Extending two-piece results to Tetris survival and to a hold mechanic

Establish complexity results analogous to the two-piece clearing results for Tetris survival under the Super Rotation System (SRS), and analyze the effect of adding a single-piece "holding" function on the complexity of survival or clearing with restricted piece sets.

Background

This work shows NP-hardness for Tetris survival in the "hard drops only" and "20G" modes using the two-piece set {I, O}, improving prior results that required five pieces. However, a comprehensive classification for survival with two-piece subsets under standard SRS is not provided.

The authors also highlight a natural gameplay feature—holding one piece—that could change complexity; understanding whether similar hardness results persist with a hold mechanic remains open.

References

Some open questions arise regarding whether our results can be extended if we consider different objectives or add additional features. For example, can we establish results for 2-piece subsets, similar to those in Section \ref{sec:2piecetetris}, for Tetris survival? If we add a "holding" function, where the player can put one piece aside for later use, can get similar results?

— Tetris with Few Piece Types (2404.10712 - Group et al., 16 Apr 2024) in Section 7 (Open Problems)