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ODDSCALC Calculate the odds of lotto games

Web site by Ion Saliu, founder of lottery software science, gambling mathematics.

Posted by Ion Saliu on January 28, 2001; updated 2008.

I wrote a comprehensive program to calculate the odds in the widest variety of lotto games, including Powerball, Mega Millions, Euromillions, Keno. There is no need to use a calculator, or, worse, pencil-and-paper. Of course, nobody can cover every possible game and the odds of every possible prize. But the program should be able to respond to most cases. For example, if a lotto-6 game draws a bonus number, you first run the program for '6 of BiggestNumber', then run it for '7 of BiggestNumber'.

There are some interesting results for some games. For example, in the Keno game 80/20, it is much easier to predict '10 of 20' than '0 of 20'. Look at the following report or keep it handy in a casino Keno lounge:

 The odds calculated as EXACTLY in a lotto game '80/10/20':

0 of 10 in 20 from 80 = 1 in 21.84 
1 of 10 in 20 from 80 = 1 in 5.57 
2 of 10 in 20 from 80 = 1 in 3.39 
3 of 10 in 20 from 80 = 1 in 3.74 
4 of 10 in 20 from 80 = 1 in 6.79 
5 of 10 in 20 from 80 = 1 in 19.44 
6 of 10 in 20 from 80 = 1 in 87.11 
7 of 10 in 20 from 80 = 1 in 620.68 
8 of 10 in 20 from 80 = 1 in 7384.47 
9 of 10 in 20 from 80 = 1 in 163381.37 
10 of 10 in 20 from 80 = 1 in 8911711.18 

 The odds calculated as AT LEAST in a lotto game '80/10/20':

0 of 10 in 20 from 80 = 1 in 1 
1 of 10 in 20 from 80 = 1 in 1.05 
2 of 10 in 20 from 80 = 1 in 1.29 
3 of 10 in 20 from 80 = 1 in 2.09 
4 of 10 in 20 from 80 = 1 in 4.72 
5 of 10 in 20 from 80 = 1 in 15.47 
6 of 10 in 20 from 80 = 1 in 75.57 
7 of 10 in 20 from 80 = 1 in 570.52 
8 of 10 in 20 from 80 = 1 in 7059.54 
9 of 10 in 20 from 80 = 1 in 160439.97 
10 of 10 in 20 from 80 = 1 in 8911711.18 

 The odds calculated as EXACTLY in a Powerball game 
 '55/5/5 AND 42/1/1':

0 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 1.68 
0 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 68.96 
1 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 3.09 
1 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 126.88 
2 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 18.18 
2 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 745.45 
3 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 290.91 
3 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 11927.18 
4 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 14254.44 
4 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 584431.85 
5 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 3563608.83 
5 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 146107962 

 The odds calculated as AT LEAST in a Powerball game 
 '55/5/5 AND 42/1/1':

0 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 1 
0 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 42 
1 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 2.56 
1 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 107.43 
2 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 16.68 
2 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 700.75 
3 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 278.28 
3 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 11687.7 
4 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 13859.61 
4 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 582103.43 
5 of 5 in 5 from 55  AND  0 of 1 in 1 from 42 = 1 in 3478761 
5 of 5 in 5 from 55  AND  1 of 1 in 1 from 42 = 1 in 146107962 

The page "Calculate Odds, Probability: Formulae, Software, Lottery, Lotto, Powerball, Mega Millions, Euromillions, Keno" gives more details on calculating the lotto odds for various prizes. The formula of hypergeometric probability distribution is the most comprehensive calculator of odds and probabilities in lottery and lotto, including Powerball, Mega Millions, Euromillions, Keno. This represents the most meaningful mathematics of calculating the odds in lottery and lotto games of any type.

How to acquire and run software and systems for lottery, lotto, gambling, science, mathematics, probability.

Go to the download page and look for OddsCalc: (version 6.0 Rocktober 2007)

Ion Saliu

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Formula of hypergeometric distribution probability is the most comprehensive calculator of odds and probabilities in lottery and lotto.


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Calculate the odds (probability) as exactly in lotto, lottery, Keno, Powerball, Mega Millions, Euromillions.