Dawson’s chess revisited

Keivan Borna () and N. A. Ashrafi Payaman ()
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Keivan Borna: Kharazmi University
N. A. Ashrafi Payaman: Kharazmi University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 6, 771-794

Abstract: Abstract In this paper we prove that in a Quasi-Dawson’s Chess (a restricted version of Dawson’s Chess) playing on a 3 × d board, the first player is loser if and only if d (mod)5 = 1 or d (mod)5 = 2. Furthermore, we have designed two algorithms that are responsible for storing the results of Quasi-Dawson’s Chess games having less than d + 1 files and finding the strategy that leads to win, if there is a possibility of winning (by a wining position, we mean one from which one can win with best play). Moreover we show that the total complexity of our algorithms is O(d 2). Finally we have implemented our algorithm in C++ which admits the main results of the paper even for large values of d.

Keywords: Combinatorial game; Dawson’s chess; impartial game; winning strategy (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0042-7

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