Chess will never be solved, here's why

Yes, many people who also don't believe in the moon landings (and lots of other stuff) have tried to interact with me over the years. So, on occasion I have had to deal with repeated PMs, friendship requests, game challenges, etc. from crackpots that don't like having their submarines torpedoed and sunk.

There are reflectors installed on the moon surface that you can use to prove to yourself that the moon landings occurred. But you won't, because crackpots don't actually want to know the truth about things.

Reflectors installed on the moon? holly wood! Lol

What do you plan to come up with next?

The earth is flat?

You (or rather a competent scientist with the necessary equipment) can SEE the reflectors on the Moon by shining a laser at them and seeing the reflected light through a telescope about 2.55 second later.

There's no essential need to exclude unreachable positions. They are just not as useful.

A flat earther would actually be agreeing with you....no moon landings.

But you are just arguing

And you're just tired, if your username is to be believed.

I can explain how to do such estimations properly using Bayesian reasoning, but the thing that is blatantly obvious to anyone is that with any reasonable assumptions it is NOT very close to zero. It is a very naive blunder to think that a small amount of uniform empirical data implies uniformity in a much larger sample.

you dont know that its perfect play, try again. you have no evidence that other moves werent better.

prediction. appeal to ignorance fallacy

@10304

"it is NOT very close to zero." ++ It is not zero, otherwise the 17 ICCF (grand)masters would agree to a draw in all 30 ongoing games. There are external factors: illness, accident, fire, flood, earthquake, meteorite, power blackout, computer crash, war, revolution...

"a small amount of uniform empirical data implies uniformity in a much larger sample"
++ Now 106 games are drawn, 30 games are ongoing.
Place your bet on at least one of the 30 ongoing games ending decisively.

That's right Elroch.
But to 'solve' chess - I believe the computers should be determining whether a legal position is legally unreachable - and also whether a position is illegal.
'Rigor' begins to collapse if you're going to allow or not determine that a position is illegal or unreachable legally.
Issue: have the computers Rigorously solved for four men?
I doubt we'd get that info out of tygxc.
(but he's still a good man nonetheless)
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My guess: computers have Rigorously solved for four and five men but not six.
Where 'Rigorously solved' - well just Solved should be verbally enough but Rigorously is added because chess is a mathematical game with perfect initial information (unlike poker) so therefore 'Solving' should be Rigorous also. Perfect. Also.
Poker computer projects - well you'll find they're statistical.
Poker computers play against humans.
Can/do they beat the top human players?
I don't know. Can they bluff the way humans do?
I don't know.
Guess: Rigorous solving of chess only goes up to five men on the board.
Not 8.
Yes maybe that's going to be looked up.
But the projects maybe wouldn't like to make that kind of thing public.

Tygxc has also never addressed the fact that exclusion criterion must each also add to the calculation time for each position evaluation. The time savings are far from the 100% assumed by Tygxc's faulty formula, whether the criteria involved are checked in-line or in a separate process (in which case, just the calculation of which positions are skipped while traversing also requires processing time).

But to 'solve' chess - I believe the computers should be determining whether a legal position is legally unreachable - and also whether a position is illegal.

Illegal means legally unreachable from the starting position by a series of legal moves (both in common sense - assuming you consider only the starting position and positions after a move is made - and as defined in the FIDE laws). By definition, a position cannot be a legal position and legally unreachable if the terms both apply to the same starting position.

As Elroch points out, it's not necessary to exclude illegal positions to solve chess with any number of pieces so long as all legal positions are included (and that while sufficient is far from necessary under competition rules - read on). If you're asked to solve a maths problem for your homework and you hand in a rigorous proof but also rigorously prove Goldbach's conjecture, nobody should complain. It doesn't diminish the rigour of your proof of what you were asked to prove.

In fact the vast majority of illegal positions are excluded (see this). The excluded positions are all illegal also in FRC. A practical algorithm to completely determine what positions are illegal from either all or particular FRC positions or just from the standard chess starting position is not currently known.

The tablebases don't rigorously solve any number of men above 2, because they don't include all legal positions (no positions with castling rights are included). I think you can say (vacuously) that two men tablebases include all legal positions; as far as I know, nobody has published a KvK tablebase, on the grounds that all positions are already drawn.

Also "position" needs to be understood in the context of which rules are in force. A position is simply a situation occurring; a chess position a situation occurring in a game of chess. As such it has a large number of attributes.

For the purposes of solving chess most of these attributes, such as White's granny has just got her new set of false teeth, are irrelevant. Only a set of attributes that fully determines what game continuations are valid need be considered and for theoretical purposes only those that can be defined in terms of the rules (and many of those, such as Black has previously adjusted a knight's position after saying, "j'adoube", or any history, or any history prior to the last time the ply count was set to 0, depending on the game rules, that is not needed to determine the castling rights or e.p. status, are also irrelevant, as are clocks and arbiters and similar which are just too inconvenient to incorporate into solving - effectively solving under competition rules really means solving under pre 2017 basic rules).

The FEN appears to have been an attempt to collect a set of attributes that fully determine what game continuations are valid, but an unsuccessful attempt even under FIDE basic rules at the time it was specified. It doesn't take account of the triple repetition rule, so positions under current FIDE competition rules with the same FEN don't in general have the same valid continuations (and the same was true under both FIDE basic and competition rules prior to 2017). It is successful for basic rules chess since 2017 (but its ply count attribute is irrelevant in that game).

For competition rules chess a PGN from the last position with ply count 0 under the 50/75 move rules is sufficient to determine forward play because no position occurring before the event which set the ply count to 0 (which could be start of game) can be subsequently eligible as a repetition under art 9.2.2 (which specifies a reduced set of FEN attributes for determining repetitions; if you accept Leibniz's identity of indiscernibles there cannot be an actual repetition of position in a game). It can contain redundant information because all that is needed is the board layout, side to move, castling rights, e.p. possibility (i.e. FEN less move number and ply count) and repetition counts for the positions that have occurred when a move has been made since the last time the ply count became 0, and there could be multiple PGNs of the type suggested that result in the same attributes. It is what a program requires over the UCI interface for correct operation (though it will accept a FEN for not necessarily correct operation).

Luckily, for a weak solution of chess, a tablebase for competition rules needs only weakly solve all ply count 0 positions because a ply count 0 position with any given material will always occur before any position with the same material and a positive ply count, which renders the latter unnecessary. So for a competition rules tablebase (i.e. Syzygy at the current time) only a very VERY tiny percentage of all legal positions is actually considered. A tablebase for a strong solution would need to cover all positions and I think such a tablebase even for KRvK would be totally impracticable.

The Nalimov tables, which are only guaranteed to work in basic rules chess, do indeed provide a strong solution in that game of each of the positions covered. (In principle at least. That assumes that the results have been adequately checked. I think you're probably safe up to 5 men at least.)

I have to correct you on one point there, @MARattigan. In a University maths exam (I am having trouble recalling if it was in the final year of my degree or in my MMath), I answered the necessary number of questions in what I thought was a perfect way in an exam on one of my best subjects and had a lot of time left, so I reconstructed the proof of another major result from the course (a likely question that had not come up) and handed that in as well for no good reason. I got a complaint in person about this from the person who set the exam and he told me I was lucky not to have been docked marks for this strange behaviour,

Serves you right for being flash.

Also, are you sure a strong solution for KRK is impossible? I think the challenge you have in mind is when some positions have been reached twice already, so that they are in the way of a win. But intuitively, it is likely to be possible to work out if there is a route to mate that avoids those positions.

This is rather like a topological problem. You need a path to mate and some of the routes are blocked. You must not either repeat a position for the third time or leave your opponent a legal move to do the same. The former cuts your legal moves down and the latter does exactly the same by eliminating all moves that would offer the escape.

The question is how efficiently a way through can be found with some enhancement of a simpler tablebase.

Indeed. Sorry - touch of the tys. I think you already pointed that out.

I think a tablebase in the traditional sense where you pass it a position and it looks it up in the table would be impracticable because of the size of the table. But you're right - an intelligent routine that works out a path would, I think be possible if currently slow. You could use a Syzygy type generation for each position that stops generating at the positions (per 9.2.2) that have been repeated twice and piggyback on the existing tablebase so as not to consider unmoves that can't win. Actually you only need the positions (per 9.2.2) that have been repeated twice for solving rather than the complete position which would hugely cut down the number of entries in a direct tablebase, but I think that would still be too big.

It would, of course, get progressively less practicable as the number of men increased.

The thing is how big the table would be for the general strong solution. No problem starting with a fixed game position and generating a new tablebase, but no hope of generating a tablebase with an entry for every possible combination of excluded positions - the size is bigger than chess!

I was imagining more a way to find a route through the blockages in a way that would be efficient, possibly helped by more information in the tablebase. I am not certain it is practical.

interesting

" have the computers Rigorously solved for four men?"

have you never seen a 7 man tablebase, ever?

and repetitions are irrelevant

the solution of the 7 man position (if we're starting from the starting position and then got here) starts when we get to 7 men, and repetitions by definition require the same number of men in each 3 (more is also required of course)