The maximum score a player can achieve in a single round of golf is 67, based on the lowest possible scores for each hole across a standard 18-hole course, assuming that the course has a par value of 72. Achieving scores lower than 67 is exceptionally rare and typically indicates an outstanding performance by the golfer, often referred to as achieving an under-par score. Excellent ball control, strategy, and putting skills are crucial to attaining such a score.