Traditional game theory has been successful at developing strategy
in games of incomplete information: when one player knows something
that the other does not. But it has little to say about games of
complete information, for example tic-tac-toe, solitaire and hex.
This is the subject of combinatorial game theory. Most board games
are a challenge for mathematics: to analyze a position one has to
examine the available options, and then the further options
available after selecting any option, and so on. This leads to
combinatorial chaos, where brute force study is impractical. In
this comprehensive volume, Jozsef Beck shows readers how to escape
from the combinatorial chaos via the fake probabilistic method, a
game-theoretic adaptation of the probabilistic method in
combinatorics. Using this, the author is able to determine exact
results about infinite classes of many games, leading to the
discovery of some striking new duality principles.
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