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1992-11-01
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IF YOU'RE GOING TO PLAY ... WHY NOT PLAY SMART ???
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LOTTO STAT (tm)
Copyright Richard J. Jones, Consulting Services
P.O. Box 8413
Westerville, Ohio 43081
_________ (tm)
__________| |___________________
_____|___ |
| |O | Association of
| ______|__ |
| | |__| Shareware
| | |
|__| O | Professionals
_______| | |_______________________
|____|____| MEMBER
Lotto Stat v2.50
LOTTO STAT IS SUPPLIED AS IS. THE AUTHOR DISCLAIMS ALL WARRANTIES, EXPRESSED
OR IMPLIED, INCLUDING, WITHOUT LIMITATION, THE WARRANTIES OF MERCHANTABILITY
AND OF FITNESS FOR ANY PURPOSE. THE AUTHOR ASSUMES NO LIABILITY FOR DAMAGES,
DIRECT OR CONSEQUENTIAL, WHICH MAY RESULT FROM THE USE OF LOTTO STAT.
ACKNOWLEDGEMENTS:
Association of Shareware Professionals (A.S.P.): For their advise and
help in making Lotto Stat a quality product.
Executive Director
Association of Shareware Professionals
545 Grover Road
Muskegon, MI 49442-9427
Public (software) Library (P.s.L.) & Nelson Ford: Their "PROGRAMMER'S
GUIDE" provided a wealth of information and the legal jargon necessary
to bring this product to market.
Public (software) Library
P.O. Box 35705
Houston, TX 77235-5705
________________
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|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
1.0 General Information 1
1.1 What is Lotto Stat 1
1.2 List of Files 2
1.3 Terminology 2
1.4 Hardware Requirements 3
1.5 Game Requirements 3
1.6 Installation 3
1.7 Drawing File 4
2.0 Philosophy 4
2.1 Lottery Processes 4
2.2 Play 6
2.3 Statistical 8
3.0 Operation 12
3.1 Load Drawing Data 13
3.2 Display Drawing History 15
3.3 Average Control 16
3.4 Display Range 18
3.5 Historical Strategy 21
3.6 Complimentary Strategy 23
3.7 Unbiased Strategy 24
3.8 Select Numbers 25
3.9 Quit 27
4.0 Evolution 28
5.0 Warranty and License Agreement 29
5.1 Copyright 29
5.2 Warranty 29
5.3 License 29
5.4 Legal Rights and Issues 30
6.0 Shareware 30
6.1 Registration 30
6.2 Technical Support 31
7.0 INDEX 32
Lotto Stat v2.50 Page 1
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| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
1.0 General Information
If you're going to play -- why not play smart ??? Lotto Stat will let
you decide what's hot and what's not. Provides the calculation and the
documentation takes you through the "play - no play" decision process. With
Lotto Stat you can analyze the history of winning drawings and use the
appropriate strategy to select your plays. Through analysis and artistry the
user may be able to improve the odds of winning to something less
prohibitive. Lotto Stat is capable of playing almost all the lottery games
available to date.
1.1 What is Lotto Stat
Lotto Stat can be used with any lottery that draws 2 through 10 numbers
in the range 0 to 99, included once in a drawing, and sorted low to high.
Lotto Stat is a set of statistical based tools that enables the user to
analyze the history of winning lottery numbers. However like any other set
of tools, you need to match the right tool to the right task to be
successful. And like any other situation, experience is the best teacher and
one purpose of Lotto Stat is to accelerate your learning curve.
The occurrences for the history of winning lottery drawings are
tabulated and provide the basis for selecting numbers for future drawings.
The user can choose from Historical, Unbiased, or Complimentary strategies.
The software also allows the user to control the selection process by using
the average of the numbers to be included in the drawing. Analysis of the
range history provides the user the ability to control the selection process
by position.
Version 2.5 is a forerunner to a more extensive version under
development and a succession of future versions with added functionality. The
next version will include a lottery definition file, file maintenance with
audit and edit capability, drawing odds calculations, user definition for hot
and cold numbers, user input to frequency table, tracking past selections,
test current strategy, expanded analysis of ranges, and much more. If you
have any suggestions for future versions I would like very much to hear from
you.
The lottery is a game of chance. By knowing when to play and what to
play Lotto Stat can give you that added ingredient -- skill.
Lotto Stat v2.50 Page 2
1.2 List of Files
The Lotto Stat evaluation package should contain the following files.
Please check that each file is present. If any of these files are missing
then the package is incomplete and is not suitable for distribution. The
complete package may be obtained directly from Richard J. Jones, Consulting
Services.
File: Purpose:
----- --------
REQUIRED: LS.EXE Lotto Stat v2.50 program
LOTTO.DTA Lottery Data File
MISC: README Last minute information.
DOC: DESCRIBE.DOC Description of Lotto Stat
FILE.LST List of Lotto Stat Files
LICENSE.DOC License and Use Information
MANUAL.DOC Manual for Lotto Stat
REGISTER.DOC Registration and order form.
BBOARD.DOC Information for Bulletin Board
Distribution
VENDOR.DOC Information for disk vendors,
distributors, user groups
WARRANTY.DOC Warranty Information
1.3 Terminology
The following terminology is used throughout the documentation so the
user better understand the material once he becomes familiar with the
definitions.
Complimentary: Develops the frequency table by replacing high occurrence
values with low occurrence values and vise-versa.
Confidence Level: The probability expressed as a percentage that the value
is contained within the range.
Confidence Interval: The range expected to include the estimate.
Drawings: The history of winning numbers for the lottery being analyzed.
Frequency Table: The list of occurrences for each possible number that may
be included in a drawing. This table provides the basis for making
selections.
Historical: Uses the number of occurrences form the drawings to build the
frequency table.
Mean: The average.
Mean Control: Allows the user to select low and high limits for the average
of the numbers to be included in the user selections.
Lotto Stat v2.50 Page 3
Ranges: The numbers to be drawn can be separated into ranges. The number of
segments will correspond to the number of numbers to be drawn. For example
if a drawing of five numbers can include numbers from 1 to 50, their will be
five ranges of ten numbers each.
Standard Deviation: The measure of the variability of the data.
Selections: Numbers to be used in the next lottery drawing.
Strategies: User may select from the three following strategies: Historical,
Complementary, and Unbiased.
Unbiased: Sets each occurrence in the frequency table to the same value.
Z-Value: The number associated with the confidence level to define the
confidence interval.
1.4 Hardware Requirements
Lotto Stat requires an IBM PC or compatible computer running DOS 3.0 or
above. You must have at least 512K bytes of memory. Lotto Stat easily fits
on a single 5 1/4' 360K floppy disk and does not require a color displays.
Lotto Stat does not have specific printed output but the user may opt to
use print screen capability if required.
1.5 Game Requirements
Lotto Stat can be used with any lottery the meets the following
criteria.
- Numbers included in drawings may range from 0 to 99.
- A drawing may consist of 1 to 10 numbers.
- A number may only appear once in each drawing.
- The drawing numbers will be ordered low to high.
1.6 Installation
Installing Lotto Stat, just copy the following to a diskette or a
subdirectory on your hard drive:
LS.EXE
LOTTO.DTA
The data file (LOTTO.DTA) may be included on the same diskette or in the
same subdirectory as the Lotto Stat program. The default is drive A: with no
subdirectory.
Lotto Stat v2.50 Page 4
1.7 Drawing File
The drawing history is stored in an ASC file in the following format:
DATE ,1st #,2nd #, 3rd #, ... ,LAST #(cr/lf)
mo/da/yr,xx,xx,xx,...,xx(cr/lf)
EXAMPLE:
04/08/90,03,08,16,22,39
10/28/91,11,15,23,34,35
The file may be changed and/or appended with any text editor.
2.0 Philosophy
Three factors come to bear when you consider playing the lottery -- the
cost, the prize, and the probability of winning. There is really nothing you
can do about the cost. You can however wait for the prize to reach a level
that makes it worthwhile to play. Although you can not really change the
probability, an analysis of the history may reveal information that could be
to your benefit.
These three factors can help you determine whether or not to play the
lottery, otherwise the lottery becomes an outright gamble.
2.1 Lottery Processes
To better understand our chances of winning, lets consider the following
lottery.
1) There are 10 balls in the tumbler, numbered from 0 through 9. Four
numbers will be selected and the ball selected will be replaced in the
tumbler before the next selection is made. Therefore the 10 balls will
available for each selection. How many different 4 number selections are
possible?
Since any of the 10 numbers may be selected each time, the calculation
looks like the following:
1st 2nd 3rd 4th
10 x 10 x 10 x 10 = 10,000
There is a 1 in 10,000 chance of selecting a matching number and the odds of
winning are 1 in 9,999.
2) Now we will change the process and make the selection of the next
ball without replacing the ball from the prior selection. How many different
4 number selections are now possible?
There is one less ball available after each selection the calculation
is as follows:
1st 2nd 3rd 4th
10 x 9 x 8 x 7 = 5,040
Lotto Stat v2.50 Page 5
You can see from the answers not replacing the ball selected makes a big
difference.
3) Again we will change the process so that after the 4 numbers are
selected, the winning number is determined after those numbers are arranged
in order lowest to highest. How does this affect the number of possible
outcomes?
The number of outcomes from the first part of the process remains
unchanged, ie. 5,040. However the ordering process changes the final
result.
Any of the 4 numbers could have been the lowest, leaving one of the
three remaining numbers to be next lowest and so forth.
Low Next Next High
4 x 3 x 2 x 1 = 24
The final calculation becomes --
5040 / 24 = 210
Ordering the numbers has also has had a significant impact on the number of
possible outcomes. The original process yielded 10,000 possibilities. As the
process was modified the outcomes went to 5,040 and finally to 210. Not only
does the number of ball to selected affect the number of outcomes but so does
the selection process. You can use the above process to determine the number
of possible outcomes for the lottery game you are considering.
4) For our final drawing process lets consider the following which
resembles the power ball game available in many states. Three of the 10 balls
will be selected without replacement and ordered lowest to highest. The three
balls drawn will be replaced in the hopper and a the fourth ball selected
which also will not be included in the ordering process.
Selecting the first 3 balls:
1st 2nd 3rd
10 x 9 x 8 = 720
Order lowest to highest:
Low Next High
3 x 2 x 1 = 6
First 3 ball possibilities:
720 / 6 = 120
Adding the drawing of the 4th ball from the hopper now containing all
10 balls:
First 3 4th
720 x 10 = 7,200
Lotto Stat v2.50 Page 6
2.2 Play
As an introduction to the playing philosophy, the first rule will be
developed. This is a bit of advice I learned from my father at very early age
and it has stuck with me through the years.
________________________________________________
| |
| RULE NUMBER ONE: |
| --------------- |
| |
| IF I CAN'T AFFORD THE LOSS -- I DO NOT PLAY! |
| -------------------------------------------- |
|________________________________________________|
This is true regardless of the game, regardless of the odds and regardless
of the potential reward. If we think back I am sure we all can recall at
least one perceived sure thing gone awry.
People who participate in games of chance can generally be divided in
to two categories, the gambler and the player. By way of definition - the
gambler knows the game and the reward. And lives by the rule if you don't
play you don't win. The player while knowing the game and the reward also
knows the odds. The player does a risk/reward sanity check and decides
whether or not to play.
The first bit of information you can find will be on the back of your
lottery ticket. If you just read the prize list classify yourself as a
gambler. Most state lotteries publish the odds on the back of the lottery
ticket or in a separate brochure. If the odds of winning are 1 in 999,999,
this means there are 1,000,000 possibilities and you have 1 possibility of
winning. With numbers of this magnitude it makes little difference. However
with smaller numbers the perception can be quite significant. Take for
example a standard deck of 52 cards. The odds of drawing a Heart are 1 in 3
or what might be considered 33%. In fact there are 13 Hearts in the 52 card
deck which is really 25%. With this bit of information would you decide to
play if the cost were $1.00 and the payoff were:
a) $3.00 ? b) $4.00 ? c) $5.00 ?
If you tend to be a gambler the answer is a) yes, b) yes, c) yes and you have
fulfilled you mission - play to win. The player does a basic evaluation;
Cost/Win % or $1.00/0.25 = $4.00 so the player comes to the following
conclusion: a) no, b) indifferent, c) definitely.
The lottery is obviously a more complex situation with other prizes;
cash, free tickets, supplemental drawings, etc. One way to cut through the
complexity is to look at the lottery payout. If 50% of the lottery receipts
are paid out in prizes, then if you are a dedicated gambler and play every
drawing, the expected value of each dollar wagered is $0.50. Unless of course
you know something about the upcoming drawing which significantly changes the
published odds.
Lotto Stat v2.50 Page 7
In his analysis the player considers the prize and probability of
winning that prize. There are two factors at work, the amount of the prize
and the value of the probability. The player has one basic rule -- When the
expected value of the ticket exceeds the cost it is time to play.
There are lotteries where the prize will grow when the winning drawing
number has not been purchased. For example suppose the lottery we are
considering has 1 million possible outcomes and one winning combination will
be selected. The prize is $400,000 and increases by $300,000 each time the
winning number has not been purchased. The cost to purchase a number is
$1.00.
Week 1: $400,000/1,000,000 = $0.40 less than $1.00 Play? NO
NO WINNER
Week 2: $700,000/1,000,000 = $0.70 less than $1.00 Play? NO
NO WINNER
Week 3: $1,000,000/1,000,000 = $1.00 equal $1.00 Play? Maybe
NO WINNER
Week 4: $1,300,000/1,000,000 = $1.30 greater than $1.00 Play? YES?
Having read the back of our lottery ticket more closely, we find if more
than one winning number has been purchased the prize will be split equally
the winning ticket holders. The news media tells us lotto tickets are being
sold at a record pace and 1.4 million lotto numbers will be sold.
$1,300,000/1,400,000 = $0.93 less than $1.00 Play? NO
NO WINNER, Again 1.4 million tickets to be sold
Week 5: $1,600,000/1,400,000 = $1.14 greater than $1.00 Play? YES?
I wonder what the tax consequences might be? Answer 25%
$1,600,000 - ($1,600,000 x 0.25) = $1,200,000
$1,200,000/1,400,000 = $0.86 less than $1.00 Play? NO
NO WINNER, Again 1.4 million tickets to be sold
Week 6: $1,900,000 - ($1,900,000 x 0.25) = $1,425,000
$1,425,000/1,400,000 = $1.02 greater than $1.00 Play? YES?
After further research we find the prize will be paid out over 5 years
or the winner may take the discounted cash value which for our hypothetical
case study is about 70% of the prize.
$1,900,000 x 0.70 = 1,330,000
$1,330,000 - ($1,330,000 x 0.25) = $997,500
$997,500/1,400,000 = $0.71 less than $1.00 Play? NO
ALL RIGHT!!! WHEN SHOULD I PLAY ???
Lotto Stat v2.50 Page 8
Analytical Speaking --
Week 9: $2,800,000 x 0.70 = $1,960,000
$1,960,000 - ($1,960,000 x 0.25) = $1,470,000
$1,470,000/1,400,000 = $1.05 greater than $1.00 Play? YES!
After first considering RULE 1, I personally start playing the lottery
at Week 3, but I do understand the consequences. Although it may not be the
smart play, it is the fun play, there must be a little gambler in every
analytical player.
As a matter of fact even after 10 consecutive weeks of no winners if I
can't comply with RULE 1, I do not play!
________________________________________________
| |
| RULE NUMBER ONE: |
| --------------- |
| |
| IF I CAN'T AFFORD THE LOSS -- I DO NOT PLAY! |
| -------------------------------------------- |
|________________________________________________|
2.3 Statistical
Although we cannot change the basic probabilities, analyzing the history
can be very rewarding. Even in a series of unbiased random events patterns
or run sequences can develop. Identifying when these "runs" will commence or
conclude before the fact, borders on an art form. But can improve your odds
while that window is open and the pattern is in effect.
In fact we can still "pick smart" even if a run is not underway.
Although the basic lottery process is a uniform generation, central
tendencies are present. As an example, the average of the numbers included
in each of the drawings will have a tendency to center around the mid-point
of the numbers to be selected.
Those who indulge in statistical analysis are generally either
technicians or artists. The technician has a head full of procedures coupled
with the appropriate prescribed situations and precedes with blinders firmly
in place. On the other hand the artist identifies the issue and applies a
process that gets around the issue although it may not be a conventional
approach. Where the artistic approach is used it will be identified in the
documentation. This will enable the statistical purists to avoid situations
where they are not comfortable.
In an unbiased situation each of the 10 balls may be selected with equal
probability (1/10). At the risk of boarding on the technical this could be
represented by the following:
Lotto Stat v2.50 Page 9
0 9
_______________________________________
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
|___|___|___|___|___|___|___|___|___|___|
LOW HIGH
UNIFORM DISTRIBUTION
After a number of drawings, we count the number of times each of the
balls has been selected which is represented below.
0 ___ 9
___ | |___ ___
| | ___| | | ___ | |
| |___| | | |___ | |___| |
| | | | | | |___| | | |
| | | | | | | | | | |
| | | | | | | | | | |
|___|___|___|___|___|___|___|___|___|___|
LOW HIGH
RESULTS
The fact that each of the numbers was not selected an equal number of
times is not surprising nor does it indicate a particular bias in the
probability or the selection process. This can be verified statistically
although that is not the point to be discussed. In fact the real surprise
would be if each number had an equal number of occurrences.
Statisticians knowing there is an underlying uniform distribution and
viewing the results will adopt one of three postures when considering what
will happen next.
The unbiased group will contend that each number can still be selected
with equal probability. A sort of I have made up my mind don't confuse
me with facts philosophy. In fact if the results remain proportionally
the same and the number of drawings were substantial, bias in the
process would be indicated.
The historical group will weight their selections based on the results -
- a jump on the bandwagon approach. If ultimately there is bias, this
selection process is on target. However if there is no long term bias
this strategy is not appropriate and counter productive.
The complimentary group believes the underlying process will generate
a uniform distribution and the tendency will be in balance over time.
The selection process will tend to weight their selections in reverse
of the results. This is the contrary philosophy. If the process turns
out to be biased the selections will not be on target.
Lotto Stat v2.50 Page 10
Another factor that comes into play is the central tendency of the
average of the numbers included in the drawings. In order to demonstrate that
point, we will consider the rolling of a pair of dice. The diagram below
depicts probabilities of using a single die.
_______________________
| | | | | | |
| | | | | | |
|___|___|___|___|___|___|
1 2 3 4 5 6
SINGLE DIE
If we consider the diagram below when two dice are used each with uniform
probabilities.
___________________________________________
| | | | | | | | | | | |
| | | | | | | | | | | |
|___|___|___|___|___|___|___|___|___|___|___|
2 3 4 5 6 7 8 9 10 11 12
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
TWO DICE
Before accepting the two dice diagram consider the following.
1 2 3 4 5 6
___________________________________
1 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 |
2 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
3 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 |
4 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 |
5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 | 5.5 |
6 | 3.5 | 4.0 | 4.5 | 5.0 | 5.5 | 6.0 |
|-----------------------------------|
AVERAGES
Which really gives us the correct diagram shown below.
___
___| |___
___| | | |___
___| | | | | |___
___| | | | | | | |___
___| | | | | | | | | |___
|___|___|___|___|___|___|___|___|___|___|___|
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
TWO DICE AVERAGE
When there are enough drawing the distribution becomes a Normal Distribution.
**
* *
* *
* *
* *
* *
* * * *
___________________________________________
LOW HIGH
Lotto Stat v2.50 Page 11
Our objective is to find a significant difference between the actual and
expected results and use that information to "pick smart". Hopefully by
selecting the right strategy we will be able to improve the odds more in our
favor when we select the numbers for the next lottery drawing.
Lotto Stat v2.50 Page 12
3.0 Operation
Running Lotto Stat
To run Lotto Stat, type LS and the following will appear on the screen.
____________________________________________________________
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| | |
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| | _________________________|
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| |________________________ |
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| | |
| | |
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| |__________________________________________|
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| |
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| |
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|____________________________________________________________|
Lotto Stat v2.50 Copyright 1992 Richard J. Jones
After a few seconds the user will be asked to answer the following question.
NUMBERS IN DRAWING, SMALLEST & LARGEST NUMBERS: 5,0,50
| | |
Numbers to be Drawn <-------------| | |
| |
Smallest Number to be Drawn <-------| |
|
Largest Number to be Drawn <-----------|
The user has defined the lottery as --
A five number drawing where numbers 0 through 50 can be selected.
NUMBERS IN DRAWING, SMALLEST & LARGEST NUMBERS: 5,0,50
NUMBER OF COMBINATIONS: 2,349,060 CONFIDENCE LEVEL: 95 Z-VALUE: 1.960
Strike Any Key to Continue ...
The defined drawing will have 2 million, 349 thousand 060 possible
outcomes The confidence level and corresponding Z-Value are initialized in
the system. These values can be changed by the user at various stages in the
process and will be explained at that time.
Lotto Stat v2.50 Page 13
The main menu will now appear. By entering the number opposite the
description will initiate the corresponding task. The logical first task
would be to load to "LOAD DRAWINGS". However this is not essential. the
program will use an unbiased strategy to select future drawing numbers
without benefit of the drawing history. If past drawing data is required for
a particular function, the user will be notified and the function will not
be performed as requested and the program will return to the menu.
The following is the main menu:
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 1
3.1 Load Drawing Data
The input data file name is predefined, however the user is given the option
to enter a drive, path and filename of his choosing. To demonstrate this
feature the predefined information was re-used.
ASC LOTTO FILE: A:\LOTTO.DTA
CHANGE INPUT FILE (Y/N): Y
ASC LOTTO FILE: A:\LOTTO.DTA
The data loaded in the ASC Lotto File is loaded into the program and will be
used during the analysis. The data should be in the following form.
MO/DA/YR,99,99,99,99,99 For a 5 number drawing
Lotto Stat v2.50 Page 14
A data loading message appears on the screen as the drawing history is
being loaded. When the data has been loaded, the following information
derived from the drawing definition and history is displayed on the screen.
COMBINATIONS: 2,349,060 CONFIDENCE LEVEL: 95 Z-VALUE: 1.960
DRAWINGS: 149
INDIVIDUAL DRAWING NUMBERS:
MEAN: 25.4 STD. DEV.: 14.62 95% INTERVAL: -3.2 - 54.1
NUMBER: 745 STD. ERR : 0.54 95% INTERVAL: 24.4 - 26.5
FREQUENCY DRAWING NUMBERS:
MEAN: 25.4 STD. DEV.: 14.62 95% INTERVAL: -3.2 - 54.1
NUMBER: 745 STD. ERR : 0.54 95% INTERVAL: 24.4 - 26.5
AVERAGE OF DRAWING NUMBERS:
SUM MEAN: 25.4 SUM STD. DEV.: 6.47 95% INTERVAL: 12.7 - 38.1
EXP MEAN: 25.0 95% Z-VALUE : 0.78 CRITICAL VALUES -1.96 <> +1.96
Strike Any Key to Continue ...
The following is an explanation of the information appearing on the screen.
COMBINATIONS: 2,349,060 CONFIDENCE LEVEL: 95 Z-VALUE: 1.960
The lottery defined has over 2 million possible outcomes and the
confidence level in the system is displayed with its corresponding Z value.
DRAWINGS: 149 The number of winning drawings on file.
The information has been determined from each number included in the
winning drawings on file. The interval at the current confidence level may
extend beyond the known range defined for the drawing. The process is
applicable to a bell shaped distribution and we know the drawing distribution
is uniform and not the bell shaped normal distribution. The expected mean
from the uniform distribution would be 25.0, ie. sum of the high number and
the low number divided by 2. The mean calculated from the data is 25.4
indicating a bias toward the higher numbers. The interval calculated using
the 95% confidence level includes the calculated mean. Therefore the bias is
not significant.
INDIVIDUAL DRAWING NUMBERS:
MEAN: 25.4 STD. DEV.: 14.62 95% INTERVAL: -3.2 - 54.1
NUMBER: 745 STD. ERR : 0.54 95% INTERVAL: 24.4 - 26.5
Lotto Stat v2.50 Page 15
The same information has been calculated from the frequency table
tabulated from the drawings as they were loaded. Since the information is
identical the frequency table represents the historical data. If there were
a difference it would indicate the frequency table has been adjusted to
reflect another strategy.
FREQUENCY DRAWING NUMBERS:
MEAN: 25.4 STD. DEV.: 14.62 95% INTERVAL: -3.2 - 54.1
NUMBER: 745 STD. ERR : 0.54 95% INTERVAL: 24.4 - 26.5
The following information has been calculated from the average of the
drawings on file. The sum mean is identical to the previous values and the
sum standard deviation is used with the confidence level 95% is used to
determine the interval. Although the individual numbers are derived from a
uniform distribution, the average of the drawings will be the bell shaped
normal distribution. Therefore the standard probability procedures and
conclusions are appropriate. The interval will theoretically include 95% of
the drawings. The difference between the mean and the expected mean have a
Z value at the 95% confidence level of 0.78 which is well within the critical
values indicating again the difference is no significant.
AVERAGE OF DRAWING NUMBERS:
SUM MEAN: 25.4 SUM STD. DEV.: 6.47 95% INTERVAL: 12.7 - 38.1
EXP MEAN: 25.0 95% Z-VALUE : 0.78 CRITICAL VALUES -1.96 <> +1.96
3.2 Display Drawing History
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 2
Lotto Stat v2.50 Page 16
The following data is displayed when the drawing display is requested.
LIMITS: 20 - 30 The low & high limits in effect
01/02/91 0 23 24 35 39 AVE: 24.2
01/04/91 8 13 14 22 30 AVE: 17.4*
01/06/91 2 6 9 12 38 AVE: 13.4*
01/08/91 17 27 29 44 48 AVE: 33.0* The date and the numbers that
01/11/91 17 19 36 42 50 AVE: 32.8* made up the drawing are shown.
01/13/91 3 27 37 42 46 AVE: 31.0*
01/15/91 1 8 15 16 40 AVE: 16.0*
01/18/91 7 15 18 19 33 AVE: 18.4* Ave. of the numbers for each
01/20/91 13 29 31 35 49 AVE: 31.4* drawing. The asterisk indicates
01/22/91 0 23 27 46 48 AVE: 28.8 averages outside the limits.
01/25/91 1 2 9 10 48 AVE: 14.0*
01/27/91 5 6 15 37 41 AVE: 20.8
01/29/91 22 28 36 38 50 AVE: 34.8*
02/01/91 16 18 20 44 46 AVE: 28.8
02/03/91 22 26 28 44 46 AVE: 33.2*
02/05/91 28 32 34 46 50 AVE: 38.0*
02/08/91 3 22 26 39 45 AVE: 27.0
02/10/91 12 20 41 47 48 AVE: 33.6*
02/12/91 7 10 19 37 40 AVE: 22.6
02/15/91 7 37 38 41 49 AVE: 34.4*
02/17/91 8 14 24 29 37 AVE: 22.4
02/19/91 8 9 17 26 41 AVE: 20.2
CONTINUE (Y/N): N
N (no) terminates the display. Y (yes) provides the next
series of drawing numbers or will return to the first screen
if you are at the end of the drawings on file.
3.3 Average Control
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 3
Lotto Stat v2.50 Page 17
The user may define the limits of the average for the selection process.
These limits may be defined by a percentage(%) or directly (#) by specifying
the lower and upper bounds.
DRAWING LIMIT % OR # : %
PERCENT (50, 60, 70, 80, 90, 95, 100): 80
LOW LIMIT: 17 HIGH LIMIT: 34 80% translates to the numbers shown.
LOW - LIMIT: 17 COUNT: 13 PCT.: 8.7 NO.: 9.0 08/27/91
HIGH - LIMIT: 34 COUNT: 14 PCT.: 9.4 NO.: 42.0 09/24/91
There were 13 drawing averages or 8.7% of the total below the low limit.
The lowest was 9.0 which occurred 08/27/91. Fourteen times, or 9.4% of the
drawings the average was above the upper limit. The highest 42.0 was the
09/24/91 winning drawing. Theoretically we would have expected 10% of the
drawing less than the low limit and 10% above the upper limit. Since the
actual percentages are less than the theoretical percentages, the limits
would seem to be appropriate.
SELECT NEW LIMITS (Y/N): Y
DRAWING LIMIT % OR # : #
LOW & HIGH LIMITS: ? 20,30
LOW LIMIT: 20 HIGH LIMIT: 30
LOW - LIMIT: 20 COUNT: 29 PCT.: 19.5 NO.: 9.0 08/27/91
HIGH - LIMIT: 30 COUNT: 34 PCT.: 22.8 NO.: 42.0 09/24/91
When limits are selected directly the theoretical percentage is not part
of the process. However the numeric limits may be selected without regard to
symmetry about the mean. Percentage limits will always be symmetrical with
regard to the expected mean.
SELECT NEW LIMITS (Y/N): N Exit
Lotto Stat v2.50 Page 18
3.4 Display Range
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 4
DRAWING RANGE VARIANCES (Y/N): Y Ranges as defined by the drawing will
be displayed.
Below are the ranges derived from the lottery definition. Numbers which
can be drawn are divided into the number of ranges according to the number
of numbers included in the drawing.
EXPECTED: 1 2 3 4 5 Number of ranges
MEAN 5.1 15.3 25.5 35.7 45.9 Mid-point of the range.
STD. DEV. 1.7 1.7 1.7 1.7 1.7 Range variability
80% LOW 0.0 10.2 20.4 30.6 40.8 Confidence limits for
80% HIGH 10.2 20.4 30.6 40.8 50.0 the range low & high
LOW COUNT 0 44 47 50 46 Below the low limit
LOW PCT. 0.0 29.5 31.5 33.6 30.9 Percent below low limit
HIGH COUNT 44 49 48 42 0 Above the high limit
HIGH PCT. 29.5 32.9 32.2 28.2 0.0 Percent above
TOTAL PCT. 29.5 62.4 63.8 61.7 30.9 Total percent
LOWEST 0.0 2.0 5.0 10.0 20.0 Lowest number selected
HIGHEST 30.0 43.0 46.0 48.0 50.0 Highest number selected
NEW CONFIDENCE INTERVAL (Y/N): N No change to the confidence limit.
These line titles are consistent for all the range data displays.
Lotto Stat v2.50 Page 19
ACTUAL RANGE VARIANCES (Y/N): Y
The information displayed is the same as it was for the previous screen
except the values have been derived from the drawing history file. The data
used is the winning drawing sequence not the order that the numbers may have
been selected. It should also be noted that the first and last ranges will
be influenced by the smallest and largest numbers included in the drawing.
ACTUAL: 1 2 3 4 5
MEAN 8.2 17.1 25.5 33.7 42.6
STD. DEV. 7.1 9.1 9.0 9.0 6.8
80% LOW 0.0 5.4 14.0 22.2 33.9
80% HIGH 17.3 28.7 37.0 45.3 50.0
LOW COUNT 0 11 16 19 14
LOW PCT. 0.0 7.4 10.7 12.8 9.4
HIGH COUNT 15 19 16 12 0
HIGH PCT. 10.1 12.8 10.7 8.1 0.0
TOTAL PCT. 10.1 20.1 21.5 20.8 9.4
LOWEST 0.0 2.0 5.0 10.0 20.0
HIGHEST 30.0 43.0 46.0 48.0 50.0
The standard deviations excluding the first and last ranges could
possibly be equal. The following F Test table attempts to determine that
possibility. Technically the F Test is used when the distributions are
normal. It is unlikely the distributions within the ranges are normal.
However, unless some bias exists we would expect the range variances to be
equal. Excepting the first and last range which are probably influence by
the numbers included in the drawing pool. The concern is that the variability
has been understated. This would understate the high limit of the first range
and the low limit of the last range.
F - TEST:
1 1.00 1.63* 1.59* 1.60* 0.91
2 0.62* 1.00 0.98 0.98 0.56*
3 0.63* 1.02 1.00 1.00 0.57*
4 0.63* 1.02 1.00 1.00 0.57*
5 1.10 1.79* 1.75* 1.76* 1.00
TEST STATISTIC 5% df 120 x 120: 0.74 < F < 1.35 VARIANCES EQUAL
NEW CONFIDENCE INTERVAL (Y/N): N
The standard deviations for the first and last ranges seem to show the
effect of the bounds of the drawing definition. A review of the standard
deviations for the middle ranges would seem to indicate a possibility they
are equal or at least close to it. The F-Test results were calculated to
provide some light on the issue.
The STATISTICAL PURIST should note: The F-Test is used to determine the
probability of equal variances from NORMAL DISTRIBUTIONS. If this
situation exceeds your comfort zone DO NOT request the calculation of
the Adjusted Range Variances.
Lotto Stat v2.50 Page 20
The results of the F Test show the limit influence of the first and last
ranges as indicated by the first and last columns and first and last rows.
The data used to calculated the adjusted variances does not include the
first and last ranges. Typically the F-Test Statistics for these ranges do
not indicate equality when tested against the middle ranges.
ADJUST RANGE VARIANCES (Y/N): Y
The table has been re-calculated the reflect the range variances being
equal which will effect the standard deviation and the low and high interval
values.
ADJUSTED: 1 2 3 4 5
MEAN 8.2 17.1 25.5 33.7 42.6
STD. DEV. 9.0 9.0 9.0 9.0 9.0
80% LOW 0.0 5.5 14.0 22.2 31.0
80% HIGH 19.8 28.6 37.1 45.3 50.0
LOW COUNT 0 11 12 19 12
LOW PCT. 0.0 7.4 8.1 12.8 8.1
HIGH COUNT 12 19 16 12 0
HIGH PCT. 8.1 12.8 10.7 8.1 0.0
TOTAL PCT. 8.1 20.1 18.8 20.8 8.1
LOWEST 0.0 2.0 5.0 10.0 20.0
HIGHEST 30.0 43.0 46.0 48.0 50.0
NEW CONFIDENCE INTERVAL (Y/N): Y A new percent can be selected.
PERCENT (50, 60, 70, 80, 90, 95, 100): 95
Below you can the effect of changing the confidence percent. The low and
high values change which in turn changes the counts and percentages. This
capability has been available for all of the range options and the effect
would be the same within the scope of the calculation of the particular
range.
ADJUSTED: 1 2 3 4 5
MEAN 8.2 17.1 25.5 33.7 42.6
STD. DEV. 9.0 9.0 9.0 9.0 9.0
95% LOW 0.0 0.0 7.9 16.0 24.9
95% HIGH 25.9 34.7 43.2 50.0 50.0
LOW COUNT 0 0 2 6 4
LOW PCT. 0.0 0.0 1.3 4.0 2.7
HIGH COUNT 6 6 2 0 0
HIGH PCT. 4.0 4.0 1.3 0.0 0.0
TOTAL PCT. 4.0 4.0 2.7 4.0 2.7
LOWEST 0.0 2.0 5.0 10.0 20.0
HIGHEST 30.0 43.0 46.0 48.0 50.0
NEW CONFIDENCE INTERVAL (Y/N): N
Lotto Stat v2.50 Page 21
3.5 Historical Strategy
The historical strategy is for those who believe the past trends will
continue regardless of the underlying process. The occurrence counts for the
historical strategy are tabulated from the drawing history.
The screens for the Historical, Complimentary, and Unbiased strategies
all contain the same information relative to the strategy being reviewed.
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 5
The heading indicates the confidence level in effect, the strategy
applicable to the table, and the numbers of selections.
CONFIDENCE LEVEL: 95 * HISTORICAL * NO.: 745
Next is the column heading for the body of information. The information
is repeated three times across the screen.
NO: The drawing number.
ACT: The actual number of times the number has been selected.
EST: The estimated number of times the number should have been selected.
LOW: The fewest number of times the number should have appeared.
HI: The most number of times the number should have appeared.
The estimated, fewest and most values are calculated based on the number
of numbers drawn and the confidence level.
NO ACT EST LOW HI | NO ACT EST LOW HI | NO ACT EST LOW HI |
Lotto Stat v2.50 Page 22
If you should change the confidence level you will see the effect in the
values recalculated for the LOW and HI.
CONFIDENCE LEVEL: 95 * HISTORICAL * NO.: 745
NO ACT EST LOW HI | NO ACT EST LOW HI | NO ACT EST LOW HI |
0 10 14 7 21 | 1 10 14 7 21 | 2 14 14 7 21 |
3 18 14 7 21 | 4 18 14 7 21 | 5 8 14 7 22 |
6 19 14 6 21 | 7 9 14 7 21 | 8 22H 14 6 21 |
9 9 14 7 21 | 10 19 14 6 21 | 11 8 14 7 22 |
12 18 14 7 21 | 13 12 14 7 21 | 14 15 14 7 21 |
15 16 14 7 21 | 16 14 14 7 21 | 17 17 14 7 21 |
18 16 14 7 21 | 19 10 14 7 21 | 20 15 14 7 21 |
21 18 14 7 21 | 22 17 14 7 21 | 23 13 14 7 21 |
24 15 14 7 21 | 25 8 14 7 22 | 26 26H 13 6 20 |
27 14 14 7 21 | 28 10 14 7 21 | 29 14 14 7 21 |
30 12 14 7 21 | 31 20 14 6 21 | 32 15 14 7 21 |
33 9 14 7 21 | 34 18 14 7 21 | 35 15 14 7 21 |
36 8 14 7 22 | 37 16 14 7 21 | 38 19 14 6 21 |
39 15 14 7 21 | 40 15 14 7 21 | 41 17 14 7 21 |
42 10 14 7 21 | 43 17 14 7 21 | 44 16 14 7 21 |
45 14 14 7 21 | 46 20 14 6 21 | 47 10 14 7 21 |
48 20 14 6 21 | 49 11 14 7 21 | 50 16 14 7 21 |
CHANGE CONFIDENCE INTERVAL (Y/N): Y
PERCENT (50, 60, 70, 80, 90, 95, 100): 80
CONFIDENCE LEVEL: 80 * HISTORICAL * NO.: 745
NO ACT EST LOW HI | NO ACT EST LOW HI | NO ACT EST LOW HI |
0 10 14 9 19 | 1 10 14 9 19 | 2 14 14 9 19 |
3 18 14 9 18 | 4 18 14 9 18 | 5 8L 14 9 19 |
6 19H 14 9 18 | 7 9 14 9 19 | 8 22H 14 9 18 |
9 9 14 9 19 | 10 19H 14 9 18 | 11 8L 14 9 19 |
12 18 14 9 18 | 13 12 14 9 19 | 14 15 14 9 19 |
15 16 14 9 19 | 16 14 14 9 19 | 17 17 14 9 18 |
18 16 14 9 19 | 19 10 14 9 19 | 20 15 14 9 19 |
21 18 14 9 18 | 22 17 14 9 18 | 23 13 14 9 19 |
24 15 14 9 19 | 25 8L 14 9 19 | 26 26H 13 9 18 |
27 14 14 9 19 | 28 10 14 9 19 | 29 14 14 9 19 |
30 12 14 9 19 | 31 20H 14 9 18 | 32 15 14 9 19 |
33 9 14 9 19 | 34 18 14 9 18 | 35 15 14 9 19 |
36 8L 14 9 19 | 37 16 14 9 19 | 38 19H 14 9 18 |
39 15 14 9 19 | 40 15 14 9 19 | 41 17 14 9 18 |
42 10 14 9 19 | 43 17 14 9 18 | 44 16 14 9 19 |
45 14 14 9 19 | 46 20H 14 9 18 | 47 10 14 9 19 |
48 20H 14 9 18 | 49 11 14 9 19 | 50 16 14 9 19 |
CHANGE CONFIDENCE INTERVAL (Y/N): N
Changing the confidence interval recalculates the low and high and the
corresponding indicators but not the count or the estimate. The (L)ow and
(H)igh indicators next to the ACT column become more noticeable. As more
Lotto Stat v2.50 Page 23
values fall outside the interval. As the confidence level decreases the range
will become narrower thus exposing more drawing numbers.
3.6 Complimentary Strategy
The complimentary strategy is for the user who knows the underlying
process and believes in the long run the numbers will reflect that process.
The calculated strategy ultimately produces an integer number and this
integer arithmetic may cause a slight adjustment in the number of drawings.
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 6
CONFIDENCE LEVEL: 80 * COMPLIMENTARY * NO.: 747
NO ACT EST LOW HI | NO ACT EST LOW HI | NO ACT EST LOW HI |
0 20H 14 9 18 | 1 20H 14 9 18 | 2 15 14 9 19 |
3 11 14 9 19 | 4 11 14 9 19 | 5 22H 14 9 18 |
6 10 14 9 19 | 7 21H 14 9 18 | 8 7L 14 10 19 |
9 21H 14 9 18 | 10 10 14 9 19 | 11 22H 14 9 18 |
12 11 14 9 19 | 13 18 14 9 18 | 14 14 14 9 19 |
15 13 14 9 19 | 16 15 14 9 19 | 17 12 14 9 19 |
18 13 14 9 19 | 19 20H 14 9 18 | 20 14 14 9 19 |
21 11 14 9 19 | 22 12 14 9 19 | 23 16 14 9 19 |
24 14 14 9 19 | 25 22H 14 9 18 | 26 0L 15 10 20 |
27 15 14 9 19 | 28 20H 14 9 18 | 29 15 14 9 19 |
30 18 14 9 18 | 31 9 14 9 19 | 32 14 14 9 19 |
33 21H 14 9 18 | 34 11 14 9 19 | 35 14 14 9 19 |
36 22H 14 9 18 | 37 13 14 9 19 | 38 10 14 9 19 |
39 14 14 9 19 | 40 14 14 9 19 | 41 12 14 9 19 |
42 20H 14 9 18 | 43 12 14 9 19 | 44 13 14 9 19 |
45 15 14 9 19 | 46 9 14 9 19 | 47 20H 14 9 18 |
48 9 14 9 19 | 49 19H 14 9 18 | 50 13 14 9 19 |
CHANGE CONFIDENCE INTERVAL (Y/N): N
Lotto Stat v2.50 Page 24
The complimentary calculation essentially flip-flops the actual
occurrences around the estimated count. Low counts become high and high
counts become low. Under this condition the numbers selected will compliment
the history so the combination of the history and the selections will reflect
the underlying unbiased process.
3.7 Unbiased Strategy
The unbiased strategy is for those who believe each new drawing is an
independent event and the underlying process is also unbiased.
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 7
CONFIDENCE LEVEL: 80 * UNWEIGHTED * NO.: 765
NO ACT EST LOW HI | NO ACT EST LOW HI | NO ACT EST LOW HI |
0 15 14 9 19 | 1 15 14 9 19 | 2 15 14 9 19 |
3 15 14 9 19 | 4 15 14 9 19 | 5 15 14 9 19 |
6 15 14 9 19 | 7 15 14 9 19 | 8 15 14 9 19 |
9 15 14 9 19 | 10 15 14 9 19 | 11 15 14 9 19 |
12 15 14 9 19 | 13 15 14 9 19 | 14 15 14 9 19 |
15 15 14 9 19 | 16 15 14 9 19 | 17 15 14 9 19 |
18 15 14 9 19 | 19 15 14 9 19 | 20 15 14 9 19 |
21 15 14 9 19 | 22 15 14 9 19 | 23 15 14 9 19 |
24 15 14 9 19 | 25 15 14 9 19 | 26 15 14 9 19 |
27 15 14 9 19 | 28 15 14 9 19 | 29 15 14 9 19 |
30 15 14 9 19 | 31 15 14 9 19 | 32 15 14 9 19 |
33 15 14 9 19 | 34 15 14 9 19 | 35 15 14 9 19 |
36 15 14 9 19 | 37 15 14 9 19 | 38 15 14 9 19 |
39 15 14 9 19 | 40 15 14 9 19 | 41 15 14 9 19 |
42 15 14 9 19 | 43 15 14 9 19 | 44 15 14 9 19 |
45 15 14 9 19 | 46 15 14 9 19 | 47 15 14 9 19 |
48 15 14 9 19 | 49 15 14 9 19 | 50 15 14 9 19 |
CHANGE CONFIDENCE INTERVAL (Y/N): N
Lotto Stat v2.50 Page 25
As you might expect the values for each drawing number have become
equal. By giving each drawing number an equal value the resulting selection
will essentially random and unbiased.
3.8 Select Numbers
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 8
The selection process will be controlled by any average and range limits
defined and the strategy chosen. Within these limitations the selection
process will generate the drawings. In addition the process will not select
duplicate drawings.
NUMBER OF SELECTIONS: ? 3 Three drawings are to be calculated.
Drawing Selection ...
Selection Complete ...
LIST (Y/N) N List the selections
MORE (Y/N) Y Select more drawings
NUMBER OF SELECTIONS: ? 12 Calculate twelve drawings
Drawing Selection ...
Selection Complete ...
LIST (Y/N) Y List selections
Lotto Stat v2.50 Page 26
LIMITS: 20 - 30 Average limits in effect
15 16 24 26 44 AVE: 25.0
4 10 28 33 37 AVE: 22.4 Original three selections
2 12 37 43 50 AVE: 28.8
6 10 22 33 37 AVE: 21.6
6 17 24 26 50 AVE: 24.6
2 5 31 34 37 AVE: 21.8
3 4 34 41 48 AVE: 26.0
3 6 27 28 41 AVE: 21.0 Next twelve selections
0 17 31 44 48 AVE: 28.0
7 18 25 33 42 AVE: 25.0
17 21 23 28 29 AVE: 23.6
6 15 28 31 43 AVE: 24.6
7 8 35 40 44 AVE: 26.8
3 21 25 28 47 AVE: 24.8
7 18 35 37 44 AVE: 28.2
CONTINUE (Y/N): N Display next selections or start over
if at the end of the list.
SAVE PREVIOUS PICKS (Y/N): Y Keep of discard prior selections
NUMBER OF SELECTIONS: ? 5 Five more selections
Drawing Selection ...
Selection Complete ...
LIST (Y/N) Y
LIMITS: 20 - 30
15 16 24 26 44 AVE: 25.0
4 10 28 33 37 AVE: 22.4
2 12 37 43 50 AVE: 28.8
6 10 22 33 37 AVE: 21.6
6 17 24 26 50 AVE: 24.6
2 5 31 34 37 AVE: 21.8
3 4 34 41 48 AVE: 26.0
3 6 27 28 41 AVE: 21.0
0 17 31 44 48 AVE: 28.0
7 18 25 33 42 AVE: 25.0
17 21 23 28 29 AVE: 23.6
6 15 28 31 43 AVE: 24.6
7 8 35 40 44 AVE: 26.8
3 21 25 28 47 AVE: 24.8
7 18 35 37 44 AVE: 28.2 First 15 (12 + 3) selections
5 10 27 39 46 AVE: 25.4
1 8 21 40 48 AVE: 23.6
0 2 27 29 47 AVE: 21.0 Five added selections
5 14 20 26 46 AVE: 22.2
3 15 20 35 46 AVE: 23.8
CONTINUE (Y/N): N
Lotto Stat v2.50 Page 27
3.9 Quit
If the analysis is complete the user may exit the program and return to
the operating system. The user may re-enter the analysis at any point on the
menu including the load drawings. However if the drawings have been loaded,
re-loading the drawings would be redundant and inflate the number of drawings
and distort the confidence results.
The documentation has covered the analysis in sequence as it appears on
the menu. The user may decide to analyze the data in an entirely different
sequence, remembering that analyzing the history requires the history first
be loaded.
________________
| ___ ___|_____ (TM)
| | | | | | ___|____________
| | | | | | | | | ___ __|
| |___|__|__|___|___ | | | |
|______| v2.50 |_____|__|_|_|__|
Copyright 1992 Richard J. Jones
MENU:
1. LOAD DRAWINGS
2. DISPLAY DRAWINGS
3. AVERAGE CONTROL
4. RANGE ANALYSIS
5. HISTORICAL STRATEGY
6. COMPLIMENTARY STRATEGY
7. UNBIASED STRATEGY
8. SELECTION
9. QUIT
RESPONSE: 9
Exit the program and returns to the system.
Lotto Stat v2.50 Page 28
4.0 Evolution
The following depicts the evolution and future development of the Lotto
Stat software. If you would like to play a part in this process please
contact me. Except where noted each version includes the capability of prior
versions.
Version Description
_______ ___________________________________________________________
0.0 Randomly selected six numbers from the range input by the
user. The numbers selected for a drawing were sorted low to
high and did not include duplicates. The selection process
also checked for duplicate drawings.
1.0 The history of the frequency of the occurance of the numbers
is loaded and used in the selection process.
2.0 The input becomes the history of winning drawings including
the date. The input is checked and sequenced by date and the
drawings are checked for validity. Allows the user to select
from a Historical, Unweighted, or Complimentary strategies.
In addition the user can limit the selections by range and by
the average of the numbers included. Comprehensive statistics
are also provided about the history and lottery parameters.
2.5 Upgraded to use the routines being developed for Version 3.0
3.0 Will include a lottery definition file, file maintenance with
audit and edit capability, drawing odds calculations, user
definition for hot and cold numbers, user input to frequency
table, tracking past selections, test current strategy,
expanded analysis of ranges, and much more.
Lotto Stat v2.50 Page 29
5.0 Warranty and License Agreement
5.1 Copyright
Lotto Stat(tm) is a trademark and copyright of the Author Richard J.
Jones.
Copyright laws apply to both Shareware and commercial software, and the
copyright holder retains all rights, with a few specific exceptions as stated
below. Shareware authors are accomplished programmers, just like commercial
authors, and the programs are of comparable quality. (In both cases, there
are good programs and bad ones!) The main difference is in the method of
distribution. The author specifically grants the right to copy and distribute
the software, either to all and sundry or to a specific group. For example,
some authors require written permission before a commercial disk vendor may
copy their Shareware.
5.2 Warranty
Lotto Stat is provided "as-is" without warranty of any kind, either
expressed or implied, including, but not limited to any implied warranty of
fitness or suitability for a particular purpose. Richard J. Jones, Consulting
Services shall not be liable or responsible to any person or entity for
damage or loss caused or alleged to be caused directly, indirectly or
consequently by the use of this program, it's documentation or it's output,
specifically including but not limited to damage or loss resulting from the
use of this product.
5.3 License
The Lotto Stat software is the property of Richard J. Jones, Consulting
Services. You are granted a license to use this software for a limited time
for the specific purpose of evaluation before purchase. If you use Lotto Stat
on a continuous basis, please register your copy to obtain a permanent
license.
You are free to make as many copies as you wish and may distribute Lotto
Stat freely in its original form, including disk based documentation.
Recipients of copies you make are granted a limited license to use Lotto Stat
on a trial and evaluation basis. If the recipient wishes to use Lotto Stat
on a continuous basis, he should register his copy.
You may not sell or ask any compensation or consideration for this
product. Special Interest Groups and Bulletin Board Systems may ask a nominal
fee to cover their copying and distribution costs. Original Equipment
Manufacturers wishing to bundle Lotto Stat with other products should contact
Richard J. Jones, Consulting Services for details.
Lotto Stat v2.50 Page 30
5.4 Legal Rights and Issues
Richard J. Jones, Consulting Services retains all rights of ownership
of the product called Lotto Stat under United States and International laws
of commerce. Lotto Stat is a copyright of Richard J. Jones, Consulting
Services. However Richard J. Jones, Consulting Services hereby expressly
authorizes the willful distribution of the enclosed software to other
individuals as long as no fee is charged for the program. A duplication
charge not to exceed $5.00 may be collected.
Richard J. Jones, Consulting Services does NOT authorize, nor waive, any
other rights provided under the protection of copyright laws, and reserves
the right to withdraw distribution rights at any future time. At such time,
notice will be given.
6.0 Shareware
Lotto Stat is a Shareware product. It is NOT a public domain or FreeWare
program. Shareware means that you are given a specific period of time in
which to use the product before you are required to register your copy. Thus,
if you decide to continue using Lotto Stat, we expect you to REGISTER your
copy with Richard J. Jones, Consulting Services.
Shareware is a distribution method, not a type of software. You should
find software that suits your needs and pocketbook, whether it's commercial
or Shareware. The Shareware system makes fitting your needs easier, because
you can try before you buy. And because the overhead is low, prices are low
also. Shareware has the ultimate money-back guarantee -- if you don't use the
product, you don't pay for it.
6.1 Registration
This program is produced by a registered member of the Association of
Shareware Professionals (A.S.P.). A.S.P. wants to make sure that the
shareware principle works for you. If you are unable to resolve a shareware
related problem with an A.S.P. member by contacting the member directly, ASP
may be able to help.
Lotto Stat is a "shareware program" and is provided at no charge to the
user for evaluation. Feel free to share it with your friends, but please do
not give it away altered or as part of another system. The essence of
"user-supported" software is to provide personal computer users with quality
software without high prices, and yet to provide incentive for programmers
to continue to develop new products. If you find this program useful and find
that you are using Lotto Stat and continue to use Lotto Stat after a
reasonable trial period, you must make a registration payment of $39.95 to
Richard J. Jones, Consulting Services. The $39.95 registration fee will
license one copy for use on any one computer at any one time. You must treat
this software just like a book. An example is that this software may be used
by any number of people and may be freely moved from one computer location
to another, so long as there is no possibility of it being used at one
location while it's being used at another. Just as a book cannot be read by
two different persons at the same time.
Lotto Stat v2.50 Page 31
Commercial users of Lotto Stat must register and pay for their copies
of Lotto Stat within 30 days of first use or their license is withdrawn.
Site-License arrangements may be made by contacting Richard J. Jones,
Consulting Services.
Anyone distributing Lotto Stat for any kind of remuneration must first
contact Richard J. Jones, Consulting Services at the address below for
authorization. This authorization will be automatically granted to
distributors recognized by the (ASP) as adhering to its guidelines for
shareware distributors, and such distributors may begin offering Lotto Stat
immediately (However Richard J. Jones, Consulting Services must still be
advised so that the distributor can be kept up-to-date with the latest
version of Lotto Stat.).
You are encouraged to pass a copy of Lotto Stat along to your friends
for evaluation. Please encourage them to register their copy if they find
that they can use it. All registered users will receive a copy of the latest
version of the Lotto Stat system.
Richard J. Jones
Richard J. Jones, Consulting Services
P.O. Box 8413
Westerville, Ohio 43081
6.2 Technical Support
Richard J. Jones is a member of the Association of Shareware
Professionals (ASP). ASP wants to make sure that the shareware principle
works for you. If you are unable to resolve a shareware-related problem with
an ASP member by contacting the member directly, ASP may be able to help. The
ASP Ombudsman can help you resolve a dispute or problem with an ASP member,
but does not provide technical support for members products. Please write to
the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442 or send a CompuServe
message via CompuServe Mail to ASP Ombudsman 70007,3536.
Lotto Stat v2.50 Page 32
7.0 INDEX Display Range 18
A distort the confidence
actual percentages 17 results 27
ACTUAL RANGE VARIANCES 19 drawing display 16
ADJUST RANGE VARIANCES 20 Drawing File 4
ADJUSTED 20 drawing history 4
Analytical 8 drawing is an independent
analyzing the history 8 event 24
arranged 5 Drawings 2
art form 8 drive 13
artistic approach 8 duplicate drawings 25
artists 8 E
ASC Lotto File 13 equal number of occurrences
average and range limits 9
25 equal probability 9
Average Control 16 Evolution 28
AVERAGE OF DRAWING NUMBERS Exit the program 27
15 expected mean 14
average of the numbers 8 F
averages outside the limits F - TEST 19
16 fewest and most values 21
B File 2
basic probabilities 8 filename 13
basic rule 7 FREQUENCY DRAWING NUMBERS
bell shaped 14 15
bias 9, 14 Frequency Table 2
bounds of the drawing 19 future development 28
brochure 6 G
C gambler 6
central tendencies 8 Game Requirements 3
central tendency 10 H
chances of winning 4 Hardware Requirements 3
change the confidence level Historical 2
22 historical group 9
COMBINATIONS 14 Historical Strategy 21
compliment the history 24 I
Complimentary 2 improve the odds 11
complimentary calculation INDIVIDUAL DRAWING NUMBERS
24 14
complimentary group 9 input data file name 13
Complimentary Strategy 23 Installation 3
Confidence Interval 2 integer arithmetic 23
Confidence Level 2, 12, interval calculated 14
14, 21 L
confidence level in effect Largest Number 12
21 Legal Rights and Issues
contrarian philosophy 9 30
Copyright 29 License 29
cost to purchase 7 limits of the average 17
Cost/Win % 6 List of Files 2
D Load Drawing Data 13
discounted cash value 7 LOAD DRAWINGS 13
Display Drawing History logical first task 13
15 lottery definition 18
Lottery Processes 4 replacing 5
lottery ticket 6 risk/reward 6
Lotto Stat 1 RULE NUMBER ONE 6, 8
low and high interval run sequences 8
values 20 Running Lotto Stat 12
lower and upper bounds 17 runs 8
M S
main menu 13 Select Numbers 25
Mean 2 Selections 3
Mean Control 2 sequences 8
mid-point 8 Shareware 30
middle ranges 19 significant difference 11
N Smallest Number 12
Normal Distribution 10, Standard Deviation 3
14 standard deviations 19
NORMAL DISTRIBUTIONS 19 Statistical 8
numbers drawn 21 statistical analysis 8
Numbers included 3 STATISTICAL PURIST 19
Numbers to be Drawn 12 statistical purists 8
O Strategies 3
objective 11 T
odds 6 tax consequences 7
Operation 12 Technical Support 31
Order lowest to highest technicians 8
5 tendency to center 8
Ordering the numbers 5 Terminology 2
outcomes 5 theoretical percentages
P 17
DO NOT PLAY! 6 U
DON'T PLAY! 8 Unbiased 3
paid out 7 unbiased group 9
past drawing data 13 unbiased situation 8
past trends 21 Unbiased Strategy 24
path 13 underlying uniform
pattern 8 distribution 9
Philosophy 4 understand the consequences
pick smart 8, 11 8
Play 6 UNIFORM DISTRIBUTION 9
player 6 uniform generation 8
playing philosophy 6 uniform probabilities 10
possible outcomes 5, 12, W
14 Warranty 29
power ball game 5 Z
prior selections 26 Z value 14
WHEN SHOULD I PLAY ??? 8 Z-Value 3, 12
Q
Quit 27
R
random and unbiased 25
range variances 20
Ranges 3
re-enter the analysis 27
re-loading the drawings
27
Registration 30
