All the Best Games May Be NP-Hard

Catullus writes "Following in the footsteps of Tetris and Minesweeper, the simple yet addictive multiplatform game Flood-It is the latest puzzle to be proven to be hard — NP-hard, to be exact. This means that there's no way to write an efficient program to beat the game, unless P=NP. This research by computer scientists from Bristol University raises the intriguing question: are these games fun precisely because they're hard for computers to solve, and need a spark of human creativity?"

Comments

The fun is in the simplicity

[Pojut]

Tetris, to me, is the ultimate video game. It can be played by anyone ranging from someone who doesn't even know what a video game is all the way to competitive level hardcore pros.

No other video game in history has that kind of audience. The fact that, although variations on the original have been released, the most popular version is still the original version (which has remain mostly untouched throughout its existence) just gives more credit to its simplistic genius.

Re:The fun is in the simplicity

[mdarksbane]

There's a problem, though - both Go and Chess are generally multiplayer games. Tetris is in its purest form singular. Any sort of competitive game is much harder to get into for a novice, as it is only fun for them to be playing other novices, and you have the situation you see in general with Chess and Go - the few people who are really good, and the many who rarely play because they do not have the dedication to compete.

Look at the many addictive "casual" games - almost all of them are single player, and the ones that are multiplayer (such as farmville, or even wow) are multiplayer mostly in the social aspect than in the competitive aspect. There's a reason the majority of WoW players are on PvE. When you are facing a controlled computer opponent, you can apply a constantly ramping difficulty level that starts at a place a novice can still have fun. When you're playing competitively, the moment you have a significant skill imbalance the fun disappears.

Just to throw this out there

[NitsujTPU]

Since I had to suffer through at least one professor who didn't understand basic complexity theory last night, and I know that Slashdot generally screws it up to.

NP-Hard means that there's no (deterministic) polynomial-time algorithm to solve the games. Additionally, you always have to generalize these games in order to make that claim. Since computational complexity is defined in terms of the length of the input, and certainly all of these games are being played on an input of fixed length.

However, there are effective approaches to solving NP-Hard problems. There are solvers for known NP-Hard problems. If you Google "sat solver" you'll find at least 5 that you can just download. SAT solvers are used in VLSI validation and other practical things. These solvers use heuristics to improve search performance, generally proposing answers and checking them (for NP-Complete problems).

Also, there are tons of games known to be NP or PSPACE complete. The reductions for those games are kind of a standard problem, since the AI community writes a bunch of these solvers.

Re:Oblig XKCD

[bondsbw]

You can play it here. I'd say it's undecidable.

Re:chess and go aren't np-hard, but they are also

[Bob Hearn]

Chess and Go are actually EXPTIME-complete, even harder than NP-complete problems and PSPACE-complete problems.

In general, one-player games of bounded length (like Flood-It, or Sudoku) tend to be NP-complete; one-player unbounded games (like sliding-block puzzles, or Sokoban) tend to be PSPACE-complete; two-player bounded-length games (like Hex, or Amazons) also tend to be PSPACE-complete, and two-player unbounded games (like Chess, Checkers, and Go) tend to be EXPTIME-complete.

I can't resist here a plug for my book (with Erik Demaine), Games, Puzzles, and Computation, which discusses all these issues in detail. A theme running throughout the book is the same as the view expressed in this paper: most interesting games and puzzles seem to be as hard as their "natural" complexity class, outlined above.

nonsense

[pydev]

This means that there's no way to write an efficient program to beat the game, unless P=NP.

All these games are small finite size in practice, so asymptotic complexity results tell you nothing about how difficult it is to solve them. In addition, the idea that "P = efficient program" is utter nonsense; for large problems, even quadratic complexity is a serious problem. A realistic notion these days is that a reasonable asymptotic complexity for "efficient programs" is no worse than n log^k n for small k. Anything larger than that and it won't scale. The converse is also nonsense. Just because a particular problem is NP hard in general doesn't mean that the problem instances you encounter in practice are hard cases. Furthermore, the assumption that you need to find an optimal solution is also wrong. In fact, in any competitive game, all you really care about is beating the other guy.

P=NP is a neat theoretical issue in computer science, but its practical significance has been completely overstated.