I was asked to write a column about Keno.
I’m familiar with the game and the math of the game. What I didn’t have handy were current paytables. So, I went to three local casinos – Red Rock, Suncoast and Rampart.
It turns out that only Red Rock plays live Keno. I remember the days when I would come here in the late 1980’s and you would sit at the buffet, the Keno runners would come and take your sheets and money and then you would watch the numbers be drawn on the boards that hung in multiple places.
Ironically, you didn’t know which games you were actually playing because there was a delay between when you handed the numbers to the runner and when she put them in. It was not a high-tech era relative to today.
Keno has diminished greatly in popularity through the decades. Fortunately, the rise of video machines has allowed players who want to partake in this game a chance to do so. Many of the multi-game slot/video poker machines also have Keno options.
Also fortunate for the player is that the video Keno versions tend to have higher paybacks than live Keno. This is for two significant reasons. The first is that the overhead on video Keno is much lower and the second is that you can play far more Keno hands on a video Keno machine, so the casino can make the same (or higher) profits because the amount wagered per hour is much higher.
Unfortunately for the player, the paybacks on any type of Keno is pretty low relative to most other games in the casino. The paybacks are likely to be rather comparable to slots with one noticeable difference. You can at least calculate the payback of Keno with absolute certainty once you know the paytable. The probability of hitting any combination is a known quantity. So, we just multiply the payout of each winning combination by the probability of that combination and sum up these values arrive at our payback.
I’m limited in space here to describe the way the probabilities are calculated. In short, the math is sort of done backwards. Keno involves the game picking 20 out of 80 possible numbers. The player may select two or more numbers that will be picked from that 20. He is paid if at least a minimum number of his numbers are picked out of the 20.
There are a few variations in which the player is paid for picking very few or a large number of numbers, but loses if it is in the middle. The math is still the same.
I use combinatorial math to calculate the probability that four out of the player’s five numbers will be in the 20 numbers picked while one is in the numbers not picked.
This is repeated for 5 out of 5 and 3 out of 5 – which are the usual paying combination for picking five numbers.
The table below has the probabilities for picking x out of 5 numbers:
I found a variety of paytables at live Keno just at the Red Rock. One paytable paid 750, 10 and 1. Following the formulate I stated earlier, this provides a payback of 68.85 percent.
Yes, you read that right. The paytable for video Keno was 810, 12 and 3 which gives the player a 91.93 percent payback. It can’t compare to even the worst video poker machines, but at least it competes with the slot machines.
If you are wondering, the probability of hitting 10 out of 10 is 0.0000112 percent or 1 in 8.9+ million. So, getting paid $50,000 for this doesn’t add much to the overall contribution.
For those who are interested, I have a Keno sheet that lists out all the probabilities for picking up to 15 numbers. You just need to plug in the payouts and do some multiplication and addition to get the payback of whatever paytable/number of pick combinations that interests you.
Head on over to www.gambatria.com if you would like to order one of these sheets. If you do order one, you are free to make as many copies as you would like for your own personal use.