Keno Odds Calculator: Hit Odds and Paytable Return

This keno odds calculator gives the exact chance of every number of hits on any keno board, from the 40-tile boards in mobile games to the classic 80-ball draw. Enter a paytable and it also tells you the part most keno games leave out: how much of every stake the game pays back, and how often a "win" actually returns more than you bet.

How the keno odds are calculated

Keno is a draw without replacement, so the odds follow the hypergeometric distribution. With a board of N numbers, D of them drawn and S spots marked, the chance of exactly H hits is:

C(S, H) × C(N − S, D − H) ÷ C(N, D)

Read it as: the ways to hit H of your spots, times the ways the rest of the draw can miss all your other spots, divided by every possible draw. The calculator evaluates it exactly for each row, so the numbers do not wobble the way a simulation would.

Two quick checks you can run. On an 80-ball board with 20 drawn, hitting all ten of ten spots is about 1 in 8,911,711. On Gift Club's 40-tile board with 10 drawn, hitting all five of five is about 1 in 2,611. Both boards draw a quarter of their numbers, so any single number is drawn 25% of the time on either.

Using it as a keno payout calculator

Switch to the lottery or custom board and type what the game pays for each number of hits, as a multiple of your stake. The calculator multiplies each payout by its probability and adds them up. That total is the return to player, and whatever is missing from 100% is the house edge.

Three numbers are worth reading together:

• Return (RTP). What the paytable pays back on average. Keno is known for returns well below most casino games, so check it before you choose a spot count.
• Pays something. How often the screen shows a win.
• Pays more than the stake. How often you are actually ahead on the round. When a paytable pays less than 1× for its most common hit, these two numbers split apart.

Gift Club's five-spot table is a good example. It pays something on 78.34% of rounds but returns more than the stake on only 36.69%, because one hit pays 0.84×. The overall return is 95%, the same for every spot count.

What the calculator cannot tell you

No calculator can pick better numbers. Every number on the board has the same chance in every draw, and past draws do not change the next one. What the odds do tell you is the shape of a spot count: fewer spots win less often per round but end a session ahead more often. The keno strategy guide works that out session by session, and how to play keno covers the rules.

If you want to see the Gift Club tables in context, with the bet tiers and the largest payout, they are on the Keno game guide.

Frequently asked questions