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Optimal Analyses for 3×n AB Games in the Worst Case

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Advances in Computer Games (ACG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6048))

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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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan Normal University, No. 88, Sec. 4, Ting-Chow Rd., Taipei, Taiwan, ROC

    Li-Te Huang & Shun-Shii Lin

Authors
  1. Li-Te Huang
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  2. Shun-Shii Lin
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Editor information

Editors and Affiliations

  1. Games and AI Group, MICC, Faculty of Humanities and Sciences, Universiteit Maastricht, Maastricht, The Netherlands

    H. Jaap van den Herik

  2. Institute for Knowledge and Agent Technology, Universiteit Maastricht,  

    Pieter Spronck

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Huang, LT., Lin, SS. (2010). Optimal Analyses for 3×n AB Games in the Worst Case. In: van den Herik, H.J., Spronck, P. (eds) Advances in Computer Games. ACG 2009. Lecture Notes in Computer Science, vol 6048. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12993-3_16

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  • DOI: https://doi.org/10.1007/978-3-642-12993-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12992-6

  • Online ISBN: 978-3-642-12993-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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