How we compute the odds

Every number on this site is computed by a program from the game's published format, never typed by hand, and checked by two independent methods before a page can be built.

The formula

For a draw of k numbers from n, the chance that exactly i of your k numbers are drawn is C(k, i) × C(n − k, k − i) ÷ C(n, k), where C is the number of combinations. A separate pool, such as Powerball's red ball or EuroMillions' Lucky Stars, multiplies by its own chance. A bonus ball drawn from the main pool can only match one of the numbers you missed, so its chance is the number of your misses divided by the balls left.

Counting every draw

On smaller versions of each kind of game, small enough to list every possible draw, the program counts outcomes directly and compares them with the formula. They must agree exactly.

Cross-check by simulation

For every real game, the program simulates two million draws against one ticket and compares how often each prize came up with the formula. Every prize common enough to measure this way must agree within five standard errors. If either check fails, the site does not build.

Formats and sources

Each game's format is copied from its operator's own page, which each game page links to, with the date the format began. Formats change; when an operator announces a change we update the format and recompute every figure.

What we do not publish

Ticket prices, prize amounts and jackpot sizes change from draw to draw, so we do not print them as facts. Where a calculation needs them, the calculator asks you.