Chess will never be solved, here's why

I've seen a lot of such comments, directed at you, recently. Also in the past week to my knowledge you've deliberately picked three or four nasty fights with people other than me and only in threads I'm aware of, because I certainly don't follow you around. There's no question about whether you bully people and if, as you claim, you're sane, then that means you must do it deliberately. That makes you a troll in itself. Given that you habitually distort the truth, invent things about others and misrepresent them as a matter of course, as well as the passive aggression that you habitually employ, it means you're quite a nasty troll. I'm just saying what I think. It doesn't mean a lot to me. It probably means more to you.

You keep saying stuff like this, but when called upon to back it up, you never can.  It's a pretty tired refrain at this point.

Suppose that we have a unit which measures whether a games' position is a win, loss, or draw. Anything above 1 is a tablebase win by definition, anything below -1 is a tablebase loss by definition. Anything in between is a tablebase draw by definition.

If both players play the best moves, the evaluation stays the same.

If one player is an Oracle who plays the best moves but the other blunders slightly, the score should drift more and more in favor of the tablebase player. But possibly not enough to convert the advantage to a win.

Since we know that this evaluation doesn't change with optimal play, the conclusion can only be that it changes with suboptimal play in the direction of the opponent. Ergo, if a position is +25 centiwins, and you make a slight inaccuracy, it could be +15 centiwins, or -30, or -200, but making best moves keeps it at +25 centiwins.

If we assume you can always blunder the same number of centiwins and it's equally likely (not true but just for the models' sake), and that a chess game is always exactly 100 moves, we can model a game as a sort of random walk and its win/loss/draw state as the evaluation position after 100 moves. If the chance of a given size inaccuracy up to a certain maximum is equal, the distribution of deviations after 2 half moves will be triangular. Since with a triangular distribution the median deviation after a full move is ~29.3% the maximum blunder a player would make, and the mean is 33.3%, we shall assume that the random walk has a scale 1/3rd of the maximum blunder the player would reasonably make on that move.

Observation 1: the random walk scale in centiwins per move is not a free value. If you want a given draw rate between players of equal skill, the innacuracies need to average a certain size. For example, if we assume a random walk size of 10 centiwins per move, then after 100 moves, the average random walk will have deviated 1.0 wins from the starting position in either direction. 50% will deviate less than that. We might guess that something like 7-8 cW/move is top level human play.

2. White's starting advantage is not a free value either. To get realistic win/draw/loss numbers, White's starting advantage should be less than a win but not 0 in this model. So for example an advantage of 0.33 will produce a distribution where white wins way more than black at high level but draws dominate, since black has twice as far to go as white. A value of 0.5 might make white win TOO often to match experimental results.

3. It is possible, given the assumptions here, to calculate the winrate of the Oracle against strong but imperfect players. If a players's maximum blunder is 22 cW, then they will lose on average 11 cW every move against an oracle. The odds that a random walk with a drift that size wouldn't go at least 150 cW from the origin point after 100 moves are vanishingly small.

To actually have a 50% chance to draw an Oracle as white, the average cW/move needs to be down to whatever (1+white's advantage) / 100, which means the maximum is twice that and the average deviation playing against itself is 1/3rd the maximum. Given this is the case, any engine with a good chance of drawing an Oracle will need circa 1.5 cW of inaccuracy on average and 1 cW of inaccuracy per move  in self-play games. One conclusion here is that any engine that sometimes loses against itself is still very far from having a chance against an oracle.

Note that I'm assuming here that the oracle plays well, trying to create positions where there are many serious blunders the opponent could make, andas few drawing lines as possible, rather than playing the minimum to preserve the draw. An oracle that will happily blunder as long as the blunder preserves a draw will lock itself at like -90 cW unless the opponent makes a 200 cW blunder.

One other result here is that the drift will just be the difference in mean cW loss. Thus, a player who averages 12 cW loss should convincingly beat one who averages 16 even with the 100 cW average deviation by the end of the game. This represents hundreds of ELO difference.

Importantly, a low rated player with 60 cW loss will be rated even more convincingly winning against a player with 80 cW loss. 2000 cW of drift with an average deviation of 500 cW requires 3.7 average deviations of drift to get a draw instead of 2.6 or whatever. The ELO difference is larger even if the difference in blunder size is the same.

All this sounds like it should produce exactly the sort of results txgxc is saying. That the game theoretic win margin and the 50% winrate margin for games of any and equal skill level are one and the same.

HOWEVER..

Anyone who's ever played more than a couple games knows this isn't perfectly representative as a statistical model of chess for a few reasons:

1. Chess does not end at 100 moves. There are moves that bring it closer and further to ending and it's naive to think nobody is trying to alter the game length deliberately for strategic reasons. E.G. Not trading down material.

2. It is widely considered true and backed up by some observation that blunder size is neither linearly distributed nor insensitive to aspects of the position. Briefly, in simpler positions simpler thought processes are sufficient to avoid serious blunders. In complex positions, complex thought processes are required to avoid serious blunders. It is usually better to try to force complex positions with objectives you understand but your opponent does not against weak opponents, and force sharp, chaotic positions with objectives both sides understand against stronger opponents.

3. It is uncertain what the effect of advantage is on blunder size. If having advantage significantly decreases mean blunder size, then it is likely that games with imperfect play will spiral out of control even with non-winning advantages, and this would cause us to think a winning advantage was smaller than it really is if we don't account for it. E.G. Thinking a pawn advantage in the opening is winning when you actually need a piece to guarantee a tablebase win. If advantage significantly increases blunder size for the advantaged player, then it is instead likely that people usually gain completely winning advantages and throw them away in real games. In which case, thinking you need a pawn to win when you just need 2 tempi in the opening or something would be the expected result.

If there is any data on blunder severity vs advantage in equally rated games that would likely give a significant clue as to how big a forcibly winning advantage really is (especially if blunder severity isn't correlated with advantage when advantage isn't enormous).

A random walk that only goes in one direction? Because remember, you said...

I realize this is fine when you're talking about two imperfect players, but you seem to keep the same setup when talking about oracle vs imperfect when you say e.g.

Why wouldn't the maximum average blunder rate simply be 1+white's advantage / 100?

I know it's just a model, but this feels too far from reality. Between two imperfect players cW loss is just regular centipawn loss... and in practice we know that someone with a much higher cp loss can win since it only takes 1 significant mistake to lose a game. For example if I lose a pawn in the middlegame which eventually goes into a lost endgame.

Also centipawn loss is based on engine evaluations which naturally inflate over time. To use that example again, let's say I win a pawn and the engine thinks it's 0.8 in my favor, but in reality it's win. Let's imagine the game continues for 50 perfect moves, and now the eval is +5 in my favor, at which point I simplify the position with trades to reduce counterplay... engines frequently count such practical measures as bad and that would make my centipawn loss higher even though I was winning the entire game.

It's an interesting thought experiment but mixing imperfect engine evals and incomplete information (such as centipawn loss and assuming chess is a draw and a tempo is worth 1/3rd of a pawn) with ideas like a perfect player and game theoretic values seems incorrect.

@7528

"Suppose that we have a unit which measures whether a games' position is a win, loss, or draw. Anything above 1 is a tablebase win by definition, anything below -1 is a tablebase loss by definition. Anything in between is a tablebase draw by definition."
++ We can suppose existence of such a unit, but such a unit does not exist unless it calculates to the 7-men endgame table base. However, good humans can indentify some positions as clear draws or clear losses, all other positions needing calculation.

"If both players play the best moves, the evaluation stays the same." ++ Of course.

"If one player is an Oracle who plays the best moves but the other blunders slightly"
++ You cannot blunder slightly. A move is an error or not, changes the game state or not.

"the score should drift more and more in favor of the tablebase player"
++ The score stays 1/2 as long as no error is made.

"But possibly not enough to convert the advantage to a win." ++ No possible win = draw.

"if a position is +25 centiwins, and you make a slight inaccuracy,
it could be +15 centiwins, or -30, or -200, but making best moves keeps it at +25 centiwins."
++ There are no centiwins, only draw, win, loss.

"we can model a game as a sort of random walk and its win/loss/draw state as the evaluation position after 100 moves"
++ After 100 moves the exact draw / win / loss of the table base is reached.

"The ELO difference is larger even if the difference in blunder size is the same."
++ Elo difference translates in number of errors, not in size of errors. An error is an error.

"Chess does not end at 100 moves"
++ It does reach the 7-men endgame table base before 100 moves: 42 moves average.
Moreover, a random walk with 4 non-transposing choices per move after 100 moves reaches 4^100 = 10^60 positions, that is more than the 10^44 legal positions, so Chess ends before 100 moves.

"Not trading down material."
++ Kings, Queens, Bishops, and Knights are stronger when in the center.
Putting these in the center compels to trade. Rooks are equally strong on any square,
that is why their trade can be avoided and why rook endings occur most.
Many rook endgames are draws even 1 or sometimes even 2 pawns down,
so not trading down rooks is indeed a valid drawing strategy.

"Thinking a pawn advantage in the opening is winning when you actually need a piece"
++ A pawn is enough to win. The plan is to queen the pawn.
A piece is enough to win. The plan is to trade it for a pawn.

"you need a pawn to win when you just need 2 tempi in the opening"
++ Yes a pawn is a win. A pawn equals 3 tempi.
White can afford to lose 2 tempi, black can afford to lose 1 tempo.

"data on blunder severity"
++ There is no blunder severity, but there are data on number of errors per game.

@7523

"Alpha go has cost over 35 million dollars"
++ Yes, but AlphaZero and Stockfish have been developed already, so are available.
Schaeffer had to develop Chinook. Also the 7-men engame table base is available.
Schaeffer had to develop his endgame table base, and that took up most of his work.

"We don’t yet have a pruning algorithm able to reduce the chess calculations to a reasonable number, whereas there was one for checkers"
++ Schaeffer used Chinook for Checkers. In the same way Stockfish can be used for Chess.
Use Stockfish to prune black moves down to 1. Justification will come after reaching the 7-men endgame table base. Use Stockfish to prune white moves down to a reasonable number e.g. 4.
If necessary an additional verification can follow.

I have no need to back it up since anyone who keeps their eyes open, regarding what you customarily do, is going to agree with me in any case. I'm just summarising. On the other hand, everyone who keeps their eyes open knows knows you habitually invent things about others and that you live in a fantasy world, a major part of which is that everyone else except you (among people you dislike) lives in a fantasy world but not you. Of course, everyone else but you is projecting and pretending that you live in a fantasy world and not them. It's why you always try to divide and rule. The fact that people get so disgusted with your behaviour that they refuse to comment any more works somewhat in your favour .... again, to anyone who isn't watching what is happening.

OK now get a diagnosis from a professional, and a prescription. We amateurs, although we may be good at understanding things like this, are laymen. You need a quack.

Trying too hard and getting flustered is not a good look for you.  You don't actually "know know" how every one feels, your "on the other hand" doesn't really qualify as one, and you can't decide if your attempted comeback is better using "professional" or "quack".  Your rationalization about people staying silent is pretty flimsy, and that's being kind.  All in all, not an effort to be proud of...stay centered and focus on what you want to say, take your time, and when you think you have it, take a second pass looking for discernible desperation on your part, and remove it.  This will make your arguments more cogent and confident.

I'll check back later.  No need to rush your reply...and avoid your usual string of "and another thing" follow ons.  Also a bad look.

Again, that's more appropriate as a remark about yourself. Completely amazing how everything supports your artificial rationale. You really are completely bonkers.

I think chess is a draw but the "zealots", as you call them, believe in nothing except deductive proofs. No deductive proofs are available so what do they do? Go round and round like satellites, swimming slowly and sluggishly through the primordial ooooze that is chess analysis devoid of any means to perform it.

@tygxc has had 5 hours to solve that question but dismally failed.

Hands up those who think in 5 years he will solve chess.

Some people try to use forced twins in 549 moves from such positions as an indication that chess isn't drawn with best play; and of course they don't take into account that the position shown is completely unbalanced even though roughly equal in force.

All this serves to do is to indicate that, insofar as definitive proofs are concerned, tygxc's assertions are incorrect. However, it doesn't help with the general project of solving chess. All you're doing is helping to perpetuate the manure that you're complaining about.

Some people try to use forced twins in 549 moves from such positions as an indication that chess isn't drawn with best play; and of course they don't take into account that the position shown is completely unbalanced even though roughly equal in force.

Do they?

I just use it to comment on @tygxc's "proof" that no chess game can last longer than 100 moves.

Doesn't advance a solution of chess much, I admit.

Hoping to cut down on @tygxc's manure rate. Don't know what we can do about yours.

You're too indiscriminate with your comments: that's the problem. I would suggest you attempt to understand it. Some manure is very fruitful. Depends on the type of soil.

@7541

"1. We have no way of every knowing how long a chess game last we perfect play."
++ We have. We have perfectly played ICCF WC draws and on average they end after 42 moves.

2. We have no way of every knowing is chess is a win, loss, or draw with perfect play. 
++ We have. We have perfectly played ICCF WC draws.
A tempo in the initial position is not enough to win.
A tempo cannot queen, a pawn can.
A pawn in the initial position is worth 3 pawns as we know from gambits.

If ICCF players have already solved chess then there's no need to wait 5 years with a supercomputer and Sveshnikov's ghost. 

That's a useful rule of thumb for practical play in opening positions. It's obviously not a rigorous game theoretic value.

S'cuse me. I didn't start my argument with any assumption about the theoretical result.

1. We do know how long a chess game can last with legal play under some sets of rules. 

Under FIDE basic rules since 2017 or FIDE rules prior to 2017 there is no finite limit, ℵ₀ can be taken as the minimal (unachievable) limit. Under FIDE competition rules since 2017 it's exactly 8849 White moves.

2. We have no way at the moment of knowing if chess is a win, loss, or draw with perfect play. Indeed you'ld need to alter the FIDE laws for the question to even make sense.

That doesn't mean there is no way of ever knowing (but the answer may be different depending on which set of rules is settled on).

The question doesn't arise in my post, because I'm not talking about perfect play, only legal play.

If you can tell what the error rates are you must have solved chess.

Congratulations - beat @tygxc by five years + the time he's going to take to con someone out of $3M (which could be about the same as a genuine solution might take).

If you want an idea of how SF15 compares with Rybka/Nalimov - which is not just perfect, but also perfectly accurate from the position below - you could always ask Coach, because SF15 is what he uses to decide.