# FORMULA.EXE v8.0: The Definitive Probability and Gambling Software

#### saliu

##### Member
• FORMULA.EXE, version 8.0, April 2003 (3 WE).
This is the definitive and the ultimate probability, gambling and
statistical software.
The program boasts several important formulae in theory of probability
and statistics:

1) The Fundamental Formula of Gambling (FFG: N from p and DC)
2) Degree of Certainty (DC from p and N)
3) Probability of FFG median (p from DC and N)
4) The Binomial Distribution Formula (BDF: EXACTLY M successes in N
trials)
5) The Probability of AT LEAST M successes in N trials
6) The Probability of AT MOST M successes in N trials
7) The Probability to WIN AT LEAST 'K of M in P from N' at Lotto &
PowerBall
8) The Binomial Standard Deviation (BSD)
9) Normal Probability Rule (more precise than Gauss curve)
10) Calculate Lotto Odds, For '0 of k' to 'm of k'
11) Hypergeometric Distribution Applied to Lotto Odds
12) Miscellanea: Sums of numbers, permutations, arrangements, shuffle numbers.

I. The Fundamental Formula of Gambling (FFG: N from p and DC)
This function applies the Fundamental Formula of Gambling (FFG). It
calculates the number of trials N necessary for an event of
probability p to appear with the degree of certainty DC.
For example, how many coin tosses are necessary to get at least one
'heads' (p = 1/2) with a degree of certainty equal to 99%? Answer: 7
tosses.

II. The Degree of Certainty (DC from p and N)
This function calculates the degree of certainty DC necessary for the
event of probability p to occur within N trials.
For example, what is the degree of certainty to get at least one

III. The Probability of FFG Median (p from DC and N)
This function calculates the probability p when DC and N are known.
There are situations when you have the statistical median of a series
N; therefore DC=50%; but you don't know the probability of the
parameter p. The program calculates the probability p leading to a
degree of certainty DC and a number of trials N.
For example, the winning reports created by LotWon software show a
series of filters and their medians. If not calculated, you can use an
editor such as QEdit and do a column blocking, then sort the column
(filter) in descending order. The median represents the middle point
of the sorted column. The median also represents the number of trials
for a degree of certainty equal to 50%. I do not describe every filter
in my software, so nobody can tell the probability of every filter.
But you can determine it using this function of FORMULA.EXE. Other
filters are described and thus their probabilities can be calculated
in advance. They will prove the validity of the fundamental formula of
gambling (FFG). For example, the probability of '3 of 6' in a 6/49
lotto is 1 in 57. FFG calculates the median for this situation
(DC=50%) as 39. Take a real draw history, such as UK 6/49 lotto. Do
the winning report for 500 past draws. Sort in descending order the
filter "Threes" (or "3 #s") for layer 1. The median is 37 or closely
around 39. Reciprocally, when you see a median equal to 37, you can
determine the probability of the parameter as 1 in 54 (very close to
the real case of 1 in 57).

IV. The Binomial Distribution Formula (BDF)
The function calculates the probability BDF of exactly M successes in
N trials for an event of probability p.
For example, we want to determine the probability of getting exactly 5
"heads' in 10 tosses. We tossed the coin 7 times and recorded 5
"heads". We toss the coin for the 8th time and get another "heads"
(the 6th). We must stop the tossing; the experiment failed. We can no
longer get EXACTLY 5 "heads" in 10 tosses. It is obvious that the
previous events influenced the coin toss number 9.
A sequence of events means that the events do not take place at the
same time. They occur one after another.
The "Binomial Distribution Formula" shows some interesting facts. For
example, the probability to toss EXACTLY 1 "heads" in 10 tosses is
only 0.98%. It is quite difficult to get only 1 "heads" and 9 "tails"
in 10 tosses.
The probability to toss EXACTLY 5 "heads" in 10 tosses is 24.6%. It is
not that usual to get exactly 5 "heads" in 10 trials, even if the
individual chance of "heads" is 50%! We might have thought that we
would get quite often 5 "heads" and 5 "tails" in 10 coin tosses. NOT!
The chance is even slimmer to get 500 "heads" and 500 "tails" in 1000
tosses: 2.52%.
The probability to get 5 "heads" in 5 tosses represents, actually, the
probability of "5 heads in a row" (3.125%).
There is a data type limit. The number of trials N must not be larger
than 1500! There will be an overflow if you use very large numbers.
Blame the permutations and the limitations of the computers…

V. The function calculates the probability of at least M successes in
N trials for an event of probability p.
For example, we want to determine the probability of getting at least
4 heads in 10 tosses. Logically, the following situations qualify as
10 heads. Obviously, the probability is better than the 'exactly 4 of
10' case.
There is a data type limit. The number of trials N must not be larger
than 1500! There will be an overflow if you use very large numbers.
Blame the permutations and the limitations of the computers…

VI. The function calculates the probability of at most M successes in
N trials for an event of probability p.
For example, we want to determine the probability of getting at most 4
heads in 10 tosses (no more than 4 in 10). In 'at least M in N' we
look at the glass as being half full. Why not look at it from the
pessimistic perspective: the glass can be empty sometimes (or present
degrees of emptiness)! Logically, the following situations qualify as
probability can be higher than the 'exactly 4 of 10' or 'at least 4 of
10' cases, but it won't be better from a player's perspective!
There is a data type limit. The number of trials N must not be larger
than 1500! There will be an overflow if you use very large numbers.
Blame the permutations and the limitations of the computers…

VII. The Probability to WIN AT LEAST 'K of M in P from N' at Lotto &
PowerBall
The official lotto odds are calculated as 'exactly K of M in P from
N'. For example, in a lotto 6/49 game, the player must play exactly 6
numbers per ticket. The lottery commission draws 6 winning numbers
from a field of 49. If the player plays only 6 numbers, the odds of
getting exactly 3 of 6 are 1 in 56.66. The player can play
combinations of 6 from a pool of 10 picks, for example. Now, the odds
can be calculated as exactly '3 of 6 in 10 from 49': 1 in 12.75.
In real life the player gets a better deal, however. The commission
does not oblige the players to 'exactly' situations. The real life
situation is 'at least K of M from N'. The commissions don't care if
you play just 6 numbers, or play a pool of picks. They don't care if
you expected 3 of 6 hits, but hit 4 of 6. They'll pay you for the
highest prize per ticket. It is clear that 'at least K of M from N' is
better than 'exactly K of M from N' from the player's perspective. If
the player plays 57 6-number random picks, the player should expect
one '3 of 6' hit. If playing 100 times 57 tickets, the expectation
should be 100 '3 of 6' hits. Sometimes, however, higher prizes can be
hit. That's why the odds of getting 'at least 3 of 6 from 49' are ' 1
in 53.66'.
Cool down, Wheely! The previous calculations do not imply that 54
lines (combinations) will guarantee 100% in one draw a '3 of 6'
49-number wheel! Calculating the minimum number of successes for a
100% guarantee is a totally different matter. It is a book in itself
if one considers also the algorithm to generate the successes! Buy me
the best wine there is and we can talk about it. Otherwise wait for
the patents…

I wrote in the message "The Fundamental Formula of Wheeling":
"…the probability of winning [exactly] '3 of 6' is 1 in 57. FFG
calculates the median for p=1/57 as 39.16, rounded up to 40 for
DC=50%. How close is that figure (40) to reality in the UK 6/49
history file? The file I've been using for this analysis has 737 draws
(contains a few so-called 'extra' draws). The file has 733 regular
draws from the beginning of the game to the draw of January 1, 2003.
The median for the '3 of 6' case is around 38."
The calculations are correct, as far as the standard deviation is
concerned. The median, however is precisely in accordance with the
probability of at least '3 of 6': 1 in 54. It's right on the money!
discrepancy in all the data files I analyzed. The filter medians are
always a few points lower than the FFG medians. Now it fully makes
sense. The medians are the result of at least K of M in N probability,
NOT the exactly K of M in N probability!
We may consider from now on the Fundamental Formula of Gambling to be
the most precise instrument in games theory. There are a few posts at
this web site dealing with Markov chains: "Suspicion is mother of the
intellect; Markov chains".
Searching on Markov chains at Google yields close to 100,000 hits! The
topic is hot! I stated, however, that FFG outruns Markov by several
steps. Again, once and for all, the Fundamental Formula of Gambling is
be the most precise instrument in games theory. Unlike Markov chains,
FFG considers previous events to be of the essence for future events.
The events repeat precisely, according to the Fundamental Formula of
Gambling.

- continues ->

Ion Saliu

#### saliu

##### Member
- conclusion -

VIII. The Binomial Standard Deviation (BSD)
This function calculates the binomial standard deviation for binomial
events (i.e., experiments characterized by two and only two outcomes:
win or loss; success or failure). This is the theoretical or expected
value of the standard deviation. The standard deviation can also be
calculated post facto: after the experiment. Its name is
self-explanatory. You can see in the WS-3 reports generated by LotWon
a standard deviation for every filter. A filter goes up and down from
an average value. The standard deviation calculates the positive
average of all deviations (fluctuations) from an average norm.

The binomial standard deviation has great merit. It shows what
fluctuation to expect. Before starting the coin toss, one can have an
accurate idea of how many "heads" will come out in a number of trials
(tosses). Or how many winning hands one can expect playing 200
blackjack rounds.

IX. Normal Probability Rule (more precise than Gauss curve)
When we calculated the binomial standard deviation the result is a
report like this one (for 100 coin tosses):

The standard deviation for an event of probability p = .5 in 100
binomial experiments is: BSD = 5The expected
(theoretical) number of successes is: 50 Based on the Normal
Probability Rule:· 68.2% of the successes will fall within 1 Standard
Deviationfrom 50 - i.e., between 45 - 55 ·· 95.4% of the successes
will fall within 2 Standard Deviationsfrom 50 - i.e., between 40 -
60 ··· 99.7% of the successes will fall within 3 Standard
Deviationsfrom 50 - i.e., between 35 - 65
I have been working thoroughly with pairing strategies, especially in
the digit lotteries. I have encountered far better situations than
take a different approach to calculating the normal probability rule.
The traditional rule is based on Gauss or normal distribution curve.
The keyword here is curve, implying continuous. The lottery or
gambling are discrete, however. The one size fits all approach leads
to discrepancies. In the example above, the new normal probability
rule I am using gives:
72.87% of the successes will fall within 1 Standard Deviation
from 0 - i.e., between 45 - 55
One caveat, as in the binomial distribution probability case, there is
a data limit: 1500 trials. It covers a pretty good range of lottery
and gambling cases.

X. Calculate Lotto Odds, For '0 of k' to 'm of k'
For example, the odds of a lotto-49 game drawing 6 numbers: '0 of 6';
'1 of 6'; '2 of 6'; '3 of 6'; '4 of 6'; '5 of 6'; '6 of 6'. The odds
are '1 in 2.3', '1 in 2.4', '1 in 7.6', '1 in 56.7','1 in 1032.4', '1
in 54,200.8', '1 in 13,983,816', respectively.
The probability is calculated as exactly 'M of N' (not at least 'M of
N'). Sometimes such probability is 0: the event is impossible; for
example '0 of 6' or '1 of 6' for the 6/10 case.
This function handles any type of lotto game, including Keno and Power
Ball. This function incorporates the entire program ODDSCALC.EXE. The
program is still available as standalone.

XI. Hypergeometric Distribution Applied to Lotto Odds
This function calculates all the Odds of any lotto game, including
Keno and PowerBall, using the hypergeometric distribution probability.
For example: In a lotto-49 game drawing 6 winning numbers, what are
the odds of getting exactly '1 of 6' when the player plays 6 numbers,
AND the lottery draws 6 numbers from 49. In the case above: the
probability of (1,6,6,49); or (4,6,6,49); or (10,10,20,80 - Keno) . .
.
This calculator helps to figure out the odds when playing combinations
of various lengths and for various prizes.
This function incorporates the entire program ODDS.EXE. The program is
still available as standalone.

XII. Miscellanea: Sums of numbers, permutations, arrangements, shuffle
numbers
This is a collection of useful functions:
- sum-up all the numbers between N1 and N2;
- sum-up all the numbers in a data file;
- calculate N factorial (same as permutations of N);
- calculate arrangements of N taken M at a time;
- shuffle contiguous or non-contiguous numeros.

A. Sum-up all the numbers between N1 and N2
For example: the sum of all numbers from 1 to 100 is 5050; from 33 to
100 is 4522. The function calculates instantly the sums of all the
numbers from 1 to billions, or from billions to trillions, etc. It is
much faster and more convenient than using that hand-held calculator.

B. Sum-up all the numbers in a data file
This function calculates the sum of all the numbers previously saved
in a data file in text format; e.g.
17 34 2 100, 99, 1000000, 71392.
The file can have one number per line, or multiple numbers per line
separated by blank space(s), or combination of both. Do NOT leave any
blank lines in the file! The function calculates also the average. The
Pennsylvania Cash-5 data file has 2604 drawings. The average is
20.0095. Well, the game draws from 1 to 39 numbers. The theoretical
average is (1+39)/2 = 20. The numbers have varying frequencies, but
the average comes very close to the theoretical value!

C. Calculate N factorial (same as permutations of N)
This function calculates permutations of N or N factorial.
N! = 1 x 2 x 3 x ... x N
For example: permutations of 6 = 720 (1x2x3x4x5x6 = 720).
N must not be larger than 1500—overflow danger!

D. Calculate arrangements of N taken M at a time
This function calculates arrangements of N taken M at a time:
A(N,M) = N x (N-1) x ... x (N - M + 1)
For example: A(10,3) = 10 x 9 x 8 = 720.
Use this function to calculate total trifecta or superfecta
combinations in a horse race; e.g. 1,2,3; 4,2,7; 10,6,5, etc.

E. Shuffle Pools of Contiguous or Non-contiguous Numbers
SHUFFLE.EXE can shuffle (randomly arrange) a group of contiguous
numbers from 1 to N. If the user types 10 at the input prompt, the
program will start a continuous process of randomizing 10 unique
numbers, from 1 to 10. The sequences look like: 3, 7, 1, 9, 10, 4, 6,
5, 2, 8. The sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is so rare that it
is said only Almighty Number can generate it.
There is another situation: groups of non-contiguous numbers, such as:
1, 44, 33, 55 77 22 66 99 13 111 49 29 25 9 54. Function XII of
FORMULA.EXE can handle this type of randomizing situations as well.
The groups of non-contiguous numbers can be typed at screen prompts.
Or, the numbers can be saved to a text file first. The text file can
be used as an input device to FORMULA.EXE. The numbers must be
separated by space(s), or commas, or combination of both. Also, the
numbers can be placed on several lines, or in one column. The user
chooses how many times to run the randomization process. The initial
group of non-contiguous numbers can be arranged in any order,
including sequential.

"As we walk in steps and speak in words, so the Cosmos moves in laws
and thinks in formulae."
(Axiomandros of Agrimmas, "On Ionian Pillars")

"For only Almighty Number is exactly the same, and at least the same,
and at most the same, and randomly the same. May Its Almighty grant us
in our testy day the righteous proportion of being at most unlikely
the same and at least likely different. For our strength is in our
inequities."

http://www.saliu.com/infodown.html

#### saliu

##### Member
Sorry! The FTP upload didn't work well yesterday.
The program is now where it should be.

http://www.saliu.com/infodown.html

FORMULA.EXE, version 8.0, April 21, 2003 (3 WE).

Best of luck to all!

Ion Saliu

#### Dennis Bassboss

##### Member
How much does it cost???

#### Dennis Bassboss

##### Member
I might be wrong ...but I have never seen any numbers from you and your stuff! Save some ink post some numbers!

#### thornc

##### Member
Hello Ion!

Glad to see you back to action, did you managed to solve your problems?!

...

How much does it cost???
This is one here is free!

...

I might be wrong ...but I have never seen any numbers from you and your stuff! Save some ink post some numbers!
You're not tottally right! You never saw posts from Ion Saliu with playing numbers but a few of the other members have posted numbers/combinations obtained from with his software, including me!

...
Dennis you really need to slow down a bit and enjoy live more and stop worring about what others are doing!!

#### Dennis Bassboss

##### Member
I am enjoying life ...but I find it very strange to see somebody giving expert advices on this or that and to see that same person having nothing to show about it...
I just wanted to point out that everybody can write on statistics and stuff like that...in order to do so you just need a basic course in statistics and probabilities...That copyrighted package is pretty much basic stuff...
But at one point you need to put everything to the test...
But Ion learning process is not there yet I guess...In time he will learn more...

#### Dennis Bassboss

##### Member
And what is your name Ion thornc? This was for Ion Saliu not for you...so you're the one that should start enjoying life...

#### Beaker

##### Member
saliu said:
Sorry! The FTP upload didn't work well yesterday.
The program is now where it should be.

http://www.saliu.com/infodown.html

FORMULA.EXE, version 8.0, April 21, 2003 (3 WE).

Best of luck to all!

Ion Saliu
Thanks for that link but unfortunately I won't download anything from that site. Last time I did, I was erroneously accused of trying to hack it

#### thornc

##### Member
Dennis Bassboss said:
And what is your name Ion thornc? This was for Ion Saliu not for you...so you're the one that should start enjoying life...

My real name is Cristiano Lopes, which may be difficult for a native english speaker or even a french one to pronouce correctly
; So I use thornc which has been with me since my old IRC days...

That last part of my post was not regarding this thread in particular but all of the threads were I see your posts, you tend to be hostile towards people; hence my advice to lighten up a bit!
Forgive me if my choice of words aren't very polite then again some yours are not as well, the only thing else that comes to mind is Don't worry, be happy!

#### Dennis Bassboss

##### Member
thornc said:
My real name is Cristiano Lopes, which may be difficult for a native english speaker or even a french one to pronouce correctly
; So I use thornc which has been with me since my old IRC days...

That last part of my post was not regarding this thread in particular but all of the threads were I see your posts, you tend to be hostile towards people; hence my advice to lighten up a bit!
Forgive me if my choice of words aren't very polite then again some yours are not as well, the only thing else that comes to mind is Don't worry, be happy!
If asking your friend to post some numbers is consider hostile now ....I give up.....It only confirms my thinking about the whole issue....Nothing that I have said is hostile ...but what you are posting now is.....You just pick the wrong custommer....Believe me!

#### thornc

##### Member
Dennis Bassboss said:
If asking your friend to post some numbers is consider hostile now ....I give up.....
No it's not, that's not what I call hostile!

It only confirms my thinking about the whole issue....Nothing that I have said is hostile ...
Well in my book, everytime you direct some newcomer directly to Gilles is hostile, specially if you keep on doing it!!

but what you are posting now is.....You just pick the wrong custommer....Believe me!
And sorry if you think so, I didn't meant to offend you that much.
Pardonnez-moi!
And if you think this is picking on you, "desculpa outra vez" (go look it up, it's portugueese) because it was not may intention I was just trying to make you see my point of view which my differ from yours being I Latin-European and you Native-Canadian!

#### Dennis Bassboss

##### Member
I'm Atikamek ...and you just officially made my ignore list!Congarulations!

#### thornc

##### Member
Dennis Bassboss said:
I'm Atikamek ...and you just officially made my ignore list!Congarulations!

First sorry but I forgot about the actual name Atikamek!

I know you won't be reading this but in my native language what you're doing is called "amuar"!

Since I'not bowing to you and giving in to your point of view you're now chosing to ignore me! We really have different cultures!

#### saliu

##### Member
Cristiano:
You expressed your own opinion, totally in good faith. I didn’t ask you for any favor. We exchanged two emails today, after about a month, I think. Congratulations for your professional promotion! It is an achievement to be proud of!

I see you attracted some negative reactions simply by responding to my post. Here is my rule of thumb. I always look at the source of a reaction: The person. Most persons are positive, no doubt about it. Positive persons argue in a positive manner. They don’t attack; they offer logical and factual arguments against ideas.
On the other hands, there are negative persons, a minority. They don’t argue; they attack! My rule of thumb originates in mathematics and logic:

Double negative is positive; double negation is affirmation.

Thus, I always take a negative reaction from a negative person as a solid compliment. The more intense the negative reaction, or the more intense the negative person, the stronger my argument is! Of course, we need to defend ourselves sometimes when threatened by negative persons. I am just going through such a process now, in my physical life. I have taken the compliment as a real compliment; but I had to take some self-defensive measures as well.

The negative persons react because they cannot achieve the positive. Instead of channeling their energy to positive goals, the ‘negatives’ try to destroy the ‘positives’ of others. There was a curious case in my cyber life. A guy attacked me first for my fundamental formula of gambling. Then he begged me not once but twice to remove FFG from my site! In reality, he wanted to claim FFG as his own work! You know, when I launched LotWon in the late 1980’s, I was attacked for using such terms as strategy, filters, triggers! Look now! Just about everybody in the lottery field uses such terms as a matter of fact! (Albeit most confuse filtering with grouping numbers!) I bet you that Garbantz and his gang will start talking soon about the ‘average’ in lotto data files and “strategies” based on that average. Just you wait! Let’s give them a head start…

My data file in Pennsylvania lottery pick-3 game has 3899 drawings. The average is 4.4817. The game draws 3 digits from 0 to 9. The theoretical average is (0+9)/2 = 4.5. My data file in Pennsylvania lottery pick-4 game has 6056 drawings. The average is 4.4964. The game draws 4 digits from 0 to 9. The theoretical average is (0+9)/2 = 4.5. My Pennsylvania lotto-6 data file has 475 drawings. The average is 34.2589. The game draws from 1 to 69 numbers. The theoretical average is (1+69)/2 = 35.
How about the more complicated game, powerball? There was a PowerBall game with 5 regular numbers from 1 to 49 plus one power ball from 1 to 42. The theoretical average is the weighted average: {(((1+49)/2)*5) + ((1+42)/2)} / 6 = 24.4167. My PowerBall 49/5/42 data file has 514 draws. The average is 24.356. The current PowerBall game has 5 regular numbers from 1 to 53 plus one power ball from 1 to 42. The theoretical average is the weighted average: {(((1+53)/2)*5) + ((1+42)/2)} / 6 = 26.0833. My PowerBall 53/5/42 data file has 54 draws. The average is 25.605. The actual average is close to the theoretical value even for a small amount of draws!

Best of luck, positives! Worst of misfortune, negatives (that’s a double -)!

Ion Saliu

http://www.saliu.com/formula.html

#### Dennis Bassboss

##### Member
Just post some numbers like this....
quote:
--------------------------------------------------------------------------------
Originally posted by Dennis Bassboss
Here I go Atlantic Keno...
05-49-04 at least one from these three maybe two
68-45-36-26-03 another 2 for sure but maybe 3 of them
69-66-65-59-52-48-42-41-40-30-20-13-12 at least 6 but it could be 8 of them
19 should come up...We shall see later!
--------------------------------------------------------------------------------

Well 12 out of 21 tonite +19 as DN right on target for a total of 12 out of 22 !here...I finally blast the only one that I never blasted in the past! I think that I have found out how to play it now..I Hope that Sheba sees this...

Last edited by Dennis Bassboss on 04-22-2003 at 05:29 PM
charles2 said:
Dennis Bassboss said:
Here are some good good goodies...
01-04-08-11-16-24-27-29-33-34-37-43-46

Hints...Hints...16-27

Holy Cow batman How'd you do that !

Dennis Bassboss said:

Now I know that there are lots of funny people here at times....But watch this...
National U:K:draw results for February 05...
01-13-17-26-42-46 Bonus 30

I'd say that it is funny!!!
My little 8 numbers set struck for 04 in there....But even better.... one of my hints came up...
So we can see the positive...

#### saliu

##### Member
By the by: The correct version of FORMULA.EXE is 8.1; the date is embedded in the program as well: April 22, 2003. The previous versions didn’t handle huge data files, with thousands of combinations; e.g. output files generated by MDIEditor and Lotto. The current version handles humongous data files with ease. The sum-up function is also much faster.

http://www.saliu.com/infodown.html

Everybody is free to download my freeware by clicking on the corresponding listing. Trying to access the FTP folder via a different form of navigation is not allowed. The web servers nowadays treat such attempts as hacking.

Ion Saliu

Ion Saliu

#### Beaker

##### Member
saliu said:
<snip>
Everybody is free to download my freeware by clicking on the corresponding listing. [rying to access the FTP folder via a different form of navigation is not allowed. The web servers nowadays treat such attempts as hacking.

Ion Saliu
Thanks for that heads up on FTP access Ion. I have downloaded some of your free software before from navigation at your site. I would not want to be accused of attempting any form of hacking - just following your directions