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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Optimal Analyses for 3×n AB Games in the Worst Case
verfasst von : Li-Te Huang, Shun-Shii Lin
Erschienen in: Advances in Computer Games
Verlag: Springer Berlin Heidelberg
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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.