Chess will never be solved, here's why

@11870

"Suppose a robot flips a fair coin into a box, puts the lid on and gives it to you.
What is your belief about the state of the coin flip? Is it a head? Is it a tail?"
++ It is 50% head 50% tail, because if the robot does it 100 times and I open 100 boxes,
I expect to find 50 heads and 50 tails. I can relate to an experiment. The essence is the box.
Box + coin is not the same as coin, just like cat + box is not the same as cat.

"1 in a million tickets wins, so my Bayesian belief is that there is a 0.0001% chance that the ticket in the box is a winner" ++ This is correct: if I open 1,000,000 boxes with all 1,000,000 lottery tickets I am sure 1 of them to be the winning ticket. Box + ticket is not the same as ticket.

"No-one has solved chess. No strong, weak or ultra-weak solution exists."
++ I consider Chess as ultra-weakly solved by the 112 ICCF WC finals draws as well as by the compelling argument initiative = advantage of +1 tempo = +0.33 pawn = not enough to win and each further move dilutes it.

I consider Chess as being weakly solved by the 112 ICCF WC finals draws: redundant,
but not yet complete. They looked at too many black moves and not yet enough white moves.
The 112 draws are at least part of a weak solution of Chess.

I expect Chess to be strongly solved before 2100 by quantum computers performing retrograde analysis from the 7 men endgame tablebase all the way to 8, 9...32 men.

"you need a population to make a probabilistic statement about chess meaningful."
++ Yes. To express a probability you need an experiment, either a real or a thought experiment.
It is meaningless to say Chess is 99.9% sure to be a draw. What is the experiment?

"We could construct one by generating a huge number of games rather like chess."
++ No. We can let AlphaZero play games against itself with increasing time per move.

"do a computer evaluation to check if the position seems balanced" + No, this is unreliable.

"some of these games are winning for white and some are winning for black"
++ That is what the TCEC superfinals do: they impose 50 humanly selected, slightly unbalanced openings and let 2 different engines play 1 white and 1 black game against each other.
Most end draw/draw: balanced opening,
some end win/loss: busted opening,
the more interesting end win/draw: the opening is unbalanced enough for 1 engine to win,
but balanced enough for the same engine to hold the draw,
none end win/win: the 2 engines are of comparable strength.

"a dumb looking sacrifice by one of the players on move 2 turns out to be good"
++ Chess is not about the looks. Botvinnik wrote Chess, like any game, is a generalised trade. Material is a value. You can sacrifice, i.e. trade it for something immaterial.
After 1 e4 e5 2 Ba6? you just give up material for naught. That can be dismissed right away.
1 e4 e5 2 d4 exd4 3 c3 is less clear: you give up material, but get a tempo in return.

"I consider Chess as being weakly solved by the 112 ICCF WC finals draws: redundant,
but not yet complete. They looked at too many black moves and not yet enough white moves.
The 112 draws are at least part of a weak solution of Chess."

and this is why you never made it past highschool math proofs. heck, I literally know middle schoolers who understand what a weak solution is better than you.

no rigorous proof of any result means no solution.

"I expect Chess to be strongly solved before 2100 by quantum computers performing retrograde analysis from the 7 men endgame tablebase all the way to 8, 9...32 men."

Ah yes, the worlds largest computer is ~10^31 atoms (270 tons and each atom is assumed to be hydrogen). the number of chess positions is 10^44.

you really expect there to be a billion positions processed and recorded on each atom?

"Material is a value"

no it isnt. as you yourself said, the position is only determinable as one of the three game theoretic values.

"After 1 e4 e5 2 Ba6? you just give up material for naught. "

According to what? you still havent given any deductive evidence.

" I consider Chess as ultra-weakly solved by the 112 ICCF WC finals draws as well as by the compelling argument initiative = advantage of +1 tempo = +0.33 pawn = not enough to win and each further move dilutes it."

how about you go correct the wiki article then if you are SOOO confident about it.

"++ This shows you do not understand probability.
1 a4 b5 like any position is either a white win, or a draw, or a black win.
Probability is always tied to an experiment, either a real experiment or a thought_experiment. You cannot look into 10^50 parallel universes and find one where 1 a4 b5 is a black win."

actually this shows that you do not understand probability lmfao. if a position or state hasnt been proven to be a specific case, then unless there is some axiomatic issue (which chess, as a finite system, does not have), you can assign a probablity.

tygxc why havent you addressed the fact that Ive had my arguments (pertaining to your weak solution claims) personally verified by mathematicians?

It's an appeal to authority. Authorities can be and very often are wrong.

That is not a correct example of the fallacy, given that he is referring to questions about mathematics. Appealing to a relevant expert (or more than one) is NOT an "appeal to authority" (which more accurately termed "appeal to false or unqualified authority").

An appeal to authority would be more like an example from the above:

"For example, to cite Einstein in an argument about education is fallacious, while it’s perfectly legitimate to cite him in a discussion about physics."

To be right as often as possible, you should refer to the statements of real authorities in a balanced way!

The article also lists a number of relevant subtypes of "appeal to authority". @MEGACH3SE could be accused of an "appeal to anonymous authority". It is the anonymity and the lack of any possibility of verification that detracts from the value, even if the opinions are indeed highly relevant.

To give @tygxc all the credit he deserves here, the less than 10000 positions in those games MIGHT be part of the proof tree of a weak solution of chess, and probably are valid to be (i.e. it's probably true that chess is a draw and probably true that the games contain no blunders. The latter is less clear). But this still needs proving, and it is a horrendously slow way to generate a proof tree that might be 10^30 positions (an estimate with much uncertainty).

You don't need proof but some grounds for the statement would be useful.

And @tygxc has not given exact details of if and how he plans to create a solution.

@11878

"a proof tree that might be 10^30 positions "
++ This is way too many. Checkers has 5*10^20 legal positions, 10^14 = (5*10^20)^0.67 positions considered to weakly solve it and a proof tree of 10^7 = (5*10^20)^0.34 positions.

For chess from 1 luxury box of 34 chess men that would convert to considering (10^38)^0.67 = 2.8*10^25 positions to consider and a proof tree of 8*10^12 positions.

Chess engines have evolved more than Chinook and thus come closer to perfect alpha-beta pruning. Chess is easier to prune than Checkers, as Checkers is a more calculative game, more like a pawn endgame in chess. Thus the exponent should be closer to 0.5 for positions to consider and 0.25 for the proof tree.

That would be 10^19 positions to consider and a proof tree of 3*10^9 positions.

This is even without discounting obvious nonsense positions counted in the 10^38.
Discounting those leaves 10^17 positions relevant to weakly solve Chess and a proof tree of 316 million positions, or 4 million games of average 39 moves.

@11879

"some grounds for the statement would be useful"
Statement 1: Chess is a draw.
Ground 1.1: 112 ICCF WC games are all draws. Even if 1 game has 0 errors, Chess is a draw.
Ground 1.2: White has the initiative, an advantage of +1 tempo = +0.33 pawn, not enough to win.
Ground 1.3: Each further move dilutes the advantage of +1 tempo.

Statement 2: The 112 ICCF WC draws are perfect games with 0 errors.
Ground 2.1: An error distribution of 0 - 112 - 0 - 0 - 0 or e.g. 0 - 60 - 0 - 52 - 0 is absurd and would require collusion of the 17 finalists to avoid 1 error or 3 errors.
Ground 2.2: An error distribution of e.g. 60 - 0 - 52 - 0 is absurd and would require all errors to be paired to avoid a game with 1 error. There are arguments for some errors to be paired, but not for all errors to be paired and no unpaired error to occur.
Ground 2.3: An error distribution of e.g. 110-0-2-0-0 cannot be ruled out, but the 2 games with 2 errors can be removed because of the redundancy, leaving 110-0-0-0-0 and thus 110 perfect games with 0 error.
Ground 2.4: An error distribution of 112-0-0-0-0 is the most plausible explanation for 112 draws out of 112 ICCF WC games, thus the 112 draws being most probably perfect games with 0 error.

"how he plans to create a solution" ++ Wait for more ICCF WC Finals games to finish. As long as more draws come in, or even decisive games attributable to human error like clerical error,
the set of perfect games with 0 error grows and the weak solution becomes more complete.

Statement 2 is patently unsound.

There is a sizeable probability that at least one of the ICCF games has a double blunder - two consecutive moves, one of which gives away a win and the other of which fails to take advantage of this - somewhere, a possibility that requires more computation to reveal it.

This blunder would first be beyond Stockfish to see for the first player, then for the second, so both went straight past it. Note that there is no necessity for the difficult part of the path to a win to be early in the analysis tree. It could be deep in a branch.

Double blunders are quite common in human chess when analysed using engines.

So are you now offering to solve chess in 5 years for us by using a future sci-fi computer that can solve it and travel back in time 71 years to tell us?

If @tygxc would just care to consullt the examples I've given him he would find that over 90% of SFvSF blunders are also adjacent to opponent blunders when analysed using Syzygy (though they're not necessarily limited to double blunders, there are examples of 6 consecutive).

Too many possible positions for chess to be solved.

weve been trying to tell @tygxc that but he wont listen, he just keeps repeating falalcies and arithmetic errors. thats literally what the 2 year forum is, just people correcting tygxc (with the occasional troll and off topic musing).

You failed to understand the point the first time, so here goes again.

If you generate a large enough set of combinatorial games with rules that are kind of similar to chess, but not the same. in some of these games there will be a move that looks as bad as 2. Ba6 to a weak player like yourself (as opposed to one with access to complete tablebases) but which wins.

YOU DON'T KNOW THAT CHESS IS NOT ONE OF THOSE GAMES.

Your feeling that it is extremely unlikely for a single game is good judgement, IMHO, but your certainty is a mistake about what to believe.

It is just like believing the lottery ticket in the box is certainly a loser. Here the lottery ticket is the arbitrary selection of chess from a quadrillion (or whatever) similar games, some of which would be counterexamples to your intuition.

You can get appropriate certainty by rigorous analysis. You don't seem to know what that is.