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Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games

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, …
Michael Albert's user avatar
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 …
Michael Albert's user avatar
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 …
Michael Albert's user avatar
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 …
Michael Albert's user avatar