Evaluating Game Difficulty in Tetris Block Puzzle

TL;DR

This paper introduces a new evaluation method for Tetris puzzle difficulty using a specialized AlphaZero variant, providing insights into how rule changes affect game complexity and offering a reproducible benchmarking approach.

Contribution

It presents Stochastic Gumbel AlphaZero (SGAZ), a novel planning agent for stochastic puzzles, and applies it to systematically assess rule modifications in Tetris.

Findings

Increasing hold and preview options reduces difficulty.

Adding more Tetris block variants increases difficulty.

SGAZ enables efficient, reproducible difficulty comparisons.

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.