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Expected Payoff - Slot Machine

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?

Solution Preview

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 ...

Solution Summary

The expected payoffs for slot machines are examined.