Let's Play Mahjong!

TL;DR

This paper introduces a mathematical and AI framework for Mahjong, defining hand deficiency and optimal discard policies to improve winning chances within a limited number of tile changes.

Contribution

It presents the first formal analysis of Mahjong's hand deficiency and develops an optimal discard strategy to enhance winning probability.

Findings

Defined and characterized the notion of hand deficiency.

Developed an optimal policy for tile discarding.

Analyzed the impact of tile changes on winning chances.

Abstract

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 $k\geq 1$.