Tetris Is Hard: NP-Hard

bughunter writes "Analysts at MIT Laboratory for Computer Science, who have been busy translating, rotating and dropping, have demonstrated what the rest of us suspected: Tetris is hard. Technically, it's 'NP-hard,' meaning that there is no efficient way to calculate the necessary moves to "win," even if you know in advance the complete order of pieces, and are given all the time you need to make each move. At least there's one geek classic that refuses to fall to the scrutiny of mathematicians."

Comments

Re:Further studies...

[Flakeloaf]

Next we'll see occultists studying Pacman.

At least Pacman has a perfect solution. No fancy math required, just a good hot meal beforehand and a little patience.

NOW I'VE GOT MY EXCUSE!

[fireboy1919]

Now whenever I lose the latest new game I can just say, "I have just determined that this game is very hard. Its NP-Hard, in fact." I'm sure that'll impress all the lady-geeks around that would otherwise have thought me intellectually inferior for losing the game.

Interesting thing about NP-hard stuff, though, especially when it comes to things like video games. There are a group of techniques that work to solve NP-hard problems SOME of the time based around searching. Because there are multiple winning solutions for Tetris, and there is are several quite obvious heuristics to aid in the search (such as planning so that you leave indentations that will fit the next piece(s), and attempting to fill lower lines before higher ones), it's probably still solvable in polynomial time MOST of the time.

Of course, solvable is relative. The optimal solution (highest score) for a finite number of moves cannot be proven without trying all combinations of states, but to simply finish, there are lots of solutions.

Re:Tetris "ends"?

[fireboy1919]

Depends on the version. For the original gameboy version, in the count up mode (starting at level 1 and going up), you got to see images of a spaceship every 10 levels (if I remember right).

It launched when you reached the final level, I think. I did it once, and was very happy, but it sure wasn't as much fun as the game itself.

If you play the countdown mode (start with 40 pieces at a constant level and eliminate all of them) at the highest level (9, I think, or maybe 10), then when you finish you got to hear all of the instruments playing together (each of the other levels had instruments playing).

The ending of Dr. Mario was a lot more interesting.

Wait a second...

[Chemical]

A lot of Tetris and Tetris type games had a two player mode that had the option for CPU controlled player two if you didn't have any friends. If you set the AI to the maximum level, you would be instantly crushed no matter how good you were. The CPU could instantly decide where to place the blocks, and never made a bad move. Try setting Tetris Attack for the SNES to play against itself for a while. It's kind of impressive.

My question is this: How is it Nintendo et. al. can program an incredibly skilled Tetris AI, but scientists at MIT cannot?

Tetiris / Eyeball RSI Warning

[Boss, Pointy Haired]

Just a warning to those becoming or already hooked on Tetris.

I used to be a serious Tetris junkie, and played on many different versions on different platforms.

Playing so much, I became "quite good", and this meant that blocks were falling extremely rapidly.

To play tetris at high speed, you glance very quickly at the arriving piece, then move your gaze back to the pile to asses the position - moving the piece without looking at it. Repeat until bored.

Then my eyes packed up. I basically developed something like "RSI" in both eyes - my eyes would twitch repeatedly up and down in the exact movements used in high speed tetris. This whilst not even playing tetris.

I diagnosed the problem myself and quit playing, but it took a few months to clear up.

Just a warning. I still play it on and off.

Earlier Tetris Papers on 'Loseability'

[Keev]

Some little-known related references: A CS student at Univ of BC, John Brzustowski, did his Master's thesis on the problem of winning at Tetris if the computer is aware of your moves and reacting to them. He apparently proved that there is a finite sequence of tetrominos, which, if the machine selects them, you must lose. His work is cited in this later paper by H. Burgiel called "How to Lose at Tetris", which proves more generally that the computer can always produce a sequence of lose-forcing tetrominos, whether or not it's aware of your moves: paper is here.