Combinatorial game theory

2 articles

Alphabeta pruning Checkers Chess Chomp Clobber Cram Disjunctive sum Domineering Example of a game without a value Expectiminimax Finite game First player and second player win Game form Game tree Hackenbush Impartial game Kuhn poker Mex Misere Monte carlo tree search Move generation Move ordering Negamax Nimber No win situation Notakto Null move Paranoid algorithm Partisan game Principal variation search Shannon number Shannon switching game Sim Solved game Spraguegrundy theorem Star Strategy stealing argument Strictly determined game Subtract a square Sylver coinage Toads and frogs Waldegrave problem Zugzwang Angel problem Blockbusting Branching factor Bulgarian solitaire Chopsticks Combinatorial explosion Cooling and heating Fibonacci nim Futile game Fuzzy game Game complexity Games puzzles and computation Generalized game Genus theory Go Grundys game Heap game Hot game Indistinguishability quotient Infinite chess Jenga Kayles Lemke howson algorithm Loopy game Map coloring games Mis re Octal game On Pairing strategy Poset game Sprague grundy theorem Subtraction game Tiny and miny Up Winning ways for your mathematical plays Zero game

Combinatorics & Discrete Math UndergraduateDeep dive10 min

The Coin in the Middle, and the Table Where It Fails

Take the centre, then mirror every move through it, and you place the last coin. The proof has three requirements and only one of them needs that opening move, which is the step a one-line answer skips. Central symmetry alone is not the condition: an annulus is centrally symmetric and the first player loses on it.

Combinatorics & Discrete Math High SchoolExplainer9 min

Say Six: The Only Opening That Wins the Race to Fifty

Counting to fifty in steps of one to ten, the first player wins, and exactly one of the ten legal openings does it. The stations are 6, 17, 28, 39 and 50, spaced eleven apart because eleven is one more than the largest legal step. The article carries the residue argument that proves the opening is unique, and the target 55 where the advantage flips.