# Deepening the lotto odds analysis; new free software for any lottery game

Calculate the probabilities (or favorable odds) for various combination lengths and for various prizes. For example, in a Keno game: Probability for the player to win EXACTLY '0 of 10' in 20 Keno numbers drawn from a field of 80?

Written by Ion Saliu on November 23, 2001.

• For starters, I have written new odds calculating software: OddsCalc. It is available as free software from the downloads site.
The program calculates the lotto odds based on the probability of the hypergeometric distribution. It calculates the probabilities (or favorable odds) for various combination lengths and for various prizes. For example, in a Keno game, they draw 20 winning numbers from a field of 80. The player can play a 10-number combination. What is the probability for the player to win EXACTLY '0 of 10' in 20 numbers drawn from a field of 80? The answer: 0.0457907 or '1 in 21.8'.

While working on the new version of “MDIEditor and Lotto”, I considered including a total Keno module. Total as in the lotto-6 format, for example. Comprehensive statistical analysis of a large number of filters followed up by employing the same filters in combination generators. I always devise the filters based on the probabilities of the respective patterns that create the respective filters! (Very clear, right?). I wrote previously how the “Two” filter eliminates a number of combinations directly proportionate with the probability of getting ' 2 of 6', for example.
In the Keno case, the number of possibilities is staggering. I needed software to automatically calculate the various pattern probabilities. I needed the same calculator for the PowerBall cases, also different from the standard lotto games (e.g. 6/49). The bottom line is I excluded the Keno cases from “MDIEditor and Lotto WE”. Keno requires a specific “MDIEditor and Lotto”, without any other types of games. The application includes, however, the PowerBall '5+1” and '6+1' for the first time in history!

OddsCalc is more than an upgrade to ODDS, 16-bit software. It offers a deeper analysis of various combination lengths, winning numbers drawn by the commissions, and a larger variety of prizes. The program is very easy to use, since I work very hard at the logical conception. The software must present the user with the most logical steps.

There are two options:
1) Standard lotto games and Keno
2) PowerBall games.

In the first option, the user wants to calculate the odds for situations such as: “exactly 4 winners in a 6-number combination, when they draw 6 winning numbers from a field of 49 numbers”. Or a Keno case: “exactly 10 winners in a 10-number combination, when they draw 20 winning numbers from a field of 80 numbers”.
The program displays the following answer:
· The probability of EXACTLY
'10 in 10' in 20 from 80 is:
.00000011
or
1 in 8,911,711.18

The PowerBall option calculates the odds INCLUDING the PowerBall. For example: the odds of getting “exactly 5 regular winners in a 5-number combination when they draw 5 regular numbers from a field of 49 AND a separate 6th PowerBall from a field of 42”. The program displays the following answer:
· The probability of EXACTLY
'5 in 5' in 5 from 49 AND a PowerBall 42 is:
.00000001
or
1 in 80089128

That situation is a clearer one. Other PowerBall situations are trickier. For example: the odds of getting “exactly 0 regular winners in a 5-number combination when they draw 5 regular numbers from a field of 49 AND a separate 6th PowerBall from a field of 42”. The first thing that crosses one's mind is: “The probability is 1 in 42, since there are 42 PowerBalls, right?” The trick is they say EXACTLY 0 (none) winners from the set of regular numbers. If they said AT LEAST the PowerBall, then the calculations would have been correct! · The probability of EXACTLY
'0 in 5' in 5 from 49 AND a PowerBall 42 is:
.01355999
or
1 in 73.75

Verification. One calculates first '0 of 5' as in a regular lotto-5 game:
· The probability of EXACTLY
'0 in 5' in 5 from 49 is:
.5695197
or
1 in 1.76
1.76 x 42 = 73.92 (the rounding induced a small difference). The more exact calculation is: 0.5695197 / 42 = 0.01355999 or '1 in 73.75'.

The way they present the odds of winning prizes is as tricky as the questions in TV game shows. Exactly, or at least, or at most, or more or less, or the least of the greater . . .

For only Almighty Number is exactly the same, and at least the same, and at most 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 differences.

Ion Saliu