Is there a perfect algorithm for chess? [closed]

Answer 1

I know this is a bit of a bump, but I have to put my 5 cents worth in here. It is possible for a computer, or a person for that matter, to end every single chess game that he/she/it participates in, in either a win or a stalemate.

To achieve this, however, you must know precisely every possible move and reaction and so forth, all the way through to each and every single possible game outcome, and to visualize this, or to make an easy way of analyising this information, think of it as a mind map that branches out constantly.

The center node would be the start of the game. Each branch out of each node would symbolize a move, each one different to its bretheren moves. Presenting it in this manor would take much resources, especially if you were doing this on paper. On a computer, this would take possibly hundreds of Terrabytes of data, as you would have very many repedative moves, unless you made the branches come back.

To memorize such data, however, would be implausable, if not impossible. To make a computer recognize the most optimal move to take out of the (at most) 8 instantly possible moves, would be possible, but not plausable... as that computer would need to be able to process all the branches past that move, all the way to a conclusion, count all conclusions that result in a win or a stalemate, then act on that number of wining conclusions against losing conclusions, and that would require RAM capable of processing data in the Terrabytes, or more! And with todays technology, a computer like that would require more than the bank balance of the 5 richest men and/or women in the world!

So after all that consideration, it could be done, however, no one person could do it. Such a task would require 30 of the brightest minds alive today, not only in chess, but in science and computer technology, and such a task could only be completed on a (lets put it entirely into basic perspective)... extremely ultimately hyper super-duper computer... which couldnt possibly exist for at least a century. It will be done! Just not in this lifetime.

Answer 2

Lots of answers here make the important game-theoretic points:

1. Chess is a finite, deterministic game with complete information about the game state
2. You can solve a finite game and identify a perfect strategy
3. Chess is however big enough that you will not be able to solve it completely with a brute force method

However these observations miss an important practical point: it is not necessary to solve the complete game perfectly in order to create an unbeatable machine.

It is in fact quite likely that you could create an unbeatable chess machine (i.e. will never lose and will always force a win or draw) without searching even a tiny fraction of the possible state space.

The following techniques for example all massively reduce the search space required:

• Tree pruning techniques like Alpha/Beta or MTD-f already massively reduce the search space
• Provable winning position. Many endings fall in this category: You don't need to search KR vs K for example, it's a proven win. With some work it is possible to prove many more guaranteed wins.
• Almost certain wins - for "good enough" play without any foolish mistakes (say about ELO 2200+?) many chess positions are almost certain wins, for example a decent material advantage (e.g. an extra Knight) with no compensating positional advantage. If your program can force such a position and has good enough heuristics for detecting positional advantage, it can safely assume it will win or at least draw with 100% probability.
• Tree search heuristics - with good enough pattern recognition, you can quickly focus on the relevant subset of "interesting" moves. This is how human grandmasters play so it's clearly not a bad strategy..... and our pattern recognition algorithms are constantly getting better
• Risk assessment - a better conception of the "riskiness" of a position will enable much more effective searching by focusing computing power on situations where the outcome is more uncertain (this is a natural extension of Quiescence Search)

With the right combination of the above techniques, I'd be comfortable asserting that it is possible to create an "unbeatable" chess playing machine. We're probably not too far off with current technology.

Note that It's almost certainly harder to prove that this machine cannot be beaten. It would probably be something like the Reimann hypothesis - we would be pretty sure that it plays perfectly and would have empirical results showing that it never lost (including a few billion straight draws against itself), but we wouldn't actually have the ability to prove it.

Additional note regarding "perfection":

I'm careful not to describe the machine as "perfect" in the game-theoretic sense because that implies unusually strong additional conditions, such as:

• Always winning in every situation where it is possible to force a win, no matter how complex the winning combination may be. There will be situations on the boundary between win/draw where this is extremely hard to calculate perfectly.
• Exploiting all available information about potential imperfection in your opponent's play, for example inferring that your opponent might be too greedy and deliberately playing a slightly weaker line than usual on the grounds that it has a greater potential to tempt your opponent into making a mistake. Against imperfect opponents it can in fact be optimal to make a losing if you estimate that your opponent probably won't spot the forced win and it gives you a higher probability of winning yourself.

Perfection (particularly given imperfect and unknown opponents) is a much harder problem than simply being unbeatable.

Answer 3

"Is there a perfect algorithm for chess?"

Yes there is. Maybe it's for White to always win. Maybe it's for Black to always win. Maybe it's for both to always tie at least. We don't know which, and we'll never know, but it certainly exist.

See also

• God's algorithm

Answer 4

I know next to nothing about what's actually been discovered about chess. But as a mathematician, here's my reasoning:

First we must remember that White gets to go first and maybe this gives him an advantage; maybe it gives Black an advantage.

Now suppose that there is no perfect strategy for Black that lets him always win/stalemate. This implies that no matter what Black does, there is a strategy White can follow to win. Wait a minute - this means there is a perfect strategy for White!

This tells us that at least one of the two players does have a perfect strategy which lets that player always win or draw.

There are only three possibilities, then:

• White can always win if he plays perfectly
• Black can always win if he plays perfectly
• One player can win or draw if he plays perfectly (and if both players play perfectly then they always stalemate)

But which of these is actually correct, we may never know.

The answer to the question is yes: there must be a perfect algorithm for chess, at least for one of the two players.

Answer 5

This is not a question about computers but only about the game of chess.

The question is, does there exist a fail-safe strategy for never losing the game? If such a strategy exists, then a computer which knows everything can always use it and it is not a heuristic anymore.

For example, the game tic-tac-toe normally is played based on heuristics. But, there exists a fail-safe strategy. Whatever the opponent moves, you always find a way to avoid losing the game, if you do it right from the start on.

So you would need to proof that such a strategy exists or not for chess as well. It is basically the same, just the space of possible moves is vastly bigger.

Answer 6

"I argued that there could not exist a deterministic Turing machine that always won or stalemated at chess."

You're not quite right. There can be such a machine. The issue is the hugeness of the state space that it would have to search. It's finite, it's just REALLY big.

That's why chess falls back on heuristics -- the state space is too huge (but finite). To even enumerate -- much less search for every perfect move along every course of every possible game -- would be a very, very big search problem.

Openings are scripted to get you to a mid-game that gives you a "strong" position. Not a known outcome. Even end games -- when there are fewer pieces -- are hard to enumerate to determine a best next move. Technically they're finite. But the number of alternatives is huge. Even a 2 rooks + king has something like 22 possible next moves. And if it takes 6 moves to mate, you're looking at 12,855,002,631,049,216 moves.

Do the math on opening moves. While there's only about 20 opening moves, there are something like 30 or so second moves, so by the third move we're looking at 360,000 alternative game states.

But chess games are (technically) finite. Huge, but finite. There's perfect information. There are defined start and end-states, There are no coin-tosses or dice rolls.