How to Measure Mahjong Luck and Skill
Every Game of Mahjong Is A Dice Roll Imagine you are playing a 4 player game of mahjong against 3 clones of yourself. The probability that you get 1st, 2nd, 3rd, or 4th place is 25% - you're all equal in skill and playing the same strategy, so there's no reason any clone would have an advantage. The average placement you would achieve is 2.50. If you were playing against weaker players and had an average placement of 2.40, we would say that you have some edge , or advantage. Now suppose you were playing perfect mahjong against competent opponents. How much edge is possible? One estimate of the maximum possible edge would be the results of the AI LuckyJ, who has the best performance of any person or AI in the Tokujou room on Tenhou. Over 1145 games, LuckyJ's spread of placements is 31.5% 1st, 27.5% 2nd, 24.1% 3rd, and 16.7% 4th. Its average placement is 2.26. There is some selection bias in estimating the edge of perfect play using the best performance we've seen