State Representation and Polyomino Placement for the Game Patchwork

TL;DR

This paper models polyomino placement in the game Patchwork using constraint programming, introduces heuristics for tile placement, and demonstrates the effectiveness of global propagation guided regret in guiding game-playing agents.

Contribution

It extends existing constraint models for polyomino placement with new features and introduces a novel heuristic based on global propagation guided regret for better game agent performance.

Findings

Global propagation guided regret improves placement decisions.

Heuristics based on packing literature enhance search efficiency.

Extended constraint model handles rotations and resource constraints effectively.

Abstract

Modern board games are a rich source of entertainment for many people, but also contain interesting and challenging structures for game playing research and implementing game playing agents. This paper studies the game Patchwork, a two player strategy game using polyomino tile drafting and placement. The core polyomino placement mechanic is implemented in a constraint model using regular constraints, extending and improving the model in (Lagerkvist, Pesant, 2008) with: explicit rotation handling; optional placements; and new constraints for resource usage. Crucial for implementing good game playing agents is to have great heuristics for guiding the search when faced with large branching factors. This paper divides placing tiles into two parts: a policy used for placing parts and an evaluation used to select among different placements. Policies are designed based on classical packing literature as well as common standard constraint programming heuristics. For evaluation, global propagation guided regret is introduced, choosing placements based on not ruling out later placements. Extensive evaluations are performed, showing the importance of using a good evaluation and that the proposed global propagation guided regret is a very effective guide.