Proposal and Generation of Endgame Puzzles for an Imperfect Information Game Geister

The generation of endgame puzzles for the imperfect information game Geister serves as a strategic training tool designed to enhance player proficiency through structured practice. By employing a depth-first proof-number search solver alongside random piece placement, researchers can identify valid endgame scenarios categorized by the visibility of opponent pieces, specifically distinguishing between not-revealed and partly-revealed configurations. This methodology effectively isolates specialized victory conditions, such as red-wall and capture-win scenarios, providing a computational framework for creating challenging board game puzzles.

Experimental results indicate that while the proposed solver is highly efficient at identifying valid endgame states, the success rate of puzzle generation decreases exponentially as the required number of winning moves increases. Furthermore, the relationship between technical complexity and human engagement is nuanced. Although higher move counts generally correlate with increased difficulty, they do not inherently guarantee a more interesting experience for the player. Predictive modeling using the LightGBM framework reveals that the number of captured pieces acts as the primary driver of perceived interestingness, whereas the number of nodes expanded by the solver serves as the most reliable indicator of puzzle difficulty.

These findings suggest that while procedural generation can successfully produce a wide array of Geister endgame puzzles, future development must move beyond simple move-count metrics to incorporate aesthetic and psychological factors. By balancing algorithmic search efficiency with models that predict human engagement, developers can create more compelling training materials. This research establishes a foundation for applying artificial intelligence to the design of imperfect information games, demonstrating that computational solvers are not only capable of mastering game mechanics but are also instrumental in quantifying the subjective elements of strategic play.