Lessons in Play: An Introduction to Combinatorial Game Theory
Taylor & Francis, Jul 2, 2007 - Mathematics - 304 pages
Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and new games, several appearing for the first time in this book.
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Alice all-small games atomic weight born by day canonical form CGSuite Chapter choose CLOBBER combinatorial game theory component compute confirm confusion interval counters define definition disjunctive sum DOMINEERING position DOTS & BOXES dyadic rationals edges equivalent example Exercise finite game G game tree games born graph HACKENBUSH Hasse diagram heap impartial game incentive infinitesimal integer left and right Left can win Left moves left options left stop Left wins moving Left's legal moves Lemma Let G long chains loony LS(G negative nim-sequence nim-values Norton product notation opponent outcome class P-position partial order partizan game Pick's Theorem positive integers positive number Prep Problem Proof remove reversible options Right moves right options right stops Right wins RS(G sequence subtraction games sum of games Suppose symmetric temperature thermograph TOPPLING DOMINOES Variants vertex vertical winning strategy wins G wins moving second