Keno Odds Calculator (Chance of Catching Your Numbers)
Calculate keno odds for any number of spots: the probability of catching exactly or at least a given number of your picks when 20 of 80 numbers are drawn, with a full catch table.
How it works
Hypergeometric: P(catch c of s spots) = C(20, c) × C(60, s − c) ÷ C(80, s) · 20 numbers are drawn from 80, so 60 of the 80 are not drawn · average catch = s × 20 ÷ 80 = s ÷ 4
In keno you choose between 1 and 20 numbers ("spots") from 1 to 80, and the game draws 20 numbers. How many of your spots are among the 20 drawn follows the hypergeometric distribution: the ways to pick your matches from the 20 drawn numbers, times the ways to pick the misses from the 60 undrawn ones, divided by all possible sets of spots. Pay tables vary by casino and lottery, but they always pay less than these odds imply; the house edge in keno is typically 25% to 40%.
Worked example
Pick 10 spots and catch exactly 5: C(20,5) × C(60,5) ÷ C(80,10) = 15,504 × 5,461,512 ÷ 1,646,492,110,120 = 5.14%, about 1 in 19.44. Catching 5 or more happens 6.47% of the time, catching all 10 only 1 in 8,911,711, and on average you catch 2.50 numbers.
Sources: Wizard of Odds — Keno · Wolfram MathWorld — Hypergeometric Distribution
Frequently asked questions
What are the odds of catching all 10 numbers in keno?
About 1 in 8,911,711 (0.000011%). Catching 5 of 10 is far more likely: 5.14%, about 1 in 19.44.
How many keno spots should I play?
No number of spots improves the expected return, which depends on the pay table. Fewer spots win more often; more spots offer bigger but much rarer top prizes. Compare pay tables using the probabilities from this calculator.
What is the most likely number of catches?
About a quarter of your spots, because 20 of 80 numbers are drawn. With 8 spots, 2 catches is the most likely result (about 30%).
Are keno odds the same everywhere?
Yes, as long as 20 numbers are drawn from 80, which is standard in casinos and most lotteries. What differs is the pay table — and therefore how much you lose on average.
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Probabilities describe the long run, not the next bet. Every casino and lottery game has a negative expected value for the player; gamble only with money you can afford to lose, and seek help if gambling stops being fun.