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Hard · Game Theory & Logic · Quant Trader interview question · random-walk, probability, recurrence, chess
A knight starts at position (0,0) on an infinite chessboard and makes random legal moves uniformly. Each legal move has an equal probability of being selected. What is the probability that the knight eventually returns to (0,0)? A knight moves two squares in one direction (horizontally or vertically) and one square in a perpendicular direction.