Precision Software Appli…tions Silver Collection 1/Precision Software Applications Silver Collection Volume One (PSM) (1993).iso/tutor/smartg11.arj/G3.TUT

Text File | 1992-11-17 | 15KB | 363 lines

                             O D D S

$mart Gamblers have a basic understanding of the mathematical
concepts related to gambling.   This tutorial covers probability,
statistical expectation, casino percentage and standard
deviation.  It also describes the $mart Gambler program report
and how to use the information it provides.


PROBABILITY

The theory of probability is as follows.  If an event is certain
to happen its probability is 1.00.  If an event is impossible to
happen its probability is 0.00.

Gambling events have a probability of winning and a probability
of losing.  The sum of those probabilities is 1.00.  The term
odds is commonly used to describe the probability of a gambling
event winning.

Consider a coin toss.  There is a 0.50 probability that it would
end up heads and a 0.50 probability that it would end up tails.
The sum of the probabilities of a coin toss is:

          (0.50 heads) + (0.50 tails) = 1.00

This could be also called having 50/50 odds of one side ending up
over the other side.

Consider a casino roulette wheel.  There are 38 numbers, 1 to 36
plus 0 and 00.  The probability or odds of the number 16 coming
up is one out of 38.  The probability for winning and losing is:

    (1/38ths for the 16) + (37/38ths for the others) = 1.0000

The probabilities expressed decimally is:

      (.0263 for the 16) + (.9737 for the others) = 1.0000



STATISTICAL EXPECTATION

When the winning and losing amounts are factored with the
probabilities, the statistical expectation of a gambling event is
developed.  This will provide a picture of what the gambler can
expect to happen over the long run.  To get the statistical
expectation, first multiply the gain amount by the probability of
winning.  Next add to it the loss amount multiplied by the
probability of losing.  The loss amount is expressed as a minus
number.  If $1 was bet on heads coming up in the coin toss, the
statistical expectation would be:

     ($1.00 win times 0.50) + (-$1.00 times 0.50) = 0.00


This would be called a fair odds game because the expectation is
neither plus or minus.  It is also called having true odds.  In
the long run a gambler would expect to end up even if they bet on
either heads or tails always.

Consider what would happen if instead of $1.00 being won, $1.25
was won.  The statistical expectation would then be:

    ($1.25 win times 0.50) + (-$1.00 times 0.50) = +0.125

Expressed as a percentage, the expectation would be +12.5%.
After 100 bets, the expected result would be a gain of $12.50.
This would be unfair odds.

Consider what would happen if instead of $1.00 being won, $0.75
was won.  The statistical expectation would then be:

     ($0.75 win times 0.50) + (-$1.00 times 0.50) = -0.125

Expressed as a percentage, the expectation would be -12.5%.
After 100 bets, the expected result would be a loss of $12.50.
This also would be unfair odds.


CASINO PERCENTAGE

If a casino offered gambling at fair odds they would not be able
to remain in business.  They would not be able to pay for
buildings, utilities, employees, taxes and other expenses and
show a profit.  To offer fair odds and succeed they would have to
be lucky in the long run.  This would be gambling.  If there is
one thing a corporate casino owner doesn't want to do, it is to
gamble.  Obviously they also would not give unfair odds favoring
the player.

Casinos offer gambling games that either have:

     (1) A built-in probability favoring their winning
     (2) A built-in payoff schedule biasing the statistical
       expectation in their favor
     (3) A combination of these

If a casino did offer a coin toss game, the payoffs would likely
be similar to the unfair odds example with $0.75 paid for
winning.  This would give them an unfair advantage percentage -
12.5%.  It is unlikely that they would offer such a game because
the unfair advantage would easily be recognized by the players.
They also could bias the results of the coin toss by adding a
weight to one side and only taking bets on the other side.  That
would equally be easily recognized by the players.  Casinos
generally prefer games in that their advantage is not obvious to
players.


Consider the roulette game example provided earlier.  There are
38 numbers, 1 to 36 plus 0 and 00.  The probability or odds of
one number coming up is 1 out of 38.  However the casino pays
only 35 to 1 for selecting one number and winning.  The
statistical expectation if $1.00 is bet on the number 16 is:

  ($35.00 times 1/38ths) + (-$1.00 times 37/38ths) = -0.0526

Expressed decimally:

    ($35.00 times .0263) + (-$1.00 times .9737) = -0.0526

              (0.9211) + (- 0.9737) = -0.0526

There is 1 chance in 38 that 16 will come up and 37 chances in 38
that it won't.  The -0.0526 is usually expressed as -5.26%.  This
is the casino percentage advantage or as it's commonly called the
"PC."  Sometimes it is called the "vigorish" or "vig."

For every $100.00 bet on roulette, the casino can expect to
retain or "hold" an average of $5.26.  The casino is not
gambling.  There may be streaks and players may win in the short
run, but over the long run they will win this percentage without
fail.  Time is on the side of the casino.  A casino may
experience a losing shift, day, week or month but over time the
PC will assert itself.

Casino percentage advantages range from -0.01% to -25.00% and
sometimes even more.  There is tremendous difference in playing a
low PC game versus a high PC game.  $mart Gamblers only play at
the very lowest PC games available.


Consider the casino's PC as the cost of the entertainment of
gambling.  A typical casino gambler may bet an average of $5.00
and experience an average 100 outcomes per hour.  The cost of
playing a -0.60% game such as six-deck blackjack would be $3.00
per hour.  It is assumed that the blackjack game is played
correctly as described in the Blackjack tutorial.  The cost of
playing a -25.00% game like the Wheel of Fortune would be $125.00
per hour.  There is no particular skill required to play the
Wheel of Fortune as discussed in the Other games tutorial.  The
difference between the two games is $122.00 per hour!


These two games are available in most casinos and often right
next to each other.  The tutorial on Games discusses the aspects
of the different casino games.  Review the tutorials on the
individual games to get full information on the casino percentage
advantages and the best bets and other strategies.


STANDARD DEVIATION


Standard deviation is a measure of dispersion.  It describes how
far the results can vary from the expected or theoretical result.
The actual calculation of it is best left to scientific
calculators and computers.


The following is a simplified example of standard deviation.
Consider again the coin toss.   The expected result would be that
half the time heads would come up and half the time tails would
come up.  In 100 tosses, the player might expect heads to come up
50 times, an even split.  Some gamblers would say that the "law
of averages" will cause this to occur.  In statistics, there is
actually no such thing as a law of averages.


While the the most frequent result will be 50 times, it may only
occur about 8% of the time over a sample of 100 tosses.  Random
events such as a coin toss result in random results.  The
standard deviation for this example could be 5.  In 68.3% of the
times, the result will be between plus and minus one standard
deviation of the expected average.  For this example that would
be between 45 and 55.


In 95.5% of the times the result will be between plus and minus
two standard deviations of the expected average.  For this
example that would be between 40 and 60.  In 99.7% of the times
the result will be between plus and minus three standard
deviations of the expected average.  For this example that would
be between 35 and 65.  This could be considered the greatest
deviation likely.


The streaks in random events must be respected.  Consider again
playing a fair odds coin toss game, betting $1 at a time and this
standard deviation example.  At the end of 100 events, the result
could be anywhere from -$30 (won 35 times) to +30 (won 65 times).
This would be a plus or minus 30% result.

As the number of events increase, the percentage away from the
expected result will become less.  However, the absolute
fluctuation amount will become greater.  At the end of 10,000
events, the result could be expected to be closer to an even
split percentage wise but could be substantially away in the
absolute amount.  The standard deviation for this example would
be 50.  At the end of 10,000 events the result could be anywhere
from -300 (won 4850 times) to +$300 (won 5150 times).  This would
be a plus or minus 3% result.

This is the law of large numbers, a statistical term.  The longer
period a gambler plays, the closer they will be to the expected
result percentage wise.  However they will require a greater
bankroll to with stand the absolute fluctuations in negative
streaks.


These examples were based on a fair odds game.  The impact of the
standard deviation is greater on unfair odds games as offered by
casinos.  Effectively the plus and minus range is shifted
accordingly to the casino's advantage or PC.  Games with a small
PC are shifted very little.  Games with a large PC are shifted a
great deal.

Casinos have two advantages besides their built-in percentages.
First they have large numbers of gamblers making bets over
extended periods of time.  That reduces the percentage from the
expected result.  Second they have huge bankrolls to handle the
absolute fluctuations that may occur in a negative streak.

$MART GAMBLER REPORT

The $mart Gambler program report shows statistical items that can
be meaningful to monitoring gambling and improving results.  Of
course the value of the report is directly related to the quality
of the data inputted.  In the Planning menu, a data collection
form is available to record gambling results in the casino.  Some
players may prefer a small notebook but in either case it is
essential to record the data as soon as practical after playing.

On a side note, casinos can be funny about players keeping
records.  Most don't care but some may.  In general it is best to
be a little discrete when recording data.

Use the Report-Input menu selection to input new data into the
$mart Gambler program as soon as practical.  Use the Report-Edit
menu selection to review the data and correct any mistakes.  Use
the Report-Compute menu selection to update the report.

If there is no data available at this time, it is recommended to
select File-Example to understand better the following report
items.  A sample database and report will be loaded.  Then either
select Report-View or Report-Print.

Summary statistics show the following items:

  Number of Sessions:  The number of entries inputted.

  Number Win:  The quantity with an even or plus result.

  Percent Win:  (Number of Sessions / Number Win) * 100

  Cum Plus/Minus: Cumulative summation of individual sessions

  Change since last report: Difference of the last cum to the new

  Best Session: The maximum individual session win

  Average Session: The arithmetic mean average of the sessions


  Worst Session: The maximum individual session loss

  +3 Std Deviations: The average + 3 standard deviations

  +2 Std Deviations: The average + 2 standard deviations

  Standard Deviation: The measure of dispersion from the average

  -2 Std Deviations: The average - 2 standard deviations

  -3 Std Deviations: The average - 3 standard deviations

The plus and minus three standard deviations show what can be
expected in 99.7% of the times.  The plus and minus two standard
deviations show what can be expected in 95.5% of the times.

Detail statistics show the following items:

Results by Casino Code:

  Code: Codes as set up in Planning and inputted in Report-Input

  Casino: Explanation of codes as set up in Planning-CasinoCodes

  Number of Sessions: The number of entries with that code

  Cum Plus/Minus: Cumulative summation of sessions with that code

  Average Session: The average of the sessions with that code

  Std Dev Session: The dispersion of sessions with that code

Results by Type Code:

  Code: Codes as set up in Planning and inputted in Report-Input

  Type: Explanation of codes as set up in Planning-TypeCodes

  Number of Sessions: The number of entries with that code

  Cum Plus/Minus: Cumulative summation of sessions with that code

  Average Session: The average of the sessions with that code

  Std Dev Session: The dispersion of sessions with that code


The $mart Gambler report provides many benefits.  By getting the
data in control, it leads to greater control over gambling.  This
will not reduce the entertainment aspect of gambling but increase
it for a specific budget.  By managing and controlling their
gambling, a player can remain in the game or "action" for a
longer period.


The summary statistics show over all results with the cum
plus/minus the most meaningful item.  The average and standard
deviation calculations show what is being experienced
statistically.  If the results differ significantly from the
expected results, a review of the game played and control in the
casino may be beneficial.

The report also transforms what is "thought" to what is "real."
A player may think they like to play at a particular casino
because they think they do well there but the actual statistical
results may not agree.  Like wise a player may think they do well
at a particular type of game but the actual statistical results
may differ.

The report shows the casinos and types of games that the gambler
is most successful at playing.  The results by casino code and
type code are sorted by the average session to make it easier to
comprehend and identify the best ones.

In addition to the report, by selecting Report-Graph, graphs on
the cum plus/minus, casino and type code average session are
available.

SUMMARY

The $mart Gambler report helps the player understand and
appreciate the mathematics of casino gambling.  It also helps in
making decisions on where to play and the types of games to play.
The data when analyzed is a valuable tool in improving success in
casino gambling.

  Copyright 1992  PC Information Systems  All rights Reserved