Keno: rules, pay tables and how to work out the house edge

Keno is a number draw. You choose some numbers from 1 to 80, the game draws 20, and you are paid based on how many of yours come up. It is easy to play and slow-looking, but its maths is unforgiving. The good news is that the odds are exact and you can check any pay table yourself, which this page shows step by step.

How keno works

1. Choose your stake.
2. Pick your spots. Choose how many numbers to play, often from 1 up to 10 or more, then pick them yourself or use quick pick.
3. The draw. The game draws 20 numbers from 80.
4. Count your catches. A "catch" or "hit" is one of your numbers that was drawn.
5. Check the pay table. Each spot count has its own table saying what each number of catches pays.

Online versions are random number generator games. Lottery keno draws run on a timetable. Either way, each draw is independent: there are no hot or cold numbers.

The odds: how to compute them

Keno odds come from counting combinations. If you pick n numbers, the chance of catching exactly k of them is:

P(k) = C(20, k) × C(60, n − k) ÷ C(80, n)

where C(a, b) is "a choose b", the number of ways to choose b items from a. This is the hypergeometric distribution. In words: ways to choose your k catches from the 20 drawn numbers, times ways to choose your misses from the 60 undrawn numbers, divided by all the ways to pick n numbers from 80.

Pick 4, worked exactly

For a 4-spot ticket there are C(80, 4) = 1,581,580 possible picks.

The rows add up to 1,581,580, so every possible ticket is counted.

Turning a pay table into a house edge

Now take an illustrative pay table (not any particular operator's or lottery's). The figures below are our calculation from it:

Multiply each payout by its chance and add: 1 × 336,300 + 5 × 68,400 + 100 × 4,845 = 1,162,800. Divide by 1,581,580 and you get 73.52%. That is the RTP. The house edge is 26.48%: on average, £100 of 4-spot tickets costs about £26.48.

Two more things the table shows:

• You win something only 25.89% of the time, and a 2-catch "win" just returns your stake.
• The top prize is underpaid. Catching all four happens about once in 326 games, but this table pays 100x. A fair price would be close to 326x on its own.

Pick 1, the simplest check

With one spot, the chance your number is among the 20 drawn is 20 ÷ 80 = 25%. A fair game would pay 4x (3 to 1 profit). If a game paid 3x (an illustrative figure), the RTP would be 25% × 3 = 75%, a 25% house edge.

Bigger tickets, longer odds

The same formula for a 10-spot ticket gives a chance of catching all 10 of about 1 in 8,911,711. Catching none of 10 (about 1 in 21.84) is more common than catching 6 (about 1 in 87).

Variants

• Multipliers or bonus balls that multiply a win on some draws. They are usually paid for with a higher stake or a lower base table, so check the RTP.
• Way tickets and combination tickets that split your spots into groups, each a separate bet.
• Fast online keno with instant draws, and lottery keno on a timetable.

Strategy, honestly

There is no way to pick better numbers. What you control:

• The pay table. Different games and spot counts can have very different RTPs. If the game shows an RTP for each spot count, compare them. In Great Britain, information on your chances of winning, such as the RTP or house edge, must be easily available before you commit to play (RTS 3). If it is not shown, use the formula above.
• Your pace. Online keno can draw in seconds. Fewer games per hour means less expected loss per hour.
• Your stake. Keno's edge applies to every pound you bet.

Myths and systems

• "Hot and cold numbers." Each draw is independent. A number that came up often last hour has the same 25% chance next draw.
• "Same numbers every game improves my odds." It does not. Every set of numbers has the same chance.
• "Quick pick is worse than choosing." It makes no difference.
• Betting systems. Raising stakes after losses changes your bet size, not the edge.

Playing keno online

• RNG vs draws. Casino keno uses a random number generator and may play instantly. Lottery keno runs scheduled draws.
• Auto-play. Many games outside Great Britain offer multi-draw or auto-play. In Great Britain, the Commission's standards require customers to commit to each game cycle individually (RTS 8).
• Demo play. Useful for learning the pay tables. It tells you nothing that the maths above does not.

Where to play

Keno is offered by some lotteries and some licensed casinos. See New Jersey lottery, New York lottery, UK casinos, Ontario casinos, New Jersey casinos, Pennsylvania casinos and Michigan casinos, or our lottery and casino market hubs. Related: scratch cards, online bingo and our guide to Powerball and Mega Millions odds.