Many people say the big jackpot games Powerball and Mega Millions are due for a matrix change. The last time the operators of these games changed the matrices, the jackpot odds went up to their current state of about 1 in 300 million for each game (give or take some millions).
Idea 1:
What if the group that runs either lottery wanted to make a new matrix resulting in 1 in 400 million jackpot odds. What matrices would give those odds? I ran a script to generate some possibilities getting as close to 1 in 400 million as possible, with the restriction of choosing between 4 to 7 white balls from 40 to 99, and no more than 99 red balls.
- Draw 6 white balls from a pool of 45, plus 49 red balls
odds = 1 in 399,107,940
- Draw 6 white balls from a pool of 57, plus 11 red balls
odds = 1 in 399,170,772
- Draw 6 white balls from a pool of 67, plus 4 red balls
odds = 1 in 399,182,784
- Draw 5 white balls from a pool of 70, plus 33 red balls
odds = 1 in 399,399,462
- Draw 7 white balls from a pool of 50, plus 4 red balls
odds = 1 in 399,537,600
- Draw 6 white balls from a pool of 41, plus 89 red balls
odds = 1 in 400,178,532
- Draw 5 white balls from a pool of 59, plus 80 red balls
odds = 1 in 400,510,880
- Draw 6 white balls from a pool of 60, plus 8 red balls
odds = 1 in 400,510,880
- Draw 5 white balls from a pool of 63, plus 57 red balls
odds = 1 in 400,644,279
Idea 2:
What if a matrix change resulted in better jackpot odds, say 1 in 200 million? What matrices would do the trick? The list is much longer
- Draw 5 white balls from a pool of 50, plus 94 red balls
odds = 1 in 199,163,440
- Draw 5 white balls from a pool of 54, plus 63 red balls
odds = 1 in 199,238,130
- Draw 4 white balls from a pool of 90, plus 78 red balls
odds = 1 in 199,304,820
- Draw 4 white balls from a pool of 96, plus 60 red balls
odds = 1 in 199,317,600
- Draw 6 white balls from a pool of 42, plus 38 red balls
odds = 1 in 199,339,868
- Draw 4 white balls from a pool of 99, plus 53 red balls
odds = 1 in 199,511,928
- Draw 6 white balls from a pool of 67, plus 2 red balls
odds = 1 in 199,591,392
- Draw 6 white balls from a pool of 40, plus 52 red balls
odds = 1 in 199,595,760
- Draw 4 white balls from a pool of 86, plus 94 red balls
odds = 1 in 199614170
- Draw 5 white balls from a pool of 51, plus 85 red balls
odds = 1 in 199,670,100
- Draw 7 white balls from a pool of 50, plus 2 red balls
odds = 1 in 199,768,800
- Draw 5 white balls from a pool of 52, plus 77 red balls
odds = 1 in 200,119,920
- Draw 4 white balls from a pool of 89, plus 82 red balls
odds = 1 in 200,213,332
- Draw 5 white balls from a pool of 59, plus 40 red balls
odds = 1 in 200,255,440
- Draw 6 white balls from a pool of 60, plus 4 red balls
odds = 1 in 200,255,440
- Draw 4 white balls from a pool of 87, plus 90 red balls
odds = 1 in 200,330,550
- Draw 4 white balls from a pool of 91, plus 75 red balls
odds = 1 in 200,450,250
- Draw 4 white balls from a pool of 85, plus 99 red balls
odds = 1 in 200,453,715
- Draw 4 white balls from a pool of 88, plus 86 red balls
odds = 1 in 200,542,540
- Draw 4 white balls from a pool of 95, plus 63 red balls
odds = 1 in 200,563,335
- Draw 5 white balls from a pool of 62, plus 31 red balls
odds = 1 in 200,601,062
- Draw 5 white balls from a pool of 53, plus 70 red balls
odds = 1 in 200,877,950
- Draw 4 white balls from a pool of 97, plus 58 red balls
odds = 1 in 200,960,720
- Draw 5 white balls from a pool of 57, plus 48 red balls
odds = 1 in 200,981,088
A possible caveat of any matrix where 7 white balls are drawn is having lots of potential prize categories. If you wanted to keep nine prize tiers, the lowest tier would have to be 3 + 1. And with a 4 white ball matrix, you have too few.
Food for thought.