Let's Play Mahjong!
This work addresses a fundamental challenge in Mahjong strategy for players and AI systems, but it appears incremental as it builds on existing mathematical and AI studies of the game.
The paper tackles the problem of evaluating the quality of a Mahjong hand and determining optimal tile discards to complete a legal hand within a specified number of tile changes, presenting an optimal policy for this purpose.
Mahjong is a very popular tile-based game commonly played by four players. Each player begins with a hand of 13 tiles and, in turn, players draw and discard (i.e., change) tiles until they complete a legal hand using a 14th tile. In this paper, we initiate a mathematical and AI study of the Mahjong game and try to answer two fundamental questions: how bad is a hand of 14 tiles? and which tile should I discard? We define and characterise the notion of deficiency and present an optimal policy to discard a tile in order to increase the chance of completing a legal hand within $k$ tile changes for each $k\geq 1$.