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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Huang, L. T., & Lin, S. S. (2010). Optimal analyses for 3×n AB games in the worst case. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6048 LNCS, pp. 170–181). https://doi.org/10.1007/978-3-642-12993-3_16
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