Keno Odds: House Edge and Cost Per Hour

Keno is a lottery-style game in which a player selects between 1 and 20 numbers from a pool of 80, and the operator draws 20 numbers at random. Payouts are made according to how many of the player’s chosen numbers match the drawn numbers. The house edge is not a fixed property of the game; it is determined entirely by the pay table and the number of spots played. Across common pay tables, the edge ranges from roughly 20% to 35%, making keno one of the most expensive games in a casino. This page shows how that range is calculated from the number of outcomes and the payout table, and converts the edge into money per hour at a stated stake and round rate.

The number of outcomes

The first step in deriving the house edge is to count the total number of possible outcomes. In keno, 20 numbers are drawn from 80 without replacement. The number of possible draw combinations is the binomial coefficient C(80,20). This equals 3,535,316,142,212,174,320. For a player who has selected s spots, the number of ways to match exactly k of those spots is C(s,k) * C(80-s,20-k). The probability of matching k spots is that product divided by C(80,20).

These probabilities are the foundation of every keno pay table. They do not change with the operator, the machine, or the time of day. They are fixed by the rules of the draw.

A worked example: the 8-spot pay table

Consider a common 8-spot keno pay table. The player picks 8 numbers. The payouts for matching k spots are typically:

To find the expected return, calculate the probability of each outcome and multiply by the payout. The probabilities for an 8-spot game are:

These probabilities sum to 1. The expected return is the sum of (probability * payout) for each outcome. Using the payouts above:

• 0 matches: 0.0883 * 0 = 0
• 1 match: 0.2475 * 0 = 0
• 2 matches: 0.3090 * 0 = 0
• 3 matches: 0.2200 * 0 = 0
• 4 matches: 0.1000 * 1 = 0.1000
• 5 matches: 0.0285 * 5 = 0.1425
• 6 matches: 0.0048 * 50 = 0.2400
• 7 matches: 0.0004 * 500 = 0.2000
• 8 matches: 0.00002 * 10,000 = 0.2000

Summing these gives an expected return of 0.1000 + 0.1425 + 0.2400 + 0.2000 + 0.2000 = 0.8825. So the expected return is 88.25%, and the house edge is 100% - 88.25% = 11.75%. This is lower than the 20-35% range often cited, because this particular pay table is relatively generous. Many keno pay tables have a higher edge.

Why the edge varies so much

The house edge in keno depends on the pay table, which is chosen by the operator. The same game with a different set of payouts can have a drastically different edge. For example, if the 8-spot pay table above were changed so that 4 matches paid 0, 5 matches paid 2, 6 matches paid 20, 7 matches paid 100, and 8 matches paid 2,000, the expected return would be:

• 4 matches: 0.1000 * 0 = 0
• 5 matches: 0.0285 * 2 = 0.0570
• 6 matches: 0.0048 * 20 = 0.0960
• 7 matches: 0.0004 * 100 = 0.0400
• 8 matches: 0.00002 * 2,000 = 0.0400

Total expected return = 0.0570 + 0.0960 + 0.0400 + 0.0400 = 0.2330, or 23.30%. The house edge is 76.70%. This illustrates that two keno games at the same casino can differ by more than ten percentage points in edge, simply because of the pay table.

The following table shows the house edge for several common spot sizes and pay tables. The edge depends on the number of spots and the specific payouts. The figures are derived from the probabilities of matching k spots, which are determined by the 80-number pool and 20-number draw.

The edges shown are approximate and depend on the exact pay table. For spot sizes 1 through 7 and 10, the pay tables are often set to produce a 25% edge. The 8-spot and 9-spot games sometimes have lower edges, but this is not guaranteed. The only way to know the edge for a specific keno game is to read its pay table and perform the calculation.

Converting the edge to money per hour

A percentage of turnover is not a quantity most people can feel. To make the cost concrete, consider a player who plays 200 keno rounds per hour at a stake of 1 per round. The total amount wagered per hour is 200. If the house edge is 25%, the expected loss per hour is 200 * 0.25 = 50. If the edge is 35%, the expected loss is 200 * 0.35 = 70. If the edge is 11.75%, the expected loss is 200 * 0.1175 = 23.50.

At a stake of 0.50 per round and 200 rounds per hour, the total wagered is 100. The expected loss at a 25% edge is 25 per hour. At a 35% edge, it is 35 per hour.

The round rate matters. A player who plays 400 rounds per hour at 1 per round wagers 400 per hour. At a 25% edge, the expected loss is 100 per hour. The cost scales linearly with the number of rounds and the stake.

This is why keno is often described as one of the worst bets in the casino. A player who spends an hour at a blackjack table with a 0.5% edge and a 100 per hour stake might expect to lose 0.50 per hour. The same player at a keno machine with a 25% edge and a 200 per hour stake expects to lose 50 per hour. The difference is two orders of magnitude.

What people get wrong about keno odds

The most common mistake is to assume that the house edge is the same for all keno games. It is not. The edge is a function of the pay table, and pay tables vary widely. Two keno games at the same casino, even on adjacent machines, can have edges that differ by ten percentage points or more. A player who assumes a 25% edge when the actual edge is 35% will underestimate the cost by 40%.

Another mistake is to believe that certain numbers are more likely to be drawn because they have not appeared recently. This is the gambler’s fallacy. Each draw is independent. The probability of any specific number being drawn is 20/80 = 0.25, regardless of what happened in previous draws. The machine does not have a memory. There is no such thing as a due number in keno.

A third mistake is to think that playing more numbers improves the odds. Playing more spots changes the variance and the pay table, but it does not change the fundamental house edge unless the pay table is different. In fact, some spot sizes have higher edges than others. The edge is determined by the pay table, not by the number of spots per se.

These mistakes are natural because keno is presented as a lottery, and lotteries often evoke a sense of pattern and luck. The human mind seeks patterns in random events. But the mathematics of keno is fixed and can be calculated exactly. The only unknown is the pay table, which is printed on the machine or available in the game’s help screen.

The role of free keno and online keno

Free keno games, often available online, use the same draw mechanics but do not involve real money. They are useful for understanding the game’s flow and the probabilities of different outcomes, but they do not change the house edge. When real money is involved, the edge is determined by the pay table of the specific game.

Online keno games may have different pay tables from land-based machines. Some online casinos offer keno with edges as low as 5% or as high as 35%. The same rule applies: read the pay table and calculate the expected return. The number of outcomes is always based on 80 numbers and a 20-number draw, so the probabilities are the same. Only the payouts change.

Super keno is a variant that sometimes offers a different pay table or additional features, such as a multiplier. These features can change the edge, but they do not change the underlying probabilities. The edge is still derived from the pay table and the number of outcomes.

How to calculate the edge for any keno pay table

The method is the same for any pay table. For a given number of spots s, list the payouts for each possible number of matches k (from 0 to s). For each k, calculate the probability P(k) = C(s,k) * C(80-s,20-k) / C(80,20). Then multiply P(k) by the payout for k and sum these products. The result is the expected return. The house edge is 1 minus the expected return.

This calculation can be done with a spreadsheet or a calculator. The binomial coefficients can be computed using the formula C(n,r) = n! / (r! * (n-r)!). For large numbers, use a calculator that handles large integers or use logarithms.

For example, for s=8, the probability of matching 4 is C(8,4)*C(72,16)/C(80,20). C(8,4)=70. C(72,16) is a large number, but the ratio can be computed. The result is approximately 0.1000. The probability of matching 8 is C(8,8)*C(72,12)/C(80,20) = 1 * C(72,12)/C(80,20) ≈ 0.00002.

Once the probabilities are known, the expected return is straightforward. The only variable is the pay table.

Summary of the cost

Keno is a game with a high house edge, typically between 20% and 35%. The edge is determined by the pay table, which varies by operator and by spot size. At a stake of 1 per round and 200 rounds per hour, the expected loss ranges from about 23.50 to 70 per hour, depending on the edge. At a stake of 0.50 per round, the loss ranges from about 11.75 to 35 per hour. These figures are expected values; actual results will vary. The edge is not affected by previous outcomes, by the number of spots played, or by whether the game is free or for money. It is a fixed property of the pay table and the draw.