Powerball Generator!

[john gustaf stebbins]

(09-23-2024 02:04 PM)lrdheat Wrote:  The Texas lottery has 6 non repeating integers chosen from 1 through 54. There are 25,827,165 individual combinations of those numbers available, 1 of which is 1,2,3,4,5,6. Each of the combinations of 6 numbers from 1,2,3,4,5,6 up to 49,50,51,52,53,54 has the same chance of occurrence. It is true that sub classes of interesting sets composed of consecutive numbers is small compared to the large number of sets with uninteresting, seemingly patternless random look to the numbers. Yet, each particular set of 6 has a 1 in 25,827,165 chance of being chosen, at which point it becomes quite interesting!

Where there is an effect is that the chance a number combination will be played is not uniformly distributed, so if there is any pot splitting, you are more likely to see the prize split up with certain number picks.

One common way for people to select their numbers is using dates, so playing the numbers 1 to 31 are more likely to match up with other players.

Arithmetic progressions are also commonly played. During one early high jackpot week the Washington State lottery put out a message warning against playing the numbers down the right side of the card. These numbers were played so often that if they came up as the winning draw the jackpot would be split so that each winner would only get a bit more than a thousand dollars.

I did some analysis and found that winning draws with arithmetic progressions for more than 3 of the numbers would get statistically more matches on the 2-, 3-, and 4- number prizes. I considered avoiding number selections like these to better my odds of being the sole winner of the jackpot. At the time the state lottery was only a 7 million to 1 odds, and if the pot got well above 7 million dollars, they would often sell more than 7 million tickets making it likely the pot would be split.

I also found some anomalies in the distribution of numbers if I let the lottery machines pick my numbers. I'm not sure what was going on, but I think they were trying to prevent selling tickets with matching sets, so the picks were not independent, but they were doing it in a way that tended to generate more 2 or 3 matches between the selections than you would expect from independent picks (a $10 ticket would have 20 sets of numbers, which was enough to get a statistically significant effect). I never figured out if that was a bug or a feature, since you would be more likely to have multiple small prizes on a single ticket. Though that was at the expense of each ticket being slightly less likely to win at all. For this reason I wrote a program for my calculator to pick numbers for me.