Chess will never be solved, here's why

@7501

"Suppose there are 10^20 good-looking lines from some hypothetical position until you reach known tablebases. 99.9999999999% are wins for the player with a conventional advantage. 10^8 are draws. Any GM is going to see this as a completely winning position."
++ No. It may be that some line is good-looking, but if it is a draw, then it is found sooner or later. That is what we see: some lines are very popular and then disappear from tournaments.

"we haven't factored the 10^50 or whatever lines that have nonsense-looking computer moves in them that only a tablebase would even think about but turn out to be important."
++ There are only 10^44 legal positions and the vast majority of them are absolute nonsense with 3 rooks or bishops at both sides, which can never happen with optimal play from both sides.

If we restrict promotions to pieces previously captured, there are only 10^37 positions and the vast majority of these cannot happen from optimal play by both sides either.
Inspection of a random sample of 10,000 such positions reveals none can result from optimal play by both sides either. You can check for yourself and take one of the 10,000 randomly sampled FEN and try to construct a game that leads to it. That leads to 10^37 / 10,000 = 10^33 positions.

Allowing only promotions to pieces previously captured is a bit too strict, as positions with 3 or 4 queens do occur in perfect games of ICCF WC Finals draws, so multiply by 10 to accept 3 or 4 queens, leaving 10^33 * 10 = 10^34 positions.

Weakly solving only needs 1 black response to draw, not all black responses. That leads to a square root: not w^2d but w^d = Sqrt (w^2d), e.g. not 20*20 = 400, but 20*1 = 20 = Sqrt (400). Thus Sqrt (10^34) = 10^17 relevant positions.

Cloud engines of a billion nodes/s can calculate that from opening to 7-men endgame table base in 5 years.

@7504

"You're not even planning a solution according to any sensible definition."
++ Weakly solving just as sone for Checkers:
calculating from the opening to a 7-men endgame table base draw.

"Problem is you don't seem to have any."
++ you < me < grandmaster
I do not qualify as one of the 3 good assistants, which would require (ICCF)(grand)masters.

"What's it got to do with your proposal to solve chess? Aren't you planning to use some version of Stockfish?" ++ Yes, Stockfish running on 3 cloud engines with 3 grandmasters using knowledge to launch and occasionally terminate calculations.

"With the current level of AI programs can'r really be said to know anything at all."
++ The peer-reviewed paper has knowledge in its title, not guess, think, or belief.

"I gave you my ranking earlier in the thread."
++ You are not qualified. Otherwise publish your findings in a peer-reviewed paper.

"There are only three possible outcomes. No such thing as opposing more."
++ There is a thing as opposing more.
If say 1 e4 leaves only a series of only moves to secure the draw, and if 1 a4 allows say 6 different moves to secure the draw, then 1 e4 opposes more to the draw than 1 a4.

"how you can do against SF15 from 1.e4 e5 2.Ba6."
++ How I, or you, or Carlsen do against SF15 has nothing to do with solving Chess.

"The fact that it's not complete means it's not a valid solution."
++ Incomplete is not the same as invalid. After the good moves are proven unable to win for white, then it is trivial to repeat the same procedure for the bad moves.

"The rest of us would need a solution."
++ Some patzers may not understand that 1 e4 e5 2 Ba6? loses.

"I tried it with two engines in Arena" ++ Two bad engines... That position cannot be lost.

Always the call to some nonexistent silent majority and the vague innuendo.  I laid out 4 examples of academic areas you have trashed repeatedly over time to back up my observations, and you laid out...nothing.  There's never a lick of substance in anything you are pushing.

You are laboring under some idea that this thread is a back and forth discussion.  It's not.  It's one crackpot who has already been refuted by everybody else, and one pot-stirrer who doesn't know diddly but likes to pretend he's the only one with the real answers.

Occasionally a new poster comes in and also refutes the crackpot, by making the same arguments already put forth dozens of times.  It is helpful, in terms of volume of dissent.  The only reason cogent posters are still here is to make sure that the crackpot's narrative does not get any traction.  There are better threads on this topic that don't run on forever...

Another whopper!

ok

     I certainly do not subscribe to the all-too-common idiocy of defending one's own nation as a paragon of virtues, a trait hardly limited to the United States. Personally, I vehemently disagree with the "America is a shining golden beacon inspiring the rest of the world" claptrap we hear too often.

     There are areas where every society is better, and worse, than many others. Knee-jerk jumping to the defense of the overall "obvious" superiority of one's own nation and discounting any criticism thereof is a confession of deliberate ignorance.

Your main superpower is to contort anything that occurs into part of a delusional narrative that keeps your ego safe.  Joseph Campbell and the monomyth has nothing on you.

Talking to yourself is a sign of dementia, @Optimissed.

Tygxc it takes a lot more than that to solve chess.  Alpha go has cost over 35 million dollars, and people  have put wayyy more into chess solving.  We don’t yet have a pruning algorithm able to reduce the chess calculations to a reasonable number, whereas there was one for checkers

More of the same...

Funny how these "hundreds" depend on you to speak for them.  I don't take tablets.  That's the narrative I was talking about.  It is not feasible for you to think that I am perfectly sane and that my observations might be accurate...you're a bit delicate that way.

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.