Keno Odds Calculator

How Keno Works Keno is a lottery-style casino game. The player chooses between 1 and 15 numbers from a pool of 1 to 80. The house then draws 20 numbers at random. The player wins based on how many of their chosen numbers match the drawn numbers.

The Mathematics Keno probabilities use the hypergeometric distribution: P(k matches) = C(n,k) * C(80-n, 20-k) / C(80, 20). Where n is how many numbers you picked, k is how many matched, C(a,b) is the combination function “a choose b”, and C(80,20) is the total number of ways to draw 20 from 80.

C(80, 20), the total combinations There are approximately 3.535 × 10^18, or 3.5 quintillion, ways to draw 20 numbers from 80. That is the denominator under every probability on this page.

Typical house edge Keno has the highest house edge of any game on a casino floor: 25% to 35% on a standard paytable, against 0.5% for blackjack and 1.4% for the craps pass line. For every $100 wagered the expected return is $65 to $75.

The usual defence is pace, and it does not hold up on the same stake. A keno lounge runs about 15 games an hour against 60 hands of blackjack, so a $1 keno ticket costs roughly $4 an hour where a $1 blackjack hand costs 30 cents. Fifteen times slower, but fifty-six times more expensive per wager, and the second number wins.

Where the defence does hold up is against the table minimum, which is the choice a real person is making. A $1 keno ticket costs about as much per hour as sitting at a $14 blackjack table, and keno will take a dollar where the pit will not. It is not cheap; it is affordable in small pieces, and those are different things.

The paytables in this calculator are Las Vegas $1-ticket shapes and they produce edges from 26% to 33% across the eight pick sizes. The panel prints the exact figure for whatever you select, computed from the same probabilities shown in the table above it, so the two cannot disagree.

Pick strategy, and a caveat about it Fewer picks give simpler odds and smaller top prizes. More picks are far harder to match but pay much larger multiples. The house edge is broadly similar across pick sizes, because the paytables are written to keep it that way, but “broadly” is doing real work in that sentence: on the tables here Pick 4 runs 29% and Pick 6 runs 33%, and a difference of one or two units on a single tier can move any of them by several points.

That is the practical warning. Paytables are set by the individual casino and by state regulation, they change without announcement, and two lounges on the same street will not match. Any keno page quoting a single edge figure for “keno” is quoting its own assumptions. Read the sheet on the table.