Optimal analyses for 3×n AB games in the worst case

Authors:
Li-Te Huang;Shun-Shii Lin
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan Normal University, Taipei, Taiwan, ROC;Department of Computer Science and Information Engineering, National Taiwan Normal University, Taipei, Taiwan, ROC
Venue:
ACG'09 Proceedings of the 12th international conference on Advances in Computer Games
Year:
2009

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Abstract

The past decades have witnessed a growing interest in research on deductive games such as Mastermind and AB game. Because of the complicated behavior of deductive games, tree-search approaches are often adopted to find their optimal strategies. In this paper, a generalized version of deductive games, called 3×n AB games, is introduced. However, traditional tree-search approaches are not appropriate for solving this problem since it can only solve instances with smaller n. For larger values of n, a systematic approach is necessary. Therefore, intensive analyses of playing 3×n AB games in the worst case optimally are conducted and a sophisticated method, called structural reduction, which aims at explaining the worst situation in this game is developed in the study. Furthermore, a worthwhile formula for calculating the optimal numbers of guesses required for arbitrary values of n is derived and proven to be final.