Will computers ever solve chess?
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cobra91 wrote:
ponz111 wrote:
Preggo_Basashi wrote:ponz in blue
Ponz, we already know the evidence points to chess being a draw.
You're arguing with the wind. Actually there are people on here who have argued that every one of my pieces of evidence do not point to chess being a draw.
When people point out you don't know 100% for sure, you should just agree, and we should all move on. I have always agreed to this. I am only 99.9999% certain chess is a draw. [approximately] for which percentage most people take as proof of anything. I take my evidence as proof that chess is a draw.
Arguably, those two extra 9's (highlighted for emphasis) are the primary reason why this debate has lasted for some 100+ pages. At one point, you stated 99.99% certainty that chess was drawn with optimal play (and 99.995% certainty for something that most would consider a proven fact). This confidence level was later raised to 99.999%, and then increased once more to 99.9999%.
So despite the overwhelming amount of evidence that the game-theoretic value of chess is indeed a draw, it is worth mentioning that the lack of consistency with regard to the above confidence levels was essentially an invitation to be attacked by anyone who does not happen to be quite as thoroughly convinced of your assessment.
Actually after reviewing the evidence [some of which you put into better words than I could] my level of confidence went up quite a bit. I delibertly added one 9 and then later another 9 as my confidence level became higher.
I am not going to lie and say my confidence level has not increased. When my confidence level was only approximately 99.99% there was one factor given by a strong chess player which gave me very slight doubts. But when I confronted him -- he did not follow through on his evidence. And then my confidence level was approximately 99.999% Then very recently when making my presentation--I discovered even more evidence and my confidence level rose again to approximately 99.9999%.
I am not going to lie just because some people do not understand that confidence levels can go up and/or down.
Your human cognition is not even capable of truly distinguishing between anything you are 99.999% sure of vs. something you are 99.9999% sure of. What you are spouting is fueled by ego and conceit, which you have aplenty. I'll get around to your "evidence" post later. Thanks for at least finally posting something definitive that we can easily refute, though.
cobra91 wrote:
...The total game tree complexity of chess is much, much larger than 10^120...
10^1200 would surely be a more accurate estimate of the game tree's actual size than 10^120.
...Of course, none of the above estimates are particularly relevant to the task of solving chess...
...I've already explained why, if it existed, a forced mate in 16 moves or less would have been found by now (see page 392).
re #1:
Do you have an academic citation for 10^1200, or anything which comes close to that value? A number of games when added to a large number may not have a big effect on the average. Also, a large number of nonsensical but very short games will also tend to pull the average down too.
re #2:
I agree that the complexity of chess may not be particularly relevant to the task of solving chess.
re #3:
Chess is a game which has received much attention from mathematicians and game theorists. To me there is a big distinction between speculation and provable statements. I'm not intending to be provocative - just pointing out that some statements might seem simple to answer, but still aren't proven.
Jul 5, 2018
0
#6006
btickler wrote:
Your human cognition is not even capable of truly distinguishing between anything you are 99.999% sure of vs. something you are 99.9999% sure of. What you are spouting is fueled by ego and conceit, which you have aplenty. I'll get around to your "evidence" post later. Thanks for at least finally posting something definitive that we can easily refute, though.
And keep in mind, he is only 99.995% sure that 1+1 = 2.
He is now more sure that perfect chess is a draw than he is 1+1 = 2.
Jul 5, 2018
0
#6007
ilovesmetuna wrote:
1 + 1 = 1 when you are adding halves. gotta specify your units properly dude.
In mathematical language expressed in English speaking countries, the integer 1 as expressed, “1” means exactly that. Quantity one, not one half. If I wanted to convey one-hlaf would have typed “1/2” or 0.5
USArmyParatrooper wrote: ponz in blue
btickler wrote:
Your human cognition is not even capable of truly distinguishing between anything you are 99.999% sure of vs. something you are 99.9999% sure of. What you are spouting is fueled by ego and conceit, which you have aplenty.
Actually, I know the difference. Butas I mentioned--both percentages are estimates.
I'll get around to your "evidence" post later. Thanks for at least finally posting something definitive that we can easily refute, though.
And keep in mind, he is only 99.995% sure that 1+1 = 2. Yes, and there is a reason for this.
He is now more sure that perfect chess is a draw than he is 1+1 = 2. This is correct and there are reasons for this.
^^^ Darn it I knew I was getting rooked. Drat!!!
Jul 5, 2018
0
#6010
s23bog wrote:
USArmyParatrooper wrote:
ilovesmetuna wrote:
1 + 1 = 1 when you are adding halves. gotta specify your units properly dude.
In mathematical language expressed in English speaking countries, the integer 1 as expressed, “1” means exactly that. Quantity one, not one half. If I wanted to convey one-hlaf would have typed “1/2” or 0.5
Exactly 1 (full) fifty cent piece + 1 (full) fifty cent piece = 1 (full) dollar
Even your little dance with words doesn’t work. You can’t change the denomination on one side of the equation, then claim 1+1 = 1.
Doing math correctly: Exactly 1 (full) fifty cent piece + 1 (full) fifty cent piece = 2 (full) fifty cent pieces
Yes, yet again. Could we please stop talking about this? Thanks, guys. I really don`t want to ask the moderators to end this silly discussion. Thanks again.
Is there proof of the negative answer? Anyway, thinking of such matters drew me even more to 960. Sure, if computers can eventually solve or become unbeatable at traditional chess, they can do the same for any starting position of 960, but at least, there remain countlessly many interesting games for humans to play, and chess retains greater interest even with familiar opponents. Also, getting back on topic, if computers solve chess, who is to say that the first player has the advantage? My prediction, however, is that solving chess will reveal that with perfect play, a draw is inevitable at least with the traditional starting position.
vickalan wrote:
cobra91 wrote:
...The total game tree complexity of chess is much, much larger than 10^120...
10^1200 would surely be a more accurate estimate of the game tree's actual size than 10^120.
re #1:
Do you have an academic citation for 10^1200, or anything which comes close to that value? A number of games when added to a large number may not have a big effect on the average. Also, a large number of non-sensical but very short games will also tend to pull the average down too.
No academic citation for a lower bound of 10^1200 possible chess games exists, because it was not intended to be an accurate estimate (it's still too small). I was merely explaining how simple it is to demonstrate that Shannon's estimate was far too small. I actually arrived at that number by merely adding a zero to the exponent in Shannon's estimate and observing that the result was still a weak lower bound on the true value.
Btw, "averages" have very little to do with approximating the game tree complexity, because it grows exponentially as a function of game length. If 2000-move games are theoretically possible (and they are 
), then there will be more than 10^2000 possible games.
To illustrate, let's suppose that a game is played in which each side makes 16 pawn moves and 4 captures. This allows the 50 move counter to be reset 40 times before the game ends. Before each reset of the 50 move counter, 49 full moves are played, so the final reset occurs on Black's 1,980th move (i.e. 49.5 x 40 = 1980). The game concludes with 50 more full moves, for a total of 2030 moves by each side. Note that each 49-move sequence within this game can consist of almost anything, provided that no pawn moves or captures are made; it would not be difficult to devise a formal strategy for shuffling the pieces in a manner which guarantees a certain minimum branching factor without ever repeating positions within a single 49-move sequence. Thus, if we use an average branching factor of 10 for each full move (recall that Shannon used 1,000 for this value), we arrive at a lower bound of 10^2030 possible games, which could still be shown to be too small by employing more rigorous methods.
vickalan wrote:
cobra91 wrote:
...Of course, none of the above estimates are particularly relevant to the task of solving chess...
re #2:
I agree that the complexity of chess may not be particularly relevant to the task of solving chess.
Actually, the game tree complexity is provably irrelevant to the task of solving chess. That is, even in the worst case scenarios (where the stronger side requires a relatively large number of moves to force a win, or the weaker side requires a relatively large number of moves to force a draw), there exist known algorithms that can weakly solve the game without traversing all nodes in the game tree.
On the other hand, the state space complexity of chess could be much more relevant. Depending on how long a perfect game turns out to be (among other things, such as accuracy of the move selection techniques being used), there may be hard limits on how many positions can be omitted from the search without jeopardizing the certainty of the end result.
vickalan wrote:
cobra91 wrote:
...I've already explained why, if it existed, a forced mate in 16 moves or less would have been found by now (see page 392).
re #3:
Chess is a game which has received much attention from mathematicians and game theorists. To me there is a big distinction between speculation and provable statements. I'm not intending to be provocative - just pointing out that some statements might seem simple to answer, but still aren't proven.
This is another example of a tautological argument: "To me there is a big distinction between speculation and provable statements." Yes, of course there is a big distinction. 
You make no distinction at all, however, between purely speculative, unsupported statements and extremely probable statements which are supported with vastly more evidence than any existing counterargument.
You have a tendency to challenge others' comments on the sole basis of them not providing a published mathematical proof, but at the same time, you never cite any actual references to illustrate why their statements even might be false. The formula is always, "I don't believe any formal proof of this has ever been published in a peer-reviewed academic paper, so there's a chance it could be false."
These conversations would be a lot more interesting if you were setting a better example, by making nontrivial assertions of your own and then backing them up with suitable references. Forcing others to do all the work is not very sporting, y'know... 
Jul 5, 2018
0
#6014
s23bog wrote:
The reasoning for this is just that there is only one best move for each position.
Look at an EGTB sometime.
There are usually a dozen "best" moves.
cobra91 wrote:
No academic citation for a lower bound of 10^1200 possible chess games exists, because it was not intended to be an accurate estimate (it's still too small). I was merely explaining how simple it is to demonstrate that Shannon's estimate was far too small. I actually arrived at that number by merely adding a zero to the exponent in Shannon's estimate and observing that the result was still a weak lower bound on the true value.
Btw, "averages" have very little to do with approximating the game tree complexity, because it grows exponentially as a function of game length. If 2000-move games are theoretically possible (and they are ), then there will be more than 10^2000 possible games.
To illustrate, let's suppose that a game is played in which each side makes 16 pawn moves and 4 captures. This allows the 50 move counter to be reset 40 times before the game ends. Before each reset of the 50 move counter, 49 full moves are played, so the final reset occurs on Black's 1,980th move (i.e. 49.5 x 40 = 1980). The game concludes with 50 more full moves, for a total of 2030 moves by each side. Note that each 49-move sequence within this game can consist of almost anything, provided that no pawn moves or captures are made; it would not be difficult to devise a formal strategy for shuffling the pieces in a manner which guarantees a certain minimum branching factor without ever repeating positions within a single 49-move sequence. Thus, if we use an average branching factor of 10 for each full move (recall that Shannon used 1,000 for this value), we arrive at a lower bound of 10^2030 possible games, which could still be shown to be too small by employing more rigorous methods...
Actually, the game tree complexity is provably irrelevant to the task of solving chess. That is, even in the worst case scenarios (where the stronger side requires a relatively large number of moves to force a win, or the weaker side requires a relatively large number of moves to force a draw), there exist known algorithms that can weakly solve the game without traversing all nodes in the game tree.
On the other hand, the state space complexity of chess could be much more relevant. Depending on how long a perfect game turns out to be (among other things, such as accuracy of the move selection techniques being used), there may be hard limits on how many positions can be omitted from the search without jeopardizing the certainty of the end result...
This is another example of a tautological argument: "To me there is a big distinction between speculation and provable statements." Yes, of course there is a big distinction. You make no distinction at all, however, between purely speculative, unsupported statements and extremely probable statements which are supported with vastly more evidence than any existing counterargument.
You have a tendency to challenge others' comments on the sole basis of them not providing a published mathematical proof, but at the same time, you never cite any actual references to illustrate why their statements even might be false. The formula is always, "I don't believe any formal proof of this has ever been published in a peer-reviewed academic paper, so there's a chance it could be false."
These conversations would be a lot more interesting if you were setting a better example, by making nontrivial assertions of your own and then backing them up with suitable references. Forcing others to do all the work is not very sporting, y'know...
My only comment was that it is unknown if there is a perfect game of chess that ends in 16 moves. If someone knows that it has been answered I would like to see the work, if for no other reason that I'm a mathematically curious person. But I'm somewhat inclined to not be impressed by guesswork presented as mathematical proof.
nope
not happening
if it did it would suck anyway
so why try?
s23bog wrote:
Preggo_Basashi wrote:
s23bog wrote:
The reasoning for this is just that there is only one best move for each position.
Look at an EGTB sometime.
There are usually a dozen "best" moves.
Usually? I find that hard to believe. I think it may depend a lot upon how one defines "best" I usually use it to mean "there is no better".
I have shown several positions where there are over a dozen best moves.
The chess engines will solve chess.
I think so, too.