Is chess a solvable game?

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dagno75

I was wondering, since there are many games that are solvable and have been solved, is there a mathematical solution to chess? An example of a solved game is tic tac toe, as in there is a proven way to win if you go first, or draw the game every time regardless of whether you go first or second. With that same logic, would it be possible to make a certain sequence of moves in chess that would guarantee a win or a draw? While chess is magnitudes more complicated than tic tac toe and the number of possible games and outcomes is incomprehensibly huge, it is still finite, right? Is there such a thing as a perfect chess game?

llamonade2
bkim777 wrote:

While chess is magnitudes more complicated than tic tac toe and the number of possible games and outcomes is incomprehensibly huge, it is still finite, right? Is there such a thing as a perfect chess game?

Yes and yes.

 

bkim777 wrote:

would it be possible to make a certain sequence of moves in chess that would guarantee a win or a draw?

Yes, although just as tic tac toe has multiple perfect games, so does chess, and of course for chess there is an enormous number of them.

 

bkim777 wrote:

Title:
Is chess a solvable game?

Mathematically, yes, it's solvable.


Practically no. The scale is too large to solve it like tic tac toe. You'd need a storage device (much) larger than the earth.

blueemu

- You'd need a storage device (much) larger than the earth.

Much, much larger. The entire visible universe contains only about 10^78 particles, and there are far more chess sequences than that.

llamonade2

You'd store positions not sequences, so that reduces it quite a lot.

But it'd still be much (much) larger than the earth like you said happy.png

llamonade2

If you have no concept of scale, then anything and everything seems possible.

Like doubling grains of rice every day. At first it's nothing, then it's enormous, but if you go on long enough, the numbers become so large they don't make sense anymore.

A storage device as large as the earth doesn't make sense.

WSama

Chess has already been been solved. It's solved by the winner of the match 😁.

Chessique mathematics states that there is no winning sequence in the beginning. You can't win a game from simply playing 1.e4, because of the counter factor.

You have to change your entire way of thinking. Chess is solvable, but it is not static in nature, therefore there is no sure win sequence so long as the opponent still possesses the counter factor.

I explained this before: there is no opponent in chess, only two partners working together to test the boundaries of mathematical precision. The counter factor makes chess a draw under perfect play, and yet chess is to see the draw and avoid it by all means until the two minds 'crack'.

bong711

100 TB SSD

Strangemover
Chebyshevv wrote:

If you have no concept of scale, then anything and everything seems possible.

Like doubling grains of rice every day. At first it's nothing, then it's enormous, but if you go on long enough, the numbers become so large they don't make sense anymore.

A storage device as large as the earth doesn't make sense.

It's true that enormous numbers mean little as they are hard to conceptualise. For example, the national debt of the UK was recorded earlier this year as £1823,000,000,000. The US is somewhere around 20 trillion dollars - even more 0's. 

WSama

As it stands, standard chess is a draw, that's the simple truth. That's the easy part.

Chess is a game of strategy. The game is already drawn in the technical sense, but that's not the point. The board facilitates a game of strategy. The board is a medium for two players to test each other's stategy. 

llamonade2

As far as humans are concerned, it might as well be solved. If you can memorize everything engines put out (the solution to solved chess would not be simpler) then you'll win every game you play.

Of course that's impossible, but in human games there's more. Because we're not perfect the extra element involves practical decision making, for example a "bad" gambit that forces the opponent to be accurate while your moves are easy. In timed games (which include long FIDE games between professionals) these types of decisions are very important. I recall Aronian making a "bad" sacrifice against Grischuk and winning because Grischuk was in his characteristic time trouble.

WSama

In other words, chess is a gaming platform that allows two players to create a game of strategy. The platform is non-biased, and thus allows for equal opportunities right from the get go.

bong711

Chess engines play almost Perfect chess. Humans can't including Super GMs. Chess solved doesn't make chess less fun.

llamonade2
bong711 wrote:

almost Perfect chess

that's hard to quantify tongue.png

bong711

Someday when i bought myself an expensive computer, i will prove the Ruy Lopez Berlin Wall is a Win for White happy.png

GameChanger2020

I think this is my answer, that it is hard to truly "solve" a game, in which "solve" is not defined. In chess, you don't really solve something. I guess, you could mean to become a perfect chess master, which is next to impossible.

llamonade2

He defined it pretty well by using words like "mathematical solution" and "prove" and comparing it to tic tac toe. In other words a true and total solution (like a 32 man EGTB).

Whether or not we could ever make something that could e.g. draw >95% of its games against a 32 man EGTB is an interesting question. I have no idea.

Also interesting is the idea that a 32 man EGTB is not a perfect player in the sense that it treats all drawing (or winning) moves with an equal value. If we imagine an engine that can draw 95% of its games against an EGTB that randomly selects a best move, it's not hard to further imagine that this engine will preform much worse against a version that favors drawing moves that lead to the highest complexity.

FindingFreeNameIsHard

I think they will be solved once we master quantum computers and probably even before we truly "master" them. Even if we want to store such data (tho I wouldn't do it, as it doesn't make sense for me), there will be solution. We are constantly solving problems that by some were seen as unthinkable... Solving chess wouldn't break any rules of physics IMO.

I would reccomend some videos on quantum computers to grasp, why chess would be just small problem for quantum computers. Here's good video for starters I believe : https://www.youtube.com/watch?v=JhHMJCUmq28

 

However - unless perfect game will be like 10 moves*, than I don't think anyone will ever learn what move to play against every other move from opponent. You can probably ignore many, many, many moves opponent can do, if they are not interfering with optimal play enough, but still there would be a lot of moves to learn... So I would guess/hope that finding solution won't destroy human-chess... But than there will be cyborgs, so we fill find some variant of chess for cyborgs, etc. etc. Future problems - future solutions, we do it all the time - problem solving.

 

* - I don't know how many moves computers already calculated, but I would guess number will be to big for human anyway.

Jacks_Return_Home
WSama wrote:

As it stands, standard chess is a draw, that's the simple truth. That's the easy part.

Chess is a game of strategy. The game is already drawn in the technical sense, but that's not the point. The board facilitates a game of strategy. The board is a medium for two players to test each other's stategy. 

I dont think your assumption is correct. There is almost definitely a way to play chess where one side wins. It is not known if it is black or white yet, but it is almost a certainty. But since the possible chess games are more numerous than atoms in the universe, it may take long time for humans to find this game. 

tygxc

Chess has been conjectured to be a draw by Steinitz, Lasker, Capablanca, Fischer, Kasparov and TCEC and ICCF and AlphaZero corroborate that. Checkers was also conjectured to be a draw long before it was mathematically proven to be a draw by forward calculating towards a 10 men table base.
Chess is more complicated than checkers. Chess has 10^45 possible positions.
https://tromp.github.io/chess/chess.html Many of these are either illegal or irrelevant. There are probably 10^20 relevant positions. The Sesse computer looks at 10^8 nodes per second, so it would need 10^12 seconds = 31000 years. A quantum computer can do in 200 s what a supercomputer takes 10000 years. https://www.bloomberg.com/news/articles/2019-10-23/google-says-quantum-computer-beat-10-000-year-task-in-minutes So a quantum computer is expected to solve chess in 600 seconds.

DLPB

No, it isn't.