153.Pair-Flip Coin Game
★★★expected valueCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
You flip 4 fair coins and observe the outcomes. You may then repeatedly turn over any 2 coins at a time (you cannot turn over just 1). Turning a coin flips it from heads to tails or tails to heads. Playing optimally to maximize heads, what is the expected number of heads you end up with?
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What happens to the parity of the number of heads when you turn over two coins at once?
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