Ryan B. Hayward | Searcharxiv

arXiv2025

A Proof of the 2004 Albert-Grossman-Nowakowski-Wolfe Conjecture on Alternating Linear Clobber

Clobber is an alternate-turn two-player game introduced in 2001 by Albert, Grossman, Nowakowski and Wolfe. The board is a graph with each node colored black (x), white (o), or empty (-). Player Left has black stones, player Right has white stones. On a turn, a player takes one of their stones that is adjacent to an opponent stone and clobbers the opponent's stone (replaces it with theirs). Whoever cannot move loses. Linear clobber is clobber played on a path, for example, one row of a Go board. In 2004 Albert et al. conjectured that, for every even-length alternating-color linear clobber position except oxoxox, the first player has a winning strategy. We prove their conjecture.

math.CO↗

arXiv2017

A Reverse Hex Solver

We present Solrex,an automated solver for the game of Reverse Hex.Reverse Hex, also known as Rex, or Misere Hex, is the variant of the game of Hex in which the player who joins her two sides loses the game. Solrex performs a mini-max search of the state space using Scalable Parallel Depth First Proof Number Search, enhanced by the pruning of inferior moves and the early detection of certain winning strategies. Solrex is implemented on the same code base as the Hex program Solver, and can solve arbitrary positions on board sizes up to 6x6, with the hardest position taking less than four hours on four threads.

cs.AI↗