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SOME PRELIMINARY RESULTS OF THREE COMBINATORIAL BOARD GAMES
 

Summary: SOME PRELIMINARY RESULTS OF THREE
COMBINATORIAL BOARD GAMES
Samee Ullah Khan
Ishfaq Ahmad
Abstract
This paper analyzes a certain class of combinatorial board games that in-
cludes Ayo, Tchoukaillon and Modular N­queen. We refine the existing re-
sults by providing simple and intuitive proofs using abstract combinatorics,
and also reveal some interesting game positions.
1 Introduction
Chess and its variants, are pure strategic games without any random moves. It
should, at least in principle, be possible to decide whether there is a winning strat-
egy for the first or the second player, or whether the game always ends with a
draw (assuming a perfect play). Such games are called combinatorial games, and
combinatorial game theory (CGT) is a branch of mathematics devoted to their
analysis [2]. A rich theory on how to evaluate game positions has been developed
in recent years, and it has been successfully applied to analyze certain endgame
positions of Chess [6] and Go [1], for example. Unfortunately, CGT cannot di-
rectly be applied to Chess, Shogi and Xiangqi, due to the fact that draws do not
qualify as a game in CGT [2, 4]. Moreover, CGT also fails to help analyze var-

  

Source: Ahmad, Ishfaq - Department of Computer Science and Engineering, University of Texas at Arlington

 

Collections: Computer Technologies and Information Sciences