Fast Algorithm for Calculating Probability of Chess Winning Streaks

Motivated by the controversy in the chess community, where Hikaru Nakamura, a renowned grandmaster, has posted multiple impressive winning streaks over the years on the online platform chess.com, we derive the probabilities of various types of streaks in online chess and/or other sports. Specifically, given the winning/drawing/losing probabilities of individual games, we derive the probabilities of "pure" winning streaks, non-losing streaks, and "in-between" streaks involving at most one draw over the course of games played in a period. The performance of the developed algorithms is examined through numerical studies.