What is chuckaluck is a game in which a player picks a numbe

chuck-a-luck is a game in which a player picks a number from 1 to 6 and an operator rolls three dice. If the number chosen by the player comes up on all three dice, the player wins $3; if it comes up on two of the three dice, the player wins $2; if it comes up on one of the three dice, the player wins $1. Only if the chosen number does not appear at all does the player pay $1. Is Chuck-a-luck a fair game? What is its average payoff?

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