運用牌張間的關聯設計麻將程式

Abstract

麻將是一個多人且不完全資訊的機率型對局遊戲。隨著時間的推移，在不同的地區發展出許多不同的遊玩規則，本篇論文以臺灣麻將做為研究主題。 本研究在分析手牌完成度時，以遞迴的方式把手牌中能成組的所有組合方式拆分出來，並且改進"A New Approach to Compute Deficiency Number of Mahjong Configurations"一文中的方法，提出一個能同時考慮序數牌與字牌且能快速計算臺灣十六張麻將手牌進胡數的方法。

本研究在捨牌的策略為進行手牌拆分後，檢視所有擁有最低進胡數的拆法，並將手牌分類為孤張、未完成組與完成組，接著評估所有孤張、未完成組、完成組之間的關聯，針對不同的情況，選擇捨棄孤張或是拆掉能擁有最多進張牌的搭子。關於防守的策略，參考「利用他家資訊模組來改良麻將程式」一文中的做法，我們提出分別針對刻子與順子做非需求度的計算，並提出潛在需求牌的想法。Mahjong is a probability game with multi-player and incomplete information. With the passage of time, it has developed various rules and regulations in different countries. In this study we will focus on Taiwan Mahjong.We use the recursive method to split a handcard into all possible combinations and use the result to analyze the completeness of the handcard. By improving the deficiency calculating algorithm proposed in "A New Approach to Compute Deficiency Number of Mahjong Configurations", we introduce a new method which can deal with the suits tiles as well as the honors tiles at the same time.

After splitting the handcard, we classify our handcard into isolated tiles, pseudo-melds and melds on the basis of the splitting result with the lowest deficiency number. We evaluate the correlation between isolated tiles, pseudo-melds and melds. According to different situation, we choose to discard a tile which belongs to isolated tiles or a tile which belongs to pseudo-melds that has maximum possibility to form melds. Referring to the idea proposed in"Using Other Players’ Information Models to Improve Mahjong Program", we propose a method to evaluate the defense weights for the triplet tiles and sequence tiles. With the information of discarded tiles from other players, we propose an approach to find out the potential demand tiles for each player.