Keno
- Page ID
- 218946
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Keno
Keno is a game where the player marks several numbers from the numbers 1 through 80. Then the house randomly selects 20 numbers. If many of the player's numbers are selected, then the player wins money. The more selected the more money. The game we will be talking about costs $2 to play. Below is a list of the payoff for each winning bet (Courtesy of Horizon Casino of Lake Tahoe). Play 1 Spot Catch 1 = $6
Play 2 Spots Catch 2 = $24
Play 3 Spots Catch 3 = $84
Play 4 Spots Catch 4 = $240
Play 5 Spots Catch 5 = $1500 Play 6 Spots Catch 6 = $3000 Play 7 Spots Catch 7 = $20500 Play 8 Spots Catch 8 = $50000 Play 9 Spots Catch 9 = $50000 Play 10 Spots Catch 10 = $50000 Play 11 Spots Catch 11 = $50000 Play 12 Spots Catch 12 = $50000 We will focus on finding the probabilities for the Play 8 spots. The rest are calculated in a similar manner. First let us look at the probability of catching 5. We can think of the eighty numbers as being divided into 20 good ones and 60 bad ones. If we caught 5 out of 8 then five of the good ones are selected and 3 of the bad ones are selected. There are C(20,5) = 15504 ways of selecting 5 good ones and C(60,3) = 34220 ways of selecting the bad ones. Hence the total number of ways of catching 5 is C(20,5) x C(60,3) = (15504)(34220) = 530546880 The total number of ways of selecting 8 numbers is C(80,8) = 28987537150 We get the probability by dividing C(20,5) x C(60,3) We can compute the probabilities of catching 6, 7, and 8 in a similar way: C(20,6) x C(60,2) C(20,7) x C(60,1) C(20,8) x C(60,0) We can find the probability of losing the $2 by subtracting from 1: P(Lose) = 1 - 0.0183 - 0.00237 - 0.000160 - 0.00000435 = 0.979 We can now write the probability distribution table:
EV = (10)(0.0183) + (208)(0.00237) + (3098)(0.00016) = -0.79 We see that if you play many times, you will lose an average of 79 cents per game.
I will leave it as an exercise to figure out the rest of the expected values. Always decide how much you are willing to spend before you begin. Never go beyond this number. If you find yourself pulling out more cash to get back what you lost, then you have a gambling problem and should call the National Council on Problem Gambling at 1-800-522-4700. |
