Probability in Keno

There are some interesting mathematics behind Keno. There are many questions to be answered: What is the chance of winning in Keno? How big is the house edge in Keno?

The chances of hitting a certain number of correct numbers in Keno is shown below.

Number of matching numbers	Chance
0	1/843.380
1	1/46.446
2	1/20.115
3	1/8.009
4	1/4.877
5	1/4.287
6	1/5.258
7	1/8.826
8	1/20.055
9	1/61.420
10	1/253.801
11	1/1,423.822
12	1/10,968.701
13	1/118,084.920
14	1/1,821,881.628
15	1/41,751,453.986
16	1/1,496,372,110.872
17	1/90,624,035,964.712
18	1/10,512,388,171,906.553
19	1/2,946,096,785,176,811.500
20	1/3,535,316,142,212,174,320.000

As can be seen, the chance of hitting 20 correct numbers is close to zero. This has led to that casino and lotteries even do not have to consider the case of someone hitting 20 correct numbers in general, since it is so extremely unlikely. However hitting 1 to 8 numbers is very likely, and is in general what occurs. For example hitting 8 numbers has a 5% chance, which means that on average you will get this 5% of the time. In simple terms, if you played Keno 100 times, you would get this roughly 5 times (on average).

References

Mark Bollman (2014). Basic Gambling Mathematics: The Numbers Behind the Neon. CRC Press. pp. 40–41.