I will agree with you if you mean "for sure" means 100% sure.
Is chess infinite?
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Chess is not infinite if you're following all rules of it!! Only Kings at both ends can make chess infinite!
Jul 3, 2012
0
#24
It seems to me you have been speaking of two different things:
- Is the number of possible unique chess positions infinite? and
- Is the number of possible unique chess games infinite?
If I am not mistaken abinoosh asked the first question and the answer is "no". Since it is not possible to write formulas and equations here to prove it reasoning will do. There are 13 possibilities when it comes to a single square: empty; white K,Q,R,B,N,P; black K,Q,R,B,N,P. We can see there is no position that would not be included. Consequently, we have proven the number of unique positions is finite and it is dead easy to prove it is less than 13^64 - we have 32 or less pieces only. And it means that at least 32 squares have to be empty. Chess rules disqualify other possibilities (e.g. 3 kings, 1 king, 10 queens of one colour, pawns on the 1st and 8th rank ...). Please note it has nothing to do with the number of moves and thus we can forget about the 50 moves rule.
My answer to the second question would be "yes" but I`ll have to think of it for a while to be able to prove it.
Jul 3, 2012
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#25
Well, are we talking different move sequences or how many moves you can play.
If you were to somehow start looking at it, you would think, yes, it is MASSIVE, but finite - constant board size, constant pieces.
However there is one infinite variable - the number of moves. Even taking in to account the 50 move rule, you could keep playing just by checking now and then, which resets the count. Say you were playing a game where both players were trying to keep playing forever. Can you think of ways to play that can keep going, round and round? I can, easily. Therefore the number of games is infinite.
But if we were to limit our calculations to only rational possible moves, where both opponents are trying to win, it is both finite and infinite. it seems inconceivable that a rational game could go on for a thousand moves, but you never know, it could. Its immense improbability deems the answer to be a shaky 'finite', but the fact that there is an infinite variable, the move number,deems the answer 'infinite', it is merely a matter of countless variables. Eventually, someone will play a thousand move game, if you had infinite numbers of people playing each other.
Jul 3, 2012
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#26
@joey, I am afraid your proof (number of positions) is not valid. Do not forget there can be up to 10 white knights on the board. Your approach could help to estimate the real number but mine seems to prove easier the number is finite for it has to be a number smaller than another finite number, i.e. 13^64 (=196,053,476,430,761,073,330,659,760,423,566,015,424,403,280,004,115,787,589,590,963,842,248,961) I will try to find this number. 
The 3 fold repetition doesn`t mean anything, does it? The question is how many unique chess games are there. I would say it is infinite for we are adding a finite number of possible moves over an infinite number of moves.
pipinghotsos wrote:
However there is one infinite variable - the number of moves. Even taking in to account the 50 move rule, you could keep playing just by checking now and then, which resets the count. Say you were playing a game where both players were trying to keep playing forever. Can you think of ways to play that can keep going, round and round? I can, easily. Therefore the number of games is infinite.
Right solution, wrong method. Checking does not reset the count, you have to move a pawn or make a capture to reset the 50-move-rule count.
However the 50-move-rule is not automatic, it has to be claimed by one of the players so if neither claims then they can keep repeating. Therefore the number if possible games is infinite.
However the number of possible positions is finite, although of course very large.
who cares LOL just njoy the game
Jul 3, 2012
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#29
According to "The Complete Chess Addict", by Mike Fox & Richard James, the longest possible game with the 50 move rule in operation is 5949 moves long. I believe that the 50 move rule was dreamt up following a paper published by Max Euwe (then a Mathematics Professor, later World Chess Champion) proving that the rules as they stood in 1929 did not prevent a game of infinite length.
FirebrandX wrote:
piphilologist wrote:
However the 50-move-rule is not automatic, it has to be claimed by one of the players so if neither claims then they can keep repeating. Therefore the number if possible games is infinite.
Depends on the playing conditions. There are a lot of servers (ICC and Playchess for example) that automatically end the game when the 50-move draw rule applies. Same thing for 3-fold.
I play on icc quite a bit and hadn't noticed this. But if that is true they do not go by the official rules of chess (although premoves and autoqueen aren't in the official rules of chess either)
As to the countable vs. uncountable issue, I would argue that the number of Chess games is uncountably infinite. Think of each position as a digit. Then each chess game can be thought of as a number (a series of digits/positions). It should be possible to create infinite Chess games without repeating the series of positions. Those would be the equivalent of non-repeating, non-ending numbers. That would put it in the realm of real numbers, which are uncountably infinite.
Clearly that's not a formal proof. But I'm at work and don't have time to think deeper on it.
chesspooljuly13 wrote:
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.
I remember reading this in a textbook on Game Theory, can't remember exactly which one.
It also said something along the lines of that if all the energy in the universe were dedicated to solving the game of chess (mapping out every single possible game) and this solving started from the big bang, right about now it would be halfway solved.
So like others have said, I think the game can be considered technically finite, but for all intents and purposes it might as well be infinite, and I am well on my way to discovering the infinite number of blunders possible :)
@ironic_begar: The fact that any particular infinite game that doesn't fall into an infinite loop of repeated positions corresponds to some irrational number doesn't imply that there are as many games as there are irrational (or real) numbers. Most of the irrational numbers correspond to impossible games.
I suspect it's countably infinite, but I'm also having trouble seeing how to prove it.
"countably infinite" - Huh? Ok, you count to infinity and I'll hide...
The difference between countable and uncountable makes a huge difference in math.
As long as you don't peek; I'm still hiding and he should still be counting.
FirebrandX wrote:
fburton wrote:
ponz111 wrote:
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!
I mean we don't know for sure i.e. with 100% certainty. Afaik, no one has yet proved it mathematically. You may be 99.999% sure, but I am only 96% sure - and that's taking into account exactly the experience you mention. There's little point in quibbling though.
I've written blogs about this, and statistics don't lie: As computers and software have gotten stronger, the performance percentage for white has gone down. I once took a statistics census of ICCF (computer aided correspondence chess) games over the past several years and noticed the percentage of draws rose by a full 5% with the advent of multi-core CPUs. Since then, the percentage of draws has continued to rise each and every year. If chess were not a draw with perfect play, the trend would be going the other way.
Besides all that, I have demonstrated in the past that if black wants to draw, white cannot stop it from happening. Most everyone agrees that 1.e4 is the most testing opening move, yet black can use the Petroff defense to nullify even the most powerful super computers. I did this myself last year, where I used my out-dated desktop to take on a 'beast' machine that calculated a full 5 times faster than mine. I played the Petroff and easily forced a draw. It's a perfect example of black wanting to draw and doing so, rather than playing for the hopes of a win and losing instead. That's how I know chess is a draw, and I'm 100% positive of that. In fact, I believe there are probably countless millions upon millions of perfect games that end in a draw.
Your arguments are compelling - so much so that my certainty has risen to 99%. However, I still think it may be a win for either white or black with best play. What if people are wrong about 1.e4 ?
Is there any mileage in arguing the case from the end backwards, using what we know from tablebases?
Jul 3, 2012
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#38
There are only two things that are infinite: the universe and human stupidity, and I'm not sure about the universe. ALBERT EINSTEIN
NimzoRoy wrote:
There are only two things that are infinite: the universe and human stupidity, and I'm not sure about the universe. ALBERT EINSTEIN
Yeah, what was his chess rating? Shows how much he knew...
Here_Is_Plenty wrote:
NimzoRoy wrote:
There are only two things that are infinite: the universe and human stupidity, and I'm not sure about the universe. ALBERT EINSTEIN
Yeah, what was his chess rating? Shows how much he knew...
They didnt have ratings back then. But here's a nice game he played.
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!
I mean we don't know for sure i.e. with 100% certainty. Afaik, no one has yet proved it mathematically. You may be 99.999% sure, but I am only 96% sure - and that's taking into account exactly the experience you mention. There's little point in quibbling though.