Solving chess

Firstly, it is virtually impossible that there is one unique perfect game: at many moves there will be alternatives that give the same result. The number of perfect games (all leading to the same result with best play by both sides) is probably very large.

Secondly, if you could find 80% of all possible positions, 100% should be no problem -  it might take 25% more time! However, if there were N possible positions and you knew N^0.8 of them, that would mean there was work to do (eg N=10^100, N^0.8 = 10^80: the ratio is 10^20). For checkers, I understand that the solution only needed about N^0.5 of the positions, which is what made it possible - to prove you can achieve a certain result, you only need to deal with all the opponents moves. With your moves you can be much more selective.

"Checkers was proven to be a draw with best play, despite the first player's opening advantage. (That's for you, Matthew11)"

Checkers and Chess are two totally different things. Chess is far more more complex.

And it's a LOT harder to draw in checkers than chess.  The only way to draw in checkers is to have king against king where one king can escape to one of two corners before being trapped.  In chess, there are so many draws that aren't just king against king.  If checkers is a draw, chess is quite likely a draw as well.

Mate in 56... how could you not see that :P

But the general principle, and line of logic is the same: someone can have an advantage, and fail to convert it to a win even with perfect play. If it can happen in checkers, there's no reason it can't happen in chess.

Even that isn't certain.

What is certain is that froot loops are delicious.

No, in checkers the men move a lot slower into the fighting area. In chess, the men can get across the board in just one move. And, if one player in checker has all of his/her men out the other player is in little or no danger, unlike chess.

Makes no difference, makes no difference and makes no difference, respectively. Once again, someone can have an advantage, and fail to convert it to a win even with perfect play. It applies to checkers, and you've given no logical reason why it shouldn't for chess.

Elroch: I don't have your databases on which to do these statistical analyses. I'm cureious about whether the increasingly high result for white in human games as rating increases is due to a higher amount of wins for white, or a lower amount of wins for black. In fact, I'd suspect that as the rating of the players goes up, both the amount of white wins and black wins goes down in favour of draws (only that the black wins goes down more sharply). This I would view as strong evidence against the implausibility of a forced white win, and I'd say analysing just white's overall results against black, finding an overall trend for white and assuming it would increase is a shallow method of analysis, since that overall trend may be due to the combination of other trends which have limits that don't allow for unlimited future expansion (i.e. black wins can never dip below zero).

So if you could do that 100 rating points bands search again, but include W/D/B statistics, that would be much appreciated.

Advantages cannot be maintained or increased all the time. A fortress in chess, for example, will draw despite the opposing side having an advantage (material advantage, space advantage, tempo advantage, etc). The same goes with the first move in chess...

Also, we cannot use statistics because the statistics are all based on imperfect games. Theoretically, there is only one possible "perfect" game, and that's all that matters...white win % vs. black win % statistics would and should become obsolete in such a debate. If anything, we should be comparing white win % vs. draw %.

Interestingly, a draw in chess would be fully consistant with the second law of thermodynamics, due to the game becoming an equilibrium of a sort.

Schubomb, my sources are public domain, namely the database chessdb, the associated free 3 million game database updated with all games available from TWIC (up to last Monday) added (plus a lot of strong correspondence chess games, but these are not essential). I am sure if you have any other ideas, you could do the analysis yourself.

The draw percentage for the 100 rating point bands (the x-axis gives the lower end of each band). Note the rapid rise up to the 2500-2599 band is followed by a decrease afterwards (while white's advantage over black continues to rise). While the downturn may or may not be important, it belies the claim that the higher the level the more draws.

An interesting historical snippet - the state of computer chess in 1982. I got my first degree in this year, and my first computer to program (48k RAM - note the reference to 32k requirement in the article).  Thought about writing a chess program, but stuck to more appropriate tasks.

Sorry to be blunt, but this post appears to consist entirely of vague proclamations without any real substance.   Try to use concrete facts and logical inferences.

A game theoretic advantage can only change if a player makes a mistake (the value of the game is always simply win/draw/loss assuming perfect play). This is entirely different to the practical advantage that corresponds to a computer's or a human player's evaluation (eg +0.2 pawns or +/=).

We can use statistics as evidence. It's all we have for a game which is too big to solve properly. Statistics do not reveal the deepest truth though, which is about perfect games and their (unique) result, not percentages. There are certainly an unimaginable number of perfect games. To see this, realise that in most endings there are many places where a player has a choice of multiple moves to get the same result. Each such choice corresponds to a bifurcation into two separate "perfect" endings.

There are connections between game theory and thermodynamics, but the claim that chess being a draw is related to thermodynamic equilibrium fails to mention any property of chess which distinguishes it from similar games which are definitely a win for the first player or a win for the second player, so can't be justified.

Cheers, Elroch, will do my own analysis indeed.

Oh, and upon what are you basing this? I seem to remember IM William Hartston saying that one of the great unanswered questions in chess was whether a game can go from "black/white is better" to something else with perfect play. It is more a rhetorical question, since clearly if with perfect play results in a change, white or black was not really better in the first place, but the point is moot, since we don't have perfect players.

At the moment, a "game theoretic advantage" only means "what grandmasters and chess engines say gives a better position". It may turn out many of those "game theoretic advantages" turn out not to really exist with perfect play. Perhaps one of those advantages is the first move.

It comes down to semantics. Advantage means nothing ultimately: as you said, with perfect play, every position is either a white win, a black win or a draw. But until we can demonstrate perfect play and have a 32-piece tablebase, advantage is all we have, and those do indeed seem to often disappear even with play of which there is no evidence of its imperfection (and may well be imperfect, but that's just my point: until we prove it, the while win/draw concrete evaluation falls flat on its face.

I think he also said that there seem to be two definitions around of "advantage" in chess. One being that the side without the advantage has more practical opportunities to go wrong, but with the disclaimer that perfect play may nullify this advantage. The other being that it is the opinion of the observer that the player with the advantage should be able to win (which runs into the problem I mentioned before about the imperfection of all current observers/players).

I don't see a good reason to assume that white's theoretical advantage can't evaporate with perfect play. The theoretical advantage as most people use it talking about chess is much more mercurial than you seem to think, and concrete theoretical advantages that endure permanently in the absence of mistakes quite simply can't be judged until chess is solved.

Sorry to be blunt, but this sentence appears to consist entirely of vague proclamations without any real substance.   Try to use concrete facts and logical inferences.

Schubomb, your post suggests you do not know what game theory (a branch of mathematics) is, or what my (precisely accurate) statement meant. Before you use terms you should learn what they mean, and particularly so before you respond to a post by someone else.

Chess is an example of a finite game of perfect information, and results from combinatorial game theory apply to it. The particular basic result I referred to is that a position in such a game always has a precise value, which is the result if both players play perfectly. In other words the only sort of advantage is having a winning position. In combinatorial game theory, a mistake is simply a move that changes the result (from winning to drawing or losing, or from drawing to losing).

Understand now?

Maybe if you read my post properly, you'd realise that I'd already addressed that, and since you clearly have some intelligence, I'm not going to patronise you (like you seem to like doing, maybe it feeds your own ego?) by baby-feeding it to you. Moving on.

I've done my own analysis based on chessdbs records with their big database, and while I don't have all the TWIC records, and I'll redo my analyses based on that when I have, the results' supposed support for your decline in draws is at best very ambiguous, at worst nonexistent.

Filtering for games with maximum 10 points of rating difference, the amount of black wins goes down with higher rating, as one would expect. White wins also goes down until, when the lower rated player goes from bands 2500-2599 to the next hundred up, when it goes up slightly, and then in the next hundred goes up a miniscule amount. However, the draws illustrate my point: they steadily increase with rating except again for 2500-99 to 2600-99 where they decrease a miniscule amount (.09%), but once again in the next hundred up the draws increase by over a full percent. With 625 games in the 27xx band, and 4124 in the 26xx band, I don't really think the lower sample size can account for that sharp a rise after so miniscule a diminuition. Of course, the 28xx band is statistically useless.

Repeating the analysis for 20 rating difference max has a similar result, a small decline in draws from 25xx to 26xx with a bigger increase from 26xx to 27xx. Raising the max to 50 makes the 25-26 decline bigger than the 26-27 increase, but the 26-27 increase is still there. Increasing to 100 makes the 26-27 increase once again bigger than the 25-26 decrease.

So what to conclude? One could go for either of two conclusions as far as I know:

a) the results for the 27xx band are aberrations, they really should have more decisive games than the database indicates.

b) the decrease in draws from the 25xx band to the 26xx band is not indicative of a further decline in draws for higher ratings.

It's hard to argue that the 27xx band is statistically insignificant while the 26xx band isn't, considering that we're dealing with thousands of games either way, except for the max 10 rating points difference 27xx band, which still has 625 games. The fact that both trends (decline in draws from 25xx to 26xx and increase in draws from 26xx to 27xx) are consistent for all four tested rating difference thresholds appears to invalidate option a.

I don't really know why this dip in draws happens, though. Maybe people in the 26xx category are fighting especially hard for the prestigious 27xx "supergrandmaster" informal title, maybe they're comfortably enough over most grandmasters that they feel secure enough to be less conservative over the board, maybe there's some fundamental threshold of chess skill/understanding after which black becomes harder to draw with, and only another ~100 rating's worth of skill brings black's drawing abilities back in line. No idea. I'd guess I'd have to be rather a lot higher rated to speculate on this.

P.S. Not posting actual statistics until after finishing downloading the additions to my database, but will then.

@Schubomb, my statement was precisely correct, and you arrogantly wrote a lengthy post arguing with it. Learn from your mistake.

With 10 point bands, it is clear to me that random noise will make unreliable any small difference in white's edge from one band to the next. If you do the appropriate statistical analysis you will verify this. My graph shows that the number of draws go down from the 2600-2699 to the 2700-2799 bands, but even with these bands the sample sizes are getting quite small by then.

Most of the higher rated games are in the more recent TWIC data, not in the original 3 million game database, so results without this are of little interest.

Dude, don't be a pompous ass. You have clearly misunderstood my post. Read it again, or if you are too proud to, at least have the decency to be quiet.

Well, sorry Elroch, my data's different to yours, and mine as as up to date as humanly possible: chessdb's just finished loading the last games. Redoing the statistics again, with rating differences capped at your favourite of 100, we get (for the lower rated player) 25xx players yielding 56.05% draws, 26xx players getting 55.33% and 27xx players at 55.16%, so initially that would appear to support your assertions. However, there are a few gigantic snags. In increasing order:

a) 28xx players get 63.41% draws! Over an 8% jump, the biggest jump of them all. Even worse, black wins 21.95% of games, a jump over the previous band of almost 5%, more black wins than since the 23xx band, and most importantly, more wins than white (14.63%) True, the sample size is only 82 but it's still not something you can just ignore, at least it's entertaining!

b) For 27xx players, compared to 26xx, while the draws go a tiiiiiiny (0.17%) bit down, white wins go down more (0.25%) and black wins takes up all of that extra (0.42%!). Sample size for 27xx players: 8940, pretty hefty. I don't think black winning more games than their black counterparts in the lower skill band really helps your argument. I suspect even the draws going down will only be for this large a rating difference threshold.

c) Even ignoring the 28xx and 27xx bands, both of which clearly don't support your assertions, the 26xx band is the only one which exhibits a decrease in draws compared to the lower band, and even then, it's only a 0.72% difference, compared to all the multiple percentage jumps in draws for all the other bands compared to the ones below them. Clearly, claiming that this tiny blip in draws has any significance as regards theories of perfect play and the likely result of solving chess is an unjustified stretch.

Allowing only smaller ratings difference only hurts your claims even more.

Ah, I do enjoy internet arguments where only one side actually knows what they're talking about. Ironically, the side with theory on their side is rarely the side that 'wins' (if there is a winner in such affairs).

It would appear SchuBomb has gotten rather mixed up in terminology. Indeed, a 'theoretical value' for the game could only truly be win, draw or lose, while the values obtained through computer and grandmaster analysis amount to a 'practical value'. We will never truly be able to reach the theoretical values for chess (unless we make some new breakthrough in physics that allows incredibly large amounts of information computation) but it is important to realise that in reality, there is no such thing as a +0.15 value or any other than "Mate in x", draw or "Lose in x".

Anyway, I recognise that the argument has diverted away somewhat from the topic of the thread (though it shouldn't) and now the discussion is of rate of draws in Grandmaster play. It should be easy to tell that performing statistical analysis on rating gaps of 10 points is useless nonsense. Imagine I look at draw rates for EVERY rating point. Curiously, there is a massive spike at rating 2345! The only logical explanation seems to be that players rated 2345 want to keep their rating a set of consecutive integers.

This conclusion is not statistically impossible, but the chance for error is so large as to make it very likely. Similar is true for gaps of 10 points- any statistics have relatively large error values. Increasing the gap to 100 points- now we're talking. While there is still some not inconsiderable error, there is a large enough pool of players in each category to come up with some reliable results.