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.
Figures & tables
Figure 1: The gameplay of Tetris Block Puzzle. (a) The player chooses an O-tetromino from three holding blocks and places it (highlighted with a red border), completing a vertical line. This clears the line and earns the player 1 point. After the O-tetromino is taken, the first preview holding block, an S-tetromino, becomes a new holding block for the next turn. Then, a new preview holding block is randomly selected from the standard blocks shown in (b) and may be rotated.
Figure 2: The training curve for the classic game with h=3 and p=0 .
Figure 3: The training curve for p=0 with different h .
h
1
2
3
Reward
39.0
4126.1
6544.0
Table 1: The training rewards of the different numbers of holding blocks.
h
1
2
3
Convergence speed
-
160
61
Table 2: Convergence iterations for different numbers of holding blocks. The “-” mark indicates that the agent did not converge within training iterations.
Figure 4: The training rewards impact of different numbers of preview holding blocks. The blank areas are expected to be optimal, as their preceding settings are already optimal.
Figure 5: The training curve of different numbers of preview holding blocks under a fixed setting of holding blocks h=1 .
Figure 6: The training curve of different numbers of preview holding blocks under a fixed setting of holding blocks h=2 .
Figure 7: Impact of different numbers of preview holding blocks on convergence iterations. The mark of “X” area indicates that the agent did not converge within training iterations.
Figure 8: The U,V,X,T-pentomino blocks.
Figure 9: The training rewards impact of adding additional blocks.
Figure 10: The convergence iterations impact of adding additional blocks.