Chess will never be solved, here's why

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)

@Elroch

I think what I suggested would work fast enough for at least KRK and correspondence chess if not tournament time controls. Generation should be hugely cut down by considering only (un)moves from an existing Syzygy tablebase and given that the 7 man versions only took about three months for the full 3000 or so versions each of which has millions more positions I can't imagine that the full KRK would take much more than a few mins on the same kit. (Not on my kit unfortunately.) New generation would be required only when the opponent repeats another position. Size would be less than the Syzygy tablebase because you can stop generating if your position turns up as won (and, less to the point, the number of winning positions may reduce).

Still true that four man chess has not been (Rigorously) solved.

Have you ever seen a 7 man tablebase with castling rights, never?

Repetitions are irrelevant for a weak solution, but not for a strong solution unless you're talking about the basic rules game.

who cares

Presumably people who post on the thread, but possibly not.

With about 2^15 positions it does seem plausible that with some efficient low level code, a tablebase with a given set of double repeated positions could be generated in a few minutes on a desktop. But it could be a few hours instead!

It's all kind of daft though. We are imagining two players who are seriously playing KRK but so badly that they don't get to the end without some double repeated position, then suddenly enlisting supercomputer help to save the win (or draw). Otherwise, the repeated positions are of no interest because they never occur in a game between competent players.

Depends what you mean by competent players. This ply count 0 position is a theoretical win for White (under both basic and competition rules). Can you spot any repetitions? (Rybka has a Nalimov tablebase, so should be pretty competent.) Admittedly a different endgame.

Elroch and MAR, are you guys considering the 50-move rule?

It's too bad there isn't a fifty-move rule for Internet arguments.

Or even a triple repetition rule.

That is not such a big issue, especially for our toy (but maybe intractable!) KRK example. Explicitly including it only multiples the number of positions by 50, and Syzergy tablebases already include DTZ.

I think I am correct in saying that this is the minimum distance to zeroing the counter that still leaves a forced mate. This is everything you need to deal with the 50 move rule in a practical situation. For example, suppose you reach a position after 30 moves counted towards the 50 move rule. You need not only to be able to force a mate, but either to force a mate in 20 moves OR to force a rezeroing of the counter within 20 moves that still leaves a forced mate. So only one computed number tells you everything you could need to know about that. It requires separate information to find the fastest mate when DTZ is not as crucial.

By contrast, explicitly including all possible combinations of previously twice-visited positions in even the KRK tablebase increases it to a number that makes numbers like 10^120 look tiny!

Nobody missed you. Nobody sane, anyway.

Rest deleted to make it look less narcissistic.

Optimissed is back

Hardly missed, narcissist...yet

To be cool, 'tis true

[Yes, that's a haiku]

Hi Martin!
Legally unreachable would be a subset - is a subset - of 'illegal'.
That one's not tough.
Do we agree on that?
I think so.
The point I'm making is that to be Rigorous the computer must determine both - whether the position is legally reachable and whether its just plain illegal also - like for example both Kings in check or a King in check from 3 pieces.
Regarding 'weak solution of chess' I tend to discount such a thing.
The more pieces that are added to the tablebase - the more the 'weak' grows and grows if its been put in in the first place.
Better would be if Nalimov just comes clean somewhere on the net and its posted here or it otherwise becomes obvious in the forum what has been Truly Solved.