How to Calculate Keno Odds

By Mal Van Valkenburg

To calculate the odds of keno, one has to have a firm grasp of math and understand probabilities and chance. If you know the game and understand the math, you can calculate the odds of successfully playing keno. The odds are the chances of correctly picking the right numbers. It's not the same as the payoffs at the casino. You will find the payoffs will be less than the actual chance of winning. That's the edge the house always holds over the player.

How the Game Works

Step 1

If you are playing a "live" game or a game machine, it works the same. There are 80 numbers and 20 will be selected. Before this is done, a player will choose between 1 and 15 numbers. Depending on how many numbers the player chooses and how many he correctly picked out of the ones selected will determine if he gets paid and how much.

Step 2

There is a formula to calculate the odds of correctly picking numbers. It comes down to this, if you mark N spots, the probability of hitting exactly K of them is given by the formula:

           C(N,K)  *  C(80-N,20-K)

p(N,K) = ------------------------------- C(80,20)

Let's try to break this down a little simpler.

If you pick one number out of 80. There will be 20 numbers drawn. so, 20 out of 80 is 25 percent. You have 25 percent chance that your number will be picked.

Step 3

When you start figuring combinations of numbers being picked, the number of combinations from 80 numbers is so large most calculators can not figure them. There are calculators and spreadsheets that have a function for calculating these type of numbers. Both Lotus 1-2-3 and Excel name this function COMBIN(n,r). The "n" stands for the total numbers possible and the "r" is the number picked from the total numbers. The function figures out the total number of combinations possible.

When figuring two numbers, the player must draw 2 out of the 20 drawn numbers to win. You figure out the total combinations—combin(80,2) = 3160—and then figure out how many winning combinations there are—combin(20,2) = 190. You then divide the numbers, 190/3160. The probability of winning is 6.01 percent.

As you go up with the number of combination, you increase the numbers to find out your odds.

There are some online calculators that can help shortcut figuring out the odds.

Step 4

Once you figure out the odds of actually winning keno and the payoffs the casino gives, you will realize that the house does not pay what the actual odds are. The math is always on the house's side. A lot of gamblers say to stay away from keno because of the high house advantage, which can be up to 20 percent. Here is an example: To catch one number, the real odds are 25 percent or 4 to 1. For the odds to be perfect, the house should pay $4 for every $1 bet. But in reality, the house pays $3 for $1 bet. That 25 percent difference is the "edge" the house possesses.