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    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 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.