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Add game "Fox and Geese" #1581

Description

@Stochastic-Batman

Game Proposal: Fox and Geese

Game Overview

Fox and Geese is a classic asymmetric, two-player, zero-sum, perfect-information medieval board game (originating in Northern Europe) played on a cross-shaped board.

  • Player 0 (The Fox): Moves or jumps over adjacent Geese into empty spaces to capture them. The Fox wins if it captures enough Geese so that they can no longer immobilize the Fox.
  • Player 1 (The Geese): Geese move to adjacent empty spaces to surround and trap the Fox. Geese win if the Fox has no legal moves remaining.

Scope

I will be focusing specifically on Fox and Geese as detailed in the section Fox and geese, with one fox and the three traditional goose counts: 13, 15, or 17. Other variants listed in the broader article (such as Fox and Hounds or Halatafl) are out of scope for this initial implementation.

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