適用於麻將之蒙地卡羅取樣演算法

Abstract

本篇論文提出一個使用蒙地卡羅取樣演算法搭配信賴區間的方法來選擇麻將遊戲的可走步。其中使用蒙地卡羅取樣來計算盤面的胡牌率，其中在取樣的過程中簡化對手的動作，並且我方使用只摸牌而不捨牌的概念來進行取樣，透過此方法來估計所有可走步的胡牌率。透過對所有可走步進行少量的取樣，並且根據可走步的胡牌率和標準差得到信賴區間對可走步進行篩選。重複取樣和篩選來選擇動作。我們使用新的方法與過去的程式VeryLongCat進行8000局的二對二比賽，新的方法胡牌次數比VeryLongCat多出了77場。

This paper proposes a method using Monte-Carlo sampling with confidence interval to select moves in Mahjong games. We use Monte-Carlo sampling to calculate the win rate of a given state. Besides, we simplify the moves by ignoring opponent moves and only drawing tiles without throwing. We use small amount of sampling to all moves of current state and filter the moves according to win rates and confidence interval. The moves are selected by repeating sampling and filtering the moves. The new program played 8000 games against old program VeryLongCat, and the won 77 games more than VeryLongCat.