347.Best of Two Tosses
★★★expected valueJane Street
You toss four fair coins and are paid for each head. You are then allowed a second toss of all four coins, and you are paid on whichever of the two tosses produced more heads. What is the expected payout?
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You need the expectation of the maximum of two independent draws. Get there through the cumulative distribution — the maximum is at most k exactly when both tosses are.
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