OpenBlock: Constructive and Verified Content Generation for Adaptive Tile-Matching Games

Abstract:Tile-matching puzzle games serve hundreds of millions of players, yet the content-generation algorithms that decide which pieces to present at each turn remain proprietary, and no open platform exists for studying adaptive difficulty in this genre. We present an adaptive tile-matching platform whose central algorithmic contribution is a dual-track content-generation architecture: a deterministic rule-based generator that is always available, and an optional learned generator, both subject to a common verification gate that establishes, by exhaustive sequential-placement search, that every delivered piece set is fully placeable so the learned track can never degrade the constructive-feasibility guarantee of the rule track. A self-play reinforcement-learning placement agent, supervised by auxiliary tasks that expose per-shape placeability to shared representations, is used to diagnose the game's dominant failure mode: at high board fill, long-bar pieces lose the majority of their legal placements. Across 234,000+ self-play episodes the agent reaches a 35.6\% win rate (median score 4,200), and controlled simulation shows that at board fill rates of 70--75\%, 33--56\% of long-bar pieces have no legal placement, while spawn difficulty distributions are statistically indistinguishable between won and lost games---evidence that board-state degeneration, not content difficulty, drives late-game failure. Head-to-head ablations show that per-shape placeability supervision---not aggregate difficulty features---drives the representation gain, and a 14-day online gray rollout (48,000 players; sample-ratio verified, CUPED-adjusted) lifts day-1 retention by 1.8 percentage points and session duration by 7\% over the rule track alone, quantifying the neural track's asymmetric upside in live play.

Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)

arXiv:2609.22177 [cs.LG]

(or arXiv:2609.22177v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.22177 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.