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The Red Sox just finished an 11-game winning streak, which made me wonder. Do most teams experience winning streaks this long over the course of a season? What is the expected value of the length of the longest winning streak for a .500 team over the course of a season?

In general: if you flip a coin N times with a probability of getting a head of P, what is the expected length of the longest series of consecutive heads embedded in the results of the N flips?

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