My Chance 3 — Lottery and betting odds mathematics | mychance3.com
Any jackpot game's odds come from one formula — C(n, k) = n! / (k! × (n−k)!) — applied to the pool sizes printed in the game's rules.
Step one is reading the rules for pool sizes: how many balls sit in the main pool, how many are drawn, and whether a separate bonus pool exists. Powerball is 5 from 69 plus 1 from 26; Mega Millions is 5 from 70 plus 1 from 25; a classic 6/49 game is 6 from 49 with no bonus pool.
Step two applies the combinations formula to the main pool. For 6/49 that is C(49,6) = 49! / (43! × 6!) = 13,983,816. The factorials cancel before they grow unmanageable: 49! / 43! is just 49 × 48 × 47 × 46 × 45 × 44, and dividing by 6! = 720 finishes the job.
On narrow screens, swipe or scroll the plate sideways.
Step three handles the bonus pool by multiplication. Powerball's white balls give C(69,5) = 11,238,513 combinations, and each can pair with any of 26 red balls, so 11,238,513 × 26 = 292,201,338. Mega Millions gives C(70,5) × 25 = 302,575,350.
Step four converts the count into odds and a break-even payout. Odds are 1 in the combination count; a fair jackpot payout would multiply the stake by the count minus one. Comparing that figure with the posted prize structure exposes the margin instantly — the same test that catches a 500-to-1 pick-3 straight against true odds of 999-to-1.
Three errors account for most wrong answers. Using permutations instead of combinations inflates the count by k!; adding the bonus pool instead of multiplying understates it by orders of magnitude; and quoting white-ball odds as jackpot odds forgets the bonus ball entirely. Avoid all three and any game's published odds can be reproduced in minutes.
Further reading