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Problem 5-17

If a soccer game ends in a tie, it goes into a penalty-kick shootout in which each team chooses five players to take penalty kicks. The team that makes the most subsequent penalty kicks wins the game. In a penalty-kick shootout, the shooter and the keeper each decide simultaneously on a direction to move. They can choose left, right, or middle. These strategies yield the following game theory table, where the first value is the shooter's probability of scoring and the second value is the keeper's probability of stopping the shot: