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You flip four fair coins and win $1 per head, and may re-flip a single coin of your choice. Playing rationally, what is your expected profit?

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Flip four fair coins and win $1 for each head. You may flip the tails again once. What is the expected value of the game?Four fair coins pay $1 per head. You may re-flip all four once but must keep the second result. What is the game worth?Two players reveal coins: both heads you win 3, both tails you win 1, a mismatch you lose 2. What is your best strategy and expected profit?

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