Bets and decisions · Carnival · difficulty 2 of 5
Chuck-a-luck
At a carnival game you bet $1 on one of the numbers 1 to 6. Then 3 fair six-sided dice are rolled. If your number shows on k of the dice, with k at least 1, you keep your $1 and win $k. If it shows on none of them, you lose your $1. What is your expected profit, in dollars, per game?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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