Pardon the emoticon, I can't post without one. Technical difficulty.

Is chess infinite? Sometimes in an opening sequence (with a computer) I blunder more or less on purpose, impatient with a century-old sequence. I first noticed this when playing with a much-loved brother (now deceased) in the summer of '72, playing a dozen games a day during a heady time in the chess world. I was 12, Jim must have been 14.

Is chess infinite? Why don't we all stick with tried-and-true sequences? Well, maybe we try. But quickly we find ourselves in a maybe-unique position, figuring it all out from scratch.

I am certified to teach high school algebra, but couldn't begin to figure out the odds that a given situation has been played before. I would like to think chess is infinite, but I'm not sure the idea is defensible, mathematically.

Does anyone have an idea?

Well, there are a finite number of squares with a finite number of pieces, so, it would seem that a truly infinite number of positions is impossible.

That said, the number of available positions is high enough that our brains are simply incapable if comprehending the number of positions available on a chess board, so, it may as well be infinite.

Is chess infinite?

No.

chess is not infinite but it might as well be infinite as to the number of possible different games. Of course chess is a draw with best play by both sides.

No. There would have to be an infinite number of squares on the board for it to be infinite. there's probably around 10^60 or so possible games.

There is a fixed number of pieces. Although pawns may get promoted, the number of pieces played at a time will never exceed 32 pieces. Once captured, the number of pieces will never increase. The rules are clearly-defined and fixed. Chess is also played on a fixed 8 by 8 board. So I believe that the number of possibilities in chess is finite. The possibilities may be many, but they are still finite.

It is possible to work it out mathematically. Perhaps one day mathematicians may discover some functions that can be used to calculate the optimum solution to a chess problem.

I suppose it's technically infinite given players of my calibre. That is, there may be an infinite "check" sequence as I struggle to make it stick. So the number of moves in a game is one variable, and technically that would be infinite.

But I don't want to trivialize my own question, which I may be doing. Specifically what got me thinking was computer chess. Is a given application recalling winning sequences from a database, or calculating individual moves? The software I'm using blunders frequently even toward the "strong" end of the slider. It seems that better software would always win, either by calculation or consulting databases.

Then again, people program the software. I think.

Hi kempo--computers running at full strength --I think they will miss some very long stragetic ideas--say maybe 15 moves in the endgame--this is only my opinion from my own games.

They might miss a tactic that is very long--again I am not sure but I have a game that might prove it.

Would love  a test of this with specific tactical and/or stragetic game.

There is an argument for finite and an argument for infinite, both based on the fifty-move rule.

If players claim the fifty-move rule when possible, then chess is finite, because that ensures that there is a maximum length of game possible, which ensures a finite number of possible games.

However, the draw is not automatic. It has to be correctly claimed by a player, and it is not mandatory to claim the draw. Therefore, if the players never claimed a draw, a game could be of arbitrary length, and thus chess is infinite (even if almost all of those infinitely many games are utterly boring games that real people would almost certainly have agreed were draws).

So, while I guess it's technically infinite, the subset of games that are interesting is certainly finite, but it's still of such a magnitude that it's beyond the mental capacity of any person to thoroughly master this finite game.

I disagree with the infinite check argument. A chess game may be very long, with infinite check and so on. It may even be impossible to thoroughly calculate as well. However, the number of possible positions (permutations, combinations, etc) on a chess board remains finite.

Note that todays computers still don't play perfect chess. They can't calculate every single possibilities right to the end of the game. We don't have the computing power yet. This is why when you try to find a solution using computers, they may suggest move A initially. After you let it run an hour later, they may recommend move B. After a day, they may suggest another different move. They are not perfect, but they play more consistent games than human (in terms of blunders).

Also, replying to abinoosh's question, today's chess computers use a combination of heuristics, database, and calculation.

All those words ! Arghhh !!

I'm not sure if the "infinite check" comment was directed at me, because I didn't mention "check" at all, but I wasn't talking about the number of positions, just the number of games. The argument was that there are an infinite number of possible games, which is true if players don't claim the draw, even though there are still necessarily a finite number of possible positions.

Nope. Not at you. Abinoosh mentioned about the infinite check sequence.

I was thinking mainly of openings, because early in the sequence it's clear that certain moves optimize the potential energy of individual pieces. But that's starting from the fixed position of 32 pieces. After that lines of play branch out quickly. We start with only 20 possible moves on each side - which comes out to 400 combinations for the first move, right? Then it gets more complex, then presumably as pieces leave the board fewer moves become available, although more squares are empty.

It seems weird to say it's infinite, for all practical purposes, given individual human players, but not infinite if we are talking about fast computers and big databases.

How do you know?

I read somewhere that a mathematician determined that there are more possible chess games than there are atoms in the universe. That may not be infinite but it's hard to imagine being closer to infinity.

Interesting also that computers haven't "solved" chess the way they solved checkers.

jontsef, I know from decades of playing chess vs very tough opposition. I know also that if you asked all the grandmasters in the world if chess is a draw--you probably would only get 1% or 2% who would say chess is not a draw--and all their experiences and chess knowledge count for something.

For something, sure - but not for everything. The 'answer' currently is we simply don't know.

Good answer, pretty much what I was going to say.

depends on what you mean by "We dont know." I am 99.999% sure that chess is a draw but of course there is always the .0001% chance that I am wrong on this particular question.

And you can negate the hundreds of thousands of years of chess knowledge and experience by chess grandmasters if you want but this experience means quite a bit!