A coin-toss game ends when the score reaches +2 or -2, and one player alone may double the $1 stake before any toss. What is that player's best strategy and expected payoff?
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A coin is tossed repeatedly; the score moves +1 on heads and -1 on tails, and the game ends at +2 (A wins) or -2 (B wins). The stake starts at $1 and A alone may double it before any toss; the loser pays the current stake. What is A's optimal strategy and expected payoff?
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