39:, only one player can move the white pieces. More strongly, when analyzed using combinatorial game theory, many chess positions have values that cannot be expressed as the value of an impartial game, for instance when one side has a number of extra tempos that can be used to put the other side into
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as its value, or else the game would be impartial. However, some nimbers can still occur as the values of game positions; see e.g.
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does not apply. However, the application of combinatorial game theory to partisan games allows the significance of
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109:, Math. Sci. Res. Inst. Publ., vol. 29, Cambridge: Cambridge Univ. Press, pp. 135–150,
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dos Santos, Carlos
Pereira (2011), "Embedding processes in combinatorial game theory",
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105:(1996), "On numbers and endgames: combinatorial game theory in chess endgames",
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32:. That is, some moves are available to one player and not to the other.
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Winning ways for your mathematical plays, Volume 1: Games in general
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to be seen, in a way that is not possible with impartial games.
92:. Berlekamp et al. use the alternative spelling "partizan".
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That is, not every position in a partisan game can have a
46:Partisan games are more difficult to analyze than
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35:Most games are partisan. For example, in
107:Games of no chance (Berkeley, CA, 1994)
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135:Discrete Applied Mathematics
90:, Academic Press, p. 17
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196:Combinatorial game theory
148:10.1016/j.dam.2010.11.019
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52:Sprague–Grundy theorem
175:On numbers and games
76:Berlekamp, Elwyn R.
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177:, Academic Press
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28:) if it is not
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50:, as the
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190:Category
173:(1976),
86:(1982),
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22:partisan
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37:chess
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