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Probability of winning chance in sucker bet

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Question: Sucker bet. Consider the following gambling game. Player 1 picks a three coin pattern (for example, HTH) and player 2 picks another (say THH). A coin is flipped repeatedly and outcomes are recorded until one of the two patterns appears. Somewhat surprisingly player 2 has a considerable advantage in this game. No matter what player 1 picks, player 2 can win with probability ≥ 2/3. Suppose without loss of generality that player 1 picks a pattern that begins with H:

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Verify the results in the table. You can do this by solving six equations in six unknowns but this is not the easiest way.

Reference no: EM131754065

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