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Results tagged with combinatorial-game-theory
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user 1907
Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games
5
votes
A Transversal Achievement Game on a Grid
Unless my code is wrong (always a real possibility) the 4x4 case is a first player win.
Vincent Vatter suggested looking at the related game where X wins by building a permutation, and O wins otherwi …
- 1,305
8
votes
Accepted
Yet another Erdős–Szekeres game
As noted in the comments (but with not quite the right reference) the game is a first player win for $n \geq 4$. The question here is about the misere form, so this is a combination of Proposition 7, …
- 1,305
8
votes
Motivation for the Sprague-Grundy theorem
There is no direct link with difficulty of computation -- for example a single Nim heap of $n$ counters has nim-value $*n$. Of course, if a game is equivalent to $*n$ it must have at least $n$ options …
- 1,305
8
votes
Accepted
efficient arithmetic with (short) Conway games?
There are indeed (relatively) efficient algorithms to do this (computing canonical form in particular, deciding equality etc.) They are implemented in the CGSuite software package written by Aaron Sie …
- 1,305