A Mahjong-Strategy based on Weighted Restarting Automata

Abstract

Mahjong is a popular and traditional tile-based game in China, which has a history of several hundred years. In general, Mahjong is played by four players, and each player begins with 13 tiles and changes (i.e., draws and discards) tiles in turn, until a player obtains a so-called winning hand consisting of 14 tiles. We are interested in the minimal number of necessary tile changes in order to obtain a winning hand, i.e., the so-called deficiency number. For this purpose, we develop a Mahjong-intelligence by using weighted restarting automata. Originally, restarting automata have been introduced as a formal model of the linguistic technique of analysis by reduction, which can be used to check the correctness of natural language sentence. In order to study quantitative aspects of restarting automata, we introduce the concept of a weighted restarting automaton. Such an automaton is defined as a pair (M, ω), where M is a restarting automaton on some input alphabet Σ, and ω is a weight function that assigns an element of a semiring S to each transition of M. Thus, each weighted restarting automaton defines a function f: Σ* → S that associates an element of S to each input word over Σ. In this work, we will construct a weighted restarting automaton over the tropical semiring that can determine the deficiency number of a hand of Mahjong-tiles.