Wang et al.: Gauging Tetris Block Puzzle Difficulty by How Fast a Strong AI Learns — Fukai Reads

TL;DR

Today I read a study that measures how the difficulty of the popular mobile game "Tetris Block Puzzle" (a single-player puzzle where you place tetromino-shaped blocks on an 8×8 grid and clear full rows or columns) shifts when you tweak its rules — by having a strong AI play it. The authors are a group from National Yang Ming Chiao Tung University and Academia Sinica in Taiwan, and it is an arXiv preprint (a not-yet-peer-reviewed manuscript) posted in March 2026.

The core idea is that instead of surveying humans, they use how fast and how high an AlphaZero-style strong AI can learn to play as a proxy for difficulty. The results largely match intuition: adding more choosable pieces (holding blocks) makes the game easier, and adding more previewable upcoming pieces also makes it slightly easier. Conversely, adding new block shapes makes it harder, and the T-shaped five-cell block (T-pentomino) slowed learning the most. This article aims to convey the gist without you opening the paper.

Introduction

The authors are Chun-Jui Wang, Jian-Ting Guo, Hung Guei, Chung-Chin Shih, Ti-Rong Wu, and I-Chen Wu — six people affiliated with National Yang Ming Chiao Tung University (NYCU, Hsinchu) and Academia Sinica (Taipei), Taiwan. It is an arXiv preprint (arXiv:2603.18994, submitted March 19, 2026, revised to v2 the next day); as far as I could confirm, the text names no peer-reviewed venue, so I treat it throughout as a preprint.

Why pick this one today? For those of us who make puzzles daily, "which way does difficulty move when I tweak one rule?" is the question we most want answered yet find hardest to measure. Human playtests are expensive, and checking only the final answer hides the difficulty along the way. This paper offers a down-to-earth tool: use "how easily a strong AI learns" as that yardstick. It is not flashy, but it is close to practice — which is why I want to introduce it.

Background

First some background. There is AlphaZero — the leading example of reinforcement learning (a framework that learns, by trial and error, the actions that raise a reward) that, using no human game records and only self-play, came to play Go, chess, and shogi at superhuman level. But AlphaZero offers no guarantee of getting stronger when the number of look-ahead "simulations" per move is small.

Gumbel AlphaZero fixes that: it is a variant that reworks how moves are chosen at the root (the current position) so that improvement is guaranteed even with few simulations. On top of that, to handle "luck-driven" settings like Tetris where blocks fall at random, there is Stochastic AlphaZero, a variant that builds its search tree by separating the effects of one's own action from the environment's random branching. Combining the two gives this paper's tool, Stochastic Gumbel AlphaZero (SGAZ); the authors note this line was already shown effective on the puzzle game 2048.

The very idea of "using a strong AI as a difficulty yardstick" is not new. The authors cite prior work that used AlphaZero to gauge the balance of chess rule variants, and say they bring the same "evaluate via a strong agent" style to this puzzle. So the novelty here, as I read it, lies less in the method itself than in applying it to a target: rule design for stochastic puzzles.

Approach

Here is the method in plain terms. The board is 8×8. Tetrominoes (blocks made of four cells) are dealt as a hand, and the player places them into empty cells in their given orientation, without rotating. When a row or column fills up it clears for 1 point, and the hand is replenished as pieces are used. The authors add three dials to this.

The first is holding blocks h (how many pieces you can currently choose from). The second is preview blocks p (how many upcoming pieces you can see ahead — an element absent from the classic rules). The third is added blocks: alongside the standard tetrominoes, they mix in the five-cell U, V, X, and T pentominoes. The classic rule is defined as h=3, p=0, no additions.

Difficulty is measured by two numbers from AI play. One is "training reward" (average score over the final 50 training iterations; higher means the AI plays well, i.e. easier). The other is "convergence iterations" (how many training iterations it takes to reliably hit the maximum score across three consecutive iterations; fewer means faster mastery, i.e. easier). The implementation uses the open framework MiniZero, and computation ran on four 1080Ti GPUs. To keep a game from running forever, the score cap is set to 6750 points.

Findings

Let me lay out the main results with the paper's own numbers. Under the classic rule (h=3, p=0), SGAZ reached an average of 6544 points after 500 training iterations — quite close to the 6750 cap, showing first that this AI can indeed play well (source: paper Fig. 2).

Changing the hand size h makes a dramatic difference. With p=0, h=1 gave a reward of just 39.0 and the AI could barely play (the authors call it "too difficult, unsuitable"); h=2 gave 4126.1 and h=3 gave 6544.0 (Table 1). For convergence iterations, h=1 did not converge within training, h=2 took 160 iterations, and h=3 took 61 (Table 2). In short, more pieces in hand clearly makes it easier.

Increasing preview p also makes it easier, but the authors say the effect is weaker than h. With small p, reward rises slowly and plateaus around 5000, while larger p easily surpasses that. Adding block types, on the other hand, lowers reward in every case (harder), and the T-pentomino has the largest impact — its convergence was always the slowest when added singly. With h=2, p=0, every experiment that added two block types failed to converge within training.

Use cases

Here are concrete ways makers can use this. First: if you are building a falling/placement puzzle and want to shape a difficulty curve, you can split roles — "hand size" as the primary coarse dial, "preview count" as the fine-tuning dial — because the paper's numbers show h has a stronger effect than p (mind the limitations below, though).

Second: when adding new piece shapes to raise the challenge, you can use the AI to guess "which shape is toughest" before human playtesting. First narrow down, by machine, the hypothesis that awkward-to-fit shapes like the T-pentomino push difficulty up a lot, then run human tests only on the shortlisted candidates.

Third: in a daily-puzzle operation that tweaks rules every day, you want to auto-check before shipping whether "this variant is solvable, and if so, whether it is hellish." Since SGAZ plays strongly even with little search, you can lightly train per variant and watch "does it converge / where does reward plateau," filtering out obviously dead configurations (like h=1) before release. Fourth, you could mechanically draft a stage ordering from easy to hard, using the AI's convergence iterations as a proxy metric.

Limitations

Now the limitations. What the authors themselves admit first: this is difficulty for an AI, and they have not yet measured how hard or how fun humans find it. The paper explicitly states plans to address variants such as "changing board size," "banning certain blocks from being chosen," and "new block shapes," together with perceived difficulty ratings from human players.

What I (Fukai) would point out here is the granularity of the metric and the danger of extrapolation. Moving the hand from h=1 to h=2 alone leaps the reward from 39 to 4126. That is less a "dial that changes difficulty smoothly" and more a cliff. So "more h makes it easier" is right as a direction, but the steps in between should be read as very coarse.

One more thing. For settings that did not converge, we learn only that they are "harder than the trainable range," not how much harder (it is, in effect, data that hit the ceiling). There is ordering information but no distance information. Also the experiments are small — one game, four GPUs, on the order of 500 iterations — and this is a brand-new preprint with no citations yet, so I would receive the conclusions only as "under these conditions, this was observed."

Fukai's Reading

From here it is my own reading. I want to place this study as a quiet but essential step from an era of "asking humans about difficulty" to one of "proxying difficulty by the learning cost of a strong solver." In the language of design criticism, this is an attempt to outsource part of playtesting to "how fast an AI learns." It cannot measure fun itself, but as a safety net for detecting signs of a dead-end or a grind before shipping, it is practical enough — and I read it as immediately useful for our own daily-puzzle operation. This paragraph alone is Fukai's personal interpretation.

Closing

In closing: if you want to dig deeper into the "measure difficulty with AI" approach, reading this paper's foundations together will give you the map — the study that used AlphaZero to gauge the balance of chess rule variants (Tomašev et al., 2020), and the one that solved 2048 with Gumbel MuZero (Kao et al., 2022), which underpins SGAZ. If you want to get hands-on, the MiniZero framework the authors used is a good entry point. For difficulty evaluation that includes human perception, I will wait for the authors' next work.

References

Papers and related materials referenced in this article:

・Evaluating Game Difficulty in Tetris Block Puzzle (Chun-Jui Wang, Jian-Ting Guo, Hung Guei, Chung-Chin Shih, Ti-Rong Wu, I-Chen Wu, 2026, arXiv preprint arXiv:2603.18994)

・Related (implementation framework): MiniZero: Comparative Analysis of AlphaZero and MuZero on Go, Othello, and Atari Games (Wu et al., IEEE Transactions on Games, 2025)

・Related: Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess (Tomašev et al., 2020) — prior work evaluating rule variants with a strong AI

・Related: Gumbel MuZero for the Game of 2048 (Kao et al., TAAI 2022) — the stochastic-environment method underpinning SGAZ