Keno Mathematics

Keno is a type of lottery gambling game where 20 numbers from 80 are randomly chosen by a computer, after a player has placed bets according to which 20 numbers he/she thinks the computer will choose from the 80. Keno can out the outset seem like an extremely simple casino game of chance, and it can be easy to mistakenly think that this apparent simplicity means you have much higher chances of winning with this game than with other more complex casino games. The truth is that your chances of winning with Keno are actually less than most other casino games, with the house edge typically varying between 4% and 30%. Nevertheless, it’s still a fun game to play and you can win handsomely if you run into a spot of good luck.

Keno odds

The chances of choosing one correct number are 20 in 80 (i.e. 1 in 4). You might therefore, according to the theory of probability, expect that the chances of choosing two correct numbers are 1 in 4 multiplied by 1 in 4, i.e. 1 in 16, but this doesn’t take into account the other mathematical variables that play an increasingly significant role as more numbers are brought into the equation. The odds of matching chosen numbers to the computer’s drawn numbers become increasingly slimmer for each subsequent number, for example the chances of matching 10 chosen numbers with 10 of the computer-drawn numbers is 1 in 253 801, while the chances of matching all 20 is 1 in 3 535 316 142 212 180 000.

Keno’s extraordinary probabilities mean that there do exist opportunities for players to make huge winnings from small bets.

Keno and the Combin Function

The Combin Function is an easy way of calculating how many ways a certain number of numbers can be selected from a specific total (in Keno, this is 80). For example, if we wanted to work out how many ways exist to draw sets of 5 different numbers out of 80, we would input these numbers into the Combin Function and obtain an answer of 24 040 016.

How to work out your chance of winning in Keno

Using the Combin Function as outlined above, it is possible to assess your chances of hitting maximum winnings on a particular round of Keno. Let’s say we are playing 2-spot Keno (i.e. only selecting two numbers, which we hope will be two of the 20 that the computer will draw. First, use the Combin Function to work out how many possible ways there are to pick two numbers from 80: Combin(80,2) = 3160. Then, remember that these two numbers have to be included in the 20 numbers the computer draws, so use the Combin Function again – Combin(20,2) – to work out how many ways there are of doing this – in this case, 190. Then divide this figure by the first figure (3160), and the answer is your percentage probability of winning (in this case 6.01%).