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Concept
Combinatorial Game Theory
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Summary
Combinatorial Game Theory
is a
Branch of mathematics
that studies
Sequential Games
with
Perfect Information
, where
Players take turns
making moves from a
Finite set of options
, and the outcome is determined solely by the players' decisions. It focuses on
Analyzing strategies
and determining
Winning and losing positions
, often using
Mathematical Structures
like
Game trees
and
Algebraic Methods
to
Evaluate positions
and outcomes.
Concepts
Game Tree
Nim Game
Sprague-Grundy Theorem
Winning Strategy
Losing Position
Impartial Game
Partisan Game
Mex Rule
Surreal Numbers
P-position
N-position
Combinatorial Structure
John Horton Conway
Combinatoriality
Relevant Degrees
Combinatorial Analysis and Graph Theory 60%
Board Games and Puzzles 30%
Mathematical Logic and Foundations 10%
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