5 people are lined up and each of them is given a hat, which is either red or blue, chosen randomly with equal probability. Each person can see the hats on the people in front of them, but not their own. One by one starting from the back of the line, they are called upon and asked to guess the color of their hat or pass. The players win if at least one player guesses correctly, and nobody guesses incorrectly. If the people work together using the optimal strategy, what is the probability they win the game?

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