The Fallacy of the Hot Hand Fallacy

Harry and Tom decide to play a game. They flip a fair coin \(n\) times. Each time the coin comes up heads, there is an opportunity to score. Harry scores a point if the next flip is heads, and Tom scores if the next flip is tails. A player wins if after all \(n\) tosses, their score is higher than their opponents. Who is more likely to win? A natural instinct is that because each flip is fair (and…