用强化学习评估俄罗斯方块谜题规则难易度，发现预览和暂存越强越简单。
Evaluating Game Difficulty in Tetris Block Puzzle
- 用随机版AlphaZero（SGAZ）模拟不同规则下的游戏表现
- 预览和暂存功能提升后，奖励更高且收敛更快，难度降低
- 新增方块类型增加难度，尤其是T形方块导致最慢
Tetris Block Puzzle 是一种单人随机性拼图游戏，玩家在8×8网格上放置方块完成行；其流行变体已获得数千万次下载。尽管影响力大，但缺乏对规则难易程度的系统评估。受此前使用AlphaZero评估国际象棋变体的启发，我们采用针对随机环境的预算感知规划代理Stochastic Gumbel AlphaZero（SGAZ），评估包括暂存块数h、预览块数p以及额外方块变体在内的规则变化。通过训练奖励和收敛迭代次数等指标进行分析，实验表明：增加h和p可降低难度（奖励更高、收敛更快），而引入更多方块变体则提高难度，其中T形五连方块造成最大性能下降。分析显示，SGAZ在小模拟预算下仍能实现强策略，支持高效、可复现的规则对比，为未来随机拼图游戏设计提供基准参考。
原文摘要 · Abstract (English)
Tetris Block Puzzle is a single player stochastic puzzle in which a player places blocks on an 8 x 8 grid to complete lines; its popular variants have amassed tens of millions of downloads. Despite this reach, there is little principled assessment of which rule sets are more difficult. Inspired by prior work that uses AlphaZero as a strong evaluator for chess variants, we study difficulty in this domain using Stochastic Gumbel AlphaZero (SGAZ), a budget-aware planning agent for stochastic environments. We evaluate rule changes including holding block h, preview holding block p, and additional Tetris block variants using metrics such as training reward and convergence iterations. Empirically, increasing h and p reduces difficulty (higher reward and faster convergence), while adding more Tetris block variants increases difficulty, with the T-pentomino producing the largest slowdown. Through analysis, SGAZ delivers strong play under small simulation budgets, enabling efficient, reproducible comparisons across rule sets and providing a reference for future design in stochastic puzzle games.
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