Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game effectively using constraint programming is hard. This abstract presents the game, contributes new generalized variants of the game suitable for benchmarking and testing, and describes a model for the presented variants.

The question of the top possible score in the standard game is an open challenge.

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. On the other hand, the complex structures increase the implementation burden, with complex rules and intricate representations needed.

We study 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 Modeling Irregular Shape Placement Problems with Regular Constraints with: explicit rotation handling; optional placements; and new constraints for exact resource usage.

Crucial for implementing good game playing agents is to have great heuristics for guiding the search when faced with large branching factors. Placing tiles is done using a strategy. The strategy is divided 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 propapation 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 propapation guided regret is effective.