cs.LGAug 27, 2026

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

Authors: Jiang Jun

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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.

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