Lottery Math

Powerball's jackpot odds are 1 in 292,201,338 — match 5 numbers from 69, then the Powerball from a separate drum of 26; C(69,5) × 26 gives that exact figure. At one ticket a week, the geometric distribution says you'd wait roughly 5.6 million years on average for a single jackpot win. Buying more tickets barely moves the needle: 10 tickets a week just cuts the wait to 560,000 years, because the odds scale linearly while the expected value per ticket stays negative — the prize pool never fully returns what was collected in ticket sales. The lottery isn't a bad investment; it's not an investment at all.

At its heart, this tool just counts. Every valid ticket is one combination, and all of them are equally likely, so the odds of any single ticket are exactly 1 divided by that count. Because order doesn't matter, you count combinations, not permutations — and that count grows explosively: adding just a few balls to the pool can multiply the total number of tickets many times over. It's that growth, not any single "unlucky" draw, that makes winning so rare.

In 1992 a syndicate led by mathematician Stefan Mandel targeted the Virginia Lottery, which had only C(44,6) = 7,059,052 possible tickets at $1 each, while the jackpot had rolled over to about $27 million. When the prize pool exceeds the cost of buying every combination, expected value flips positive — so they set out to purchase them all. They managed to print roughly 5 million tickets in time, and won. Using similar brute-force combinatorics, Mandel won lotteries 14 times.