situations that arise. It is also one of the simplest that responder comes across.

6.1.1	1X - 2X - 3X.

6.1.2	1X - 2X - 2N.

6.1.3	1X - 2X - 3N.

6.1.4	1X - 3X - 4X.

6.1.1	1X -  2X - 3X. This bidding sequence will occur most frequently for major suits. Responder should bid game with 9 FSP. Partner's bid should be interpreted as a simple request: 'Bid game if you have 9 FSP'.

6.1.2	1X - 2X - 2N. Opener is showing a balanced hand with 16-18 HCP and is seeking a balanced hand and 9 HCP from partner for game.

6.1.3	1X - 2X - 3N. 3NT rebids by opener should usually be passed. The only other option is to bid game in a major. This will only be feasible if responder has a long suit which has not already been shown.

6.1.4	1X - 3X - 4X. With a major suit fit this sequence should always be passed unless responder's  hand has values which have not been shown. Opener has shown 15 FSP, responder has shown 14 FSP therefore responder needs 5 additional points before a slam try can be made.

6.2	1X bids, no fit and responder's suit raised

This is another very common situation. Opener has support for partner's suit and shows the strength of the support  by raising the suit to different levels.

6.2.1	1X - 1Y - 2Y.

6.2.2	1X - 1Y - 3Y.

6.2.3	1X - 1Y - 4Y.

6.2.1	1X -  1Y - 2Y. This bid shows that opener's hand is in the minimum range 15-18 FSP. Responder can bid game with 13 FSP. With 11 points responder should raise to the three level.

6.2.2	1X -  1Y - 3Y. This indicates a strong hand. Opener has 19-20 FSP. Unless responder is minimal, game in a major is a very good contract. Bid 4 with 8 points.

6.2.3	1X -  1Y - 4Y. In this position Pass is the correct response. Further bidding is only possible if the hand contains the additional values required for a slam try.

6.3	1X bids, new suit followed by a rebid

6.3.1	1X - 1Y - 2X; 1X - 2Y - 2X; 1X - 1N - 2X

6.3.2	1X - 1Y - 3X; 1X - 2Y - 3X; 1X - 1N - 3X

6.3.2	1X - 1Y - 4X; 1X - 2Y - 4X; 1X - 1N - 4X

6.3.1	1X -  1Y - 2X; 1N - 1N - 2X; 1N - 2Y - 2X. Opener rebids his first suit showing 13 - 16 HCP and at least a five card suit. Responder can now (1) support with three cards, (2) Rebid his own suit with six cards in that suit (3) Bid notrumps if there is no fit and the hand is balanced. Note that responder should use the points total to decide whether game should be bid immediately or invited.

6.3.2	1X -  1Y - 3X; 1N - 1N - 3X; 1N - 2Y - 3X. Opener's bid shows 17-18 HCP and a six card suit or a very strong 5 card suit. Responder should use the points total to decide whether or not to bid game.

6.3.3	1X -  1Y - 4X; 1N - 1N - 4X; 1N - 2Y - 4X. Opener's game bid should be passed unless responder has sufficient values to make a slam try.

6.4	1X bids, new suit followed by another new suit

This is another common situation. Neither responder nor opener have fits for the other's suit and opener tries a third suit. The basic strategy for responder is to support the new suit if there is a fit. If not there are various options to consider. (1) A bid of notrumps with a balanced hand. (2)  rebid responder's own suit with 5 cards in the suit. (3) With three or more cards in partner's suit could be raised. (4) Pass since responder is not forced to make if there are 3 cards in opener's second suit and the hand is weak.

It is possible for responder to have 4 cards in partner's suit and not have shown it on the first round of bidding. This can obviously confuse opener who will not know how strong responder's hand is in the suit. This is a weakness of the Standard American system.

6.4.1	1X - 1Y - 1Z.

6.4.2	1X - 1Y - 2Z; 1X - 2Y - 2Z.

6.4.3	1X - 1Y - 2Z (Reverse); 1X - 2Y - 2Z (Reverse).

6.4.4	1X - 2Y - 3Z.

6.4.1	This shows that opener's points are in the range 13-18 HCP. With a stronger hand Opener would have jumped in the new suit.

6.4.2	1X - 1Y - 2Z; 1X - 2Y - 2Z. Similar to the above except that everything happens one level higher. Note that there are two bidding sequences and that although these two sequences look very similar there is an important difference between them. In the second case responder's hand is stronger.

6.4.3	1X - 1Y - 2Z(R); 1X - 2Y - 2Z(R). This is a bid where opener's second suit is higher ranking than the first. To have made this bid opener needed a stronger hand than the sequence 1X - ?Y - 2Z. The reason is that in order to support the first suit that opener bid which will be necessary if responder cannot support the second and has an unbalanced hand, responder will have to bid at the three level. But to play at the three level requires 25+ HCP. Responder has only shown 6 HCP so far, so assuming he has 8 FSP after a fit is found (an optimistic assumption because he may only have three cards in the first suit) opener therefore needs 17 HCP to make a reverse, which can be shaded to 16 HCP for competitive reasons.

6.4.4	This shows that opener's points are in the range 15-18 HCP. This bid is known as a high reverse and is forcing to game.

6.5	1X bids, new suit followed by notrumps

This situation arises where Opener has a balanced hand and cannot support responder's suit. Opener's bid narrow down his hand and therefore responder should be able to place the contract quite well.

6.5.1	1X - 1Y - 1N.

6.5.2	1X - 1Y - 2N.

6.5.3	1X - 1Y - 3N.

6.5.4	1X - 2Y - 2N.

6.5.5	1X - 2Y - 3N.

6.5.1	1X -  1Y - 1N. Opener has 13-16 HCP and a balanced hand. Responder should check if game is possible and if so bid 3NT. If game is not possible but responder has 10 HCP a raise to 2 NT is appropriate. Opener will bid game on the next round with 15 HCP.

6.5.2	1X -  1Y - 2N. Opener has 19-20 HCP and a balanced hand. The partnership clearly has the values for game. Responder should check for a slam and make a slam try if it is; or otherwise bid game.

6.5.3	1X -  1Y - 3N. Opener has 17-18 HCP and the game bid is based on the possession of a solid minor suit. Responder should pass. Unless he has four cards in partners first card and is delaying the raise.

6.5.4	1X -  2Y - 2N. Opener has 15-18 HCP and a balanced hand. With 15 HCP in opener's hand and at 10 HCP in responder's hand (a two level response was made) it is clear that the partnership has at least 25 HCP. The choices for responder are (1) to bid game 3NT, (2) Bid a new suit, (3) Support opener's first suit  (4) Rebid his own suit.

6.5.5	1X -  2Y - 3N. Opener has 19-20 HCP and a balanced hand. Responder should Pass unless he has additional values for a slam try.

6.6	1X bids, notrumps followed by a new suit

The situation where opener rebids his first suit after a notrump response was discussed above. Typical scenarios here are:

a.	1X - 1N - 2Y

b.	1X - 1N - 2Y(Reverse)

c.	1X - 2N - 3Y

The situation here is similar to the case where responder bids a suit instead of notrumps. The main difference being that the notrump bid limits responder's hand more than a suit bid. Responder should consider whether he has a fit for either of opener's suits and bid accordingly.

6.7	1X bids, notrumps followed by a raise

Responder should bid game, 3 NT, with 9-10 HCP. Note that responder needs a balanced hand. High notrump contracts should not be played with points based on shape.


Adjusting HCP for fit (Basic bidding)


Appendix

Percentage plays

1.	A detailed analysis of a percentage play.

It was stated that in the following hand if there is no indication that either player has the queen that the correct strategy is to play for the drop if the queen has not appeared after the king is played from dummy and a low card is led towards the South hand.

But why exactly is this the correct strategy.

By the time the decision is to be made the only possible distributions of the East and West hands are:

1.	West Q	East x

2.	West -	East Qx

The 'x' represents a small card; it is not important which one. These imply the following original distributions:

1.	West Qx	East xx

2.	West x	East Qxx

When four cards are missing the odds of them being split in particular ways can be calculated and are as follows:

2-2	40%

3-1	50%

4-0	10%

So the odds for each of the original distributions using the above percentages are as follows:

1.	West Qx	East xx	20%

2.	West x	East Qxx	18.75%

Note that case 1 is the 2-2 split and the 20% is from the observation that it is equally likely that in a 2-2 split either player could have the queen. In case 2 the odds are 25% that it is east that has the three cards; but on one in four occasions he would not have the queen that gives the figure above (25 * (3 / 4)).

So the odds favour playing East for the xx.

Related Ideas

Percentage table


Percentage table

Opponents Hold	Division	Percentages

2 cards	1-1	52%

2-0	48%

3 cards	2-1	78%

3-0	22%

4 cards	2-2	40%

3-1	50%

4-0	10%

5 cards	3-2	68%

4-1	28%

5-0	4%

6 cards	3-3	36%

4-2	48%

5-1	15%

6-0	1%

7 cards	4-3	62%

5-2	30.5%

6-1	7%

7-0	0.5%


Glossary

A

Auction

B

Bid

C

Call

Contract

Convention

D

Deal

Declarer

Defender

Denomination

Double

Dummy

G

Game

H

Hand

Honour

M

Major

Minor

O

Overtrick

P

Part-score

Play

Points

Premium points

R

Redouble

Rubber

S

Shuffle

Slam

Sort

Suit

T

Trick

Trick points

Trump

U

Undertrick

V

Vulnerability


Copyright

Bridge Assistant Tutorial

Version 3.1

This tutorial is not to be distributed separately from the Bridge Assistant program.

Copyright © 1995 - 1996 SoftTech

First published 1995


Decision PointsTM is a trademark of SoftTech

All Trademarks acknowledged


Registered version
Available in registered version

You are now using the tutorial included with Bridge Assistant that explains basic concepts. This section expands on basic concepts and is only included in the registered version.

For more information about Shareware and how to register see the shareware help file.

About Shareware.


Exercises

If you are a beginner there is a tutorial included with Bridge Assistant that explains basic concepts. This section is for you to test the skills you have acquired. However, it is only included in the registered version. Two examples of exercises are provided below. The first tests the basic skill of counting winners when declarer is playing in a notrump contract and the second is more advanced testing your ability to plan the play of an entire hand.

Exercise 1.

Exercise 2.

1.	How to register.

For more information about how to register see the following.

Registration.


Exercise 1 - counting winners
2.	Counting Winners

Question:	You are South in the deal below how many winners do you have?

Contract: 1 NT, Declarer: South, Lead: ♠2.

Click on Deal to view the hand, work out your answer then click on Solution to see if you are correct.

Deal

Solution


Exercise 2 - planning the play
3.	Planning the play.

Question:	You are South in the deal below plan the subsequent play.

Contract: 3NT, Declarer: South, Lead: ♥5.

Click on 'Declarer and Dummy' to view the hand, work out your answer then click on Solution to see if you are correct.

Declarer and Dummy

Solution

Full Deal


You have four winners.

One Spade	[Ace]

Two hearts	[Ace, King]

No diamonds	[]

One club. 	[Ace]

1(Spade)+2(Hearts)+1(Club) = 4(Winners).


Exercise 3 - analysis
Analysis

In any hand you should go through the steps (a) to (d) below, beginning with counting the winners and ending with the plan.

(a) Count winners:	Answer

(b) Extra tricks:	Answer

(c) Dangers:	Answer

(d) Plan:	Solution


You have seven winners.


Two are available from clubs once the ace has been forced out.

A 3-3 split in spades would provide one trick.

A 3-3 split in diamonds or the fall of the jack would also provide one trick.


Once a heart is won the suit will be wide open and the opponents could win four tricks.


Exercise 3 - solution
Solution.

The obvious starting point is to win the heart with the ace and then play a club. This wins if the hearts split 4-4 and loses otherwise - odds are approximately 30%. Look for slightly better odds.

What about spades and diamonds? The odd that two suit will break 3-3 is small about 10%. Reject this option.

Suppose one of the players has 5 hearts if that player also has the club ace then there is nothing you can do. But the odds are 50% that the same player will not have both. Therefore the solution is to win the third round of hearts. This means that you will win whenever the hearts split 4-4 and also on other breaks when the player with the long hearts does not have the club entry. The odds are now better than 50%.

Play:-	Do not win the opening lead.

Play:-	Do not win the probable heart continuation.

Play:-	Win the third round of hearts.

Play:-	Lead a club; the opponents' ace probably wins.

Watch:- Do the opponents play two heart winners?

At this point the contract depends on the distribution of the cards. But you have done your best to maximise the odds.