Related: in the official specification of the game the pieces ("tetrominoes") are drawn from a bag to prevent the possibility of an unfavorable sequence of pieces that force you to lose the game.<p>IIRC early implementations of the game did not always behave like that.<p><a href="https://tetris.fandom.com/wiki/Tetris_Guideline" rel="nofollow">https://tetris.fandom.com/wiki/Tetris_Guideline</a><p>> You might have heard of the result that you can play forever with bag randomizer, Hold and 3 previews (a similar setup even works with 0 previews). However, the opposite is true, if you play with a randomizer that can generate all piece sequences (e.g. memoryless randomizer). In this article we will present a piece sequence that will top you out - no matter what you do.<p><a href="https://harddrop.com/wiki/A_deadly_piece_sequence" rel="nofollow">https://harddrop.com/wiki/A_deadly_piece_sequence</a><p><a href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.8562&rep=rep1&type=pdf" rel="nofollow">https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55...</a>
If you want to test a strategy against an adversarial tetris opponent: <a href="https://qntm.org/files/hatetris/hatetris.html" rel="nofollow">https://qntm.org/files/hatetris/hatetris.html</a><p>The method by which the AI selects the worst possible piece is extremely simple to describe (test all possible locations of all possible pieces, see which of the pieces' best-case scenarios is the worst, then spawn that worst piece), but quite time-consuming to execute, so please forgive me if your browser chugs a little after locking each piece. If you can figure out a way to accelerate the algorithm without diminishing its hate-filled efficiency, do let me know. The algorithm for "weighing" possibilities is to simply maximise the highest point of the "tower" after the piece is landed.
There was a kid I knew in school who I would consider a very good tetris player. One time someone else was lamenting that they always get bad pieces and he said, "The Tetris gods will never give you a piece you can't play, you just don't know how to play it." Which has resonated with me for an oddly long time in my life.
qntm, creator of Hatetris [1], once did an analysis of this exact problem using brute force methods. While he managed to solve the problem for 4, 6 and 8 wide boards (including the minimum board height required, assuming game over if any part of a piece locks above the ceiling), solution eluded him for 10 wide, though he did prove that 6 height was insufficient.<p>As it happens, since this work assumes a 20 high board and there are some sequences (e.g. ZSOLJJJ) for which the solution here goes up to height 8 (it could potentially go up to height 9 but I have no plans to check), there's a little bit of a gap that still needs to be filled.<p>[1] <a href="https://qntm.org/hatetris" rel="nofollow">https://qntm.org/hatetris</a><p>[2] <a href="https://qntm.org/tetris" rel="nofollow">https://qntm.org/tetris</a>
Yes in "Tetris Guidelines". In fact, greater feats can be accomplished in modern Tetris games, thanks to these strong guidelines.<p><a href="https://www.youtube.com/watch?v=qmG0NcbrLTE" rel="nofollow">https://www.youtube.com/watch?v=qmG0NcbrLTE</a><p>Strong players practice these loops all the time. Its possible thanks to the "bag randomizer".<p>--------<p>The BT Cannon is a TSpin double (4 damage + B2B bonus) + TSpin Triple (6 damage + B2B bonus), for a total of 11 damage.<p>The DT-cannon followup is a TSpin Triple followed by TSpin Double for a total of 12 damage.<p>Finally, the Perfect Clear is 10 damage, for a total of 33 damage per loop.<p>--------<p>Other players practice triple-perfect clear starts, for 30-straight damage in some ~30 tetriminos dropped. But the BT-cannon + DT Cannon -> Perfect clear setup is a beautiful arrangement.<p>The whole loop is carried out over 5 bags IIRC, or 35 pieces (5 bags * 7 pieces per bag == 35 sets of each piece). That's enough for the 4x T-pieces needed for the BT-cannon + DT Cannon (which offer significant amounts of damage)<p>35 pieces * 4 pieces == 140 minos, or 14 lines (the Tetris board is exactly 10 pieces wide). Which lines up with not only a perfect bag loop (the 35th piece finishes the bag, meaning piece#36 is a new bag, allowing you to loop), but also divides perfectly with 140 minos aka 14 lines, meaning the perfect clear is possible.<p>------<p>Thanks to Tetris Guidelines bag randomizer, bag#6 is effectively the same situation as bag#1 (start of a new bag). So you loop the sequence and can continuously apply the BT-cannon / DT-cannon / perfect clear loop almost perpetually. In practice, its "only" a 90%+ chance of continuing each loop, but that's a high enough probability to effectively use the technique in competitive games.<p>EDIT: The existence of the "Hold Piece", in combination with the "easy to count" 7-bag randomizer, allows for some incredible feats in Tetris Guidelines that classic-Tetris players are unfamiliar with. Its a different game, more about quick-reaction speed and twitch reaction rather than the planning-centric classic-Tetris. But its these attributes that make Tetris-Guideline games better for player-vs-player setups. Practiced strategies are more reliable and less contingent on luck.
This is one of those questions that <i>seems</i> to be wide open for elaborate proofs - but it turns out the total number of possibilities isn't that large, and you can simply enumerate each one.
Is there a good way to reduce SAT or other decision problems to Tetris? Do we need to enlarge the grid to reduce larger problem instances, or can the duration of the play / length of the sequence be used for that?<p>I would hope for something like "This list of clauses is satisfiable iff there is a winning strategy to clear at least N lines when given the following sequence of tetrominoes". (Where the article here says that there is no hope for anything like this with N=1, but )<p>Or does knowing the whole sequence in advance make any sequence easy to play / clear any number of lines?
> Mathematically, we can formulate this a sequential zero-sum game with perfect information.<p>Is this not just restating that Tetris is NP-hard? <a href="https://arxiv.org/abs/2009.14336" rel="nofollow">https://arxiv.org/abs/2009.14336</a>
This is a classic example of: "Assume a spherical cow". The game is also about hand/eye coordination, as well as solvability. So given the helpful precis:<p>"Summary: it is possible to play Tetris and guarantee that you will score at least one line, no matter which pieces are given to you, i.e., even assuming they are chosen adversarially."<p>We can confidently respond: "bollocks".<p>Great write up and analysis.