I wonder if we could get prof Erik Demaine in here. He has a pretty good handle on what it takes to reduce a problem to a known strongly NP-hard problem.

For instance, he's shown that playing "offline" Tetris optimally, or more precisely, given a known Tetris board configuration, and some known future Tetris pieces, can we get to a board configuration that is not a game over, is NP-complete, by reducing the game to 3-PARTITION (which I believe is reducible to SAT, but don't quote me on that)..

In terms of Tetris, my question above is, if we view board configurations and pieces as *resources*, can we even produce *any* valid new resource (that being any specific board configuration) following the rules of the game without getting a game over?