418.Guess the Ball, Get the Count
★★★expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability
A box holds 2 black and 2 yellow balls, drawn one at a time without replacement. Before each draw you guess the color; a correct guess pays (in dollars) the number of balls that were in the box before that draw. Playing optimally, what is the expected payoff?
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Always guess the majority color. Set up the DP over states (black left, yellow left).
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