Keno odds calculator

A draw without replacement

Keno matches follow a hypergeometric model when 20 distinct numbers are drawn fairly from a pool of 80. The numbers within one draw are not independent, so multiplying a single-number chance ten times gives the wrong answer.

Exactly ten is different from any prize

Matching all ten selected numbers has probability of about one in 8.91 million under this model. Some paytables also return money for fewer matches, or for no matches. That requires reading every row of the actual paytable.

Enter a complete paytable to estimate return

Use gross-return multipliers, including any returned stake. Multiply each match probability by its corresponding multiplier and add the results. Blank values are missing data, not zero payouts; the tool must not invent them.

Keno mathematical formula and ten-number jackpot odds

With s selected numbers and k matches, the probability is C(s,k) × C(80−s,20−k) / C(80,20). The combinations count draws without replacement. For matching all ten selected numbers, the result is about one in 8.91 million.

For expected gross return, sum each match probability times its gross-return multiplier. Multiply that sum by the stake for expected returned money, then subtract the stake for expected net. Keno winnings are paytable-specific; a probability alone does not establish a prize.

Enter every paytable row, including zero returns. If the table quotes net win, add the returned stake before using a gross multiplier. The actual observed winnings for one draw can differ greatly from the expected value.