# Evaluating Game Difficulty in Tetris Block Puzzle

arXiv: https://arxiv.org/abs/2603.18994 · HTML: https://mlsanity.com/paper/2603.18994/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess](https://mlsanity.com/paper/2009.04374/) (2020)
- [MiniZero: Comparative Analysis of AlphaZero and MuZero on Go, Othello, and Atari Games](https://mlsanity.com/paper/2310.11305/) (2023)
- [AlphaDDA: Strategies for Adjusting the Playing Strength of a Fully Trained AlphaZero System to a Suitable Human Training Partner](https://mlsanity.com/paper/2111.06266/) (2021)

## Built on by (most cited first, 1 of 1)

- [WallZero: Mastering the Game of WallGo with Strategic Analysis](https://mlsanity.com/paper/2606.17847/) (2026)

## Abstract (arXiv)

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.