Evaluating Game Difficulty in Tetris Block Puzzle

2026-03-19

AI Summary

This study addresses the lack of systematic methods for evaluating the difficulty of different rule sets in Tetris-like puzzle games. It presents the first application of Stochastic Gumbel AlphaZero (SGAZ) to stochastic puzzle games, leveraging metrics such as training rewards and convergence speed under limited simulation budgets to efficiently and reproducibly quantify difficulty differences across rule variants. Experimental results demonstrate that increasing the number of hold pieces (h) and preview pieces (p) significantly reduces game difficulty, whereas introducing complex polyominoes—such as the T-pentomino—substantially increases it. Notably, SGAZ learns strong policies even under small computational budgets, establishing a reliable benchmark for difficulty assessment in game design.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Humans and AI: Game Design — Procedural Content Generation & Storytelling
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Game Difficulty
• Tetris Block Puzzle
• Rule Evaluation
• Stochastic Puzzle
• Difficulty Assessment

Innovation

• Stochastic Gumbel AlphaZero
• game difficulty evaluation
• Tetris Block Puzzle
• budget-aware planning
• rule variant analysis