# Expected Payoff - Slot Machine

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A standard slot machine has three reels. The first reel has 3 walnuts, 7 cherries, 3 oranges, 5 lemons, 1 bell, and 1 jackpot bar. The second reel has 7 cherries, 6 oranges, 1 lemon, 3 bells, and 3 bars. The third reel has 4 walnuts, 7 oranges, 5 lemons, 3 bells and 1 bar. The payoffs are

Reel 1 Reel 2 Reel 3 Payoff in Coins

Bar Bar Bar 85

Bell Bell Bar 18

Bell Bell Bell 18

Lemon Lemon Bar 14

Lemon Lemon Lemon 14

Orange Orange Bar 10

Orange Orange Orange 10

Cherry Cherry Bell 5

Cherry Cherry Walnut 5

Cherry Cherry Any other 3

a) What is the expected payoff if each picture on each reel is equally likely to appear?

b) In the long run, what fraction of every dollar bet will this one-armed bandit keep?

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##### Solution Summary

The expected payoffs for slot machines are examined.

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Hi there,

Thanks for letting me work on your post. Here is my explanation.

The probability for Bar Bar Bar: 1/20*(3/20)*(1/20)=0.000375

The probability for Bell Bell Bar: 1/20*(3/20)*(1/20)=0.000375

The probability for Bell Bell Bell: 1/20*(3/20)*(3/20)=0.001125

The ...

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