NP-completeness of the game Kingdomino

TL;DR

This paper proves that optimizing the score in Kingdomino is an NP-complete problem, even with complete knowledge of future moves, highlighting the game's computational complexity.

Contribution

It establishes the NP-completeness of the Kingdomino game optimization problem, a novel complexity result for this popular board game.

Findings

Kingdomino's scoring optimization is NP-complete.

Complexity holds even with perfect information.

Implications for game strategy and AI development.

Abstract

Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place $2 \times 1$ dominoes on a grid layout, and get a better score than other players. Each $1 \times 1$ domino cell has a color that must match at least one adjacent cell, and an integer number of crowns (possibly none) used to compute the score. We prove that even with full knowledge of the future of the game, in order to maximize their score at Kingdomino, players are faced with an NP-complete optimization problem.