# Keno Odds

We were trying to figure out the odds on keno the other day. There’s something about statistics that doesn’t create appropriately strong synapses in my brain. I got an A in stats in college, so I know I can retain the information long enough to be tested on it. But put me in a bar and make me figure out odds on craps or blackjack or keno and I’m lost. Thank goodness for the internet.

The formula for determining pick/catch odds at keno is

`=COMBIN(20,Caught)*COMBIN(80-20,Picked-Caught)/COMBIN(80,Picked)`

Keno is a game where to 20 numbers are selected out of 80. You can pick numbers that you think will show up in the 20. The number that actually do are “caught”. What’s the best play? I start with a matrix of picks and catches and the odds of each.

Then I create a matrix of payouts for all the cominations

Finally I multiply the top table by the bottom table. This is my expected payout for \$1 bet.

I sum up all the expected payouts for a pick and

Let’s set aside the fact that the best play is not to play. If you don’t play, \$1 yields \$1. The next best option is picking one number. If you pick-1 long enough, you’ll only lose \$.25 for every \$1 bet. Pick-20 is so bad, in part, because our local keno jobber has a maximum payout of \$50,000. If you pick 20 and catch 20 you get \$50,0000. If you pick 15 and catch 15, it’s a \$50,000 payout. With the cap, longer odds don’t pay. If you pick-8 long enough, you’ll lose \$.44 for every \$1 bet.

I put this to the test last Friday night by playing five \$1 pick-1 games. I won three of them for a net profit of \$4. I’m sure you’ll agree that five games isn’t statistically significant. And to be honest, I don’t need to “prove” the math; I think it stands on its own. But in the interest of science, I’m going to the local pizza and beer merchant to play 80 \$.25 games of pick-1. I should lose \$5.

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## 5 thoughts on “Keno Odds”

1. “I’m going to the local pizza and beer merchant to play 80 \$.25 games of pick-1. I should lose \$5.”

Wouldn’t that \$5 be better spent on another beer?

2. lhm says:

Equivalently =HYPGEOMDIST(Caught,20,Picked,80).
Try doing that in your head after a few beers :)

3. lhm: I can’t believe there’s a function for that. And it’s not even in the ATP. Thanks.

Here are the results:

Bettor Game Games Played Expected \$ Actual \$
DK 1 Spot 40 -\$2.50 -\$4.75
JC 1 Spot 40 -\$2.50 -\$2.50
TF 2 Spot 40 -\$2.78 +\$1.00

But it was \$2 Tecate night, so were there really any losers?

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