How to use it
- Enter the spots you mark on the ticket.
- Enter the least number of catches you care about, such as the smallest that pays.
- Keep 80 and 20 for standard keno, or change them for your game.
- Read the odds for all spots, for at least that many, and for each exact number of catches.
The formula
P(exactly m catches) = C(D, m) × C(N − D, k − m) ÷ C(N, k), where N is the numbers in the game, D the numbers drawn and k your spots. The average number of catches is k × D ÷ N. The calculator counts with whole numbers, so even very long odds are exact.
Worked example
10 spots, 20 of 80 drawn:
- all 10: C(20, 10) × C(60, 0) ÷ C(80, 10) = 184,756 ÷ 1,646,492,110,120 → 1 in 8,911,711.18;
- exactly 5 of 10: 1 in 19.44, at least 5: 1 in 15.47 (6.466 %);
- average: 10 × 20 ÷ 80 = 2.5 catches.
Tips
- “1 in x” is an average over many games, not a promise: each game is independent of the last.
- For a 1-spot ticket the chance is simply 20 ÷ 80 = 25 %.
- Set a budget before playing; the expected loss grows with the number of games, whatever the ticket.