" 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).
" 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)
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
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.
It's too bad there isn't a fifty-move rule for Internet arguments.
Or even a triple repetition rule.
Elroch and MAR, are you guys considering the 50-move 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!
...for the sake of arguing because he has a mental age of 11 and I wasn't around, because I've been busy for three days.
Nobody missed you. Nobody sane, anyway.
...for the sake of arguing because he has a mental age of 11 and I wasn't around, because I've been busy for three days.
Nobody missed you. Nobody sane, anyway.
It's debatable whether any sane person has been discussing this subject on this thread, [snip]
Rest deleted to make it look less narcissistic.
keep the vibes up guys
Optimissed is back
Hardly missed, narcissist...yet
To be cool, 'tis true
[Yes, that's a haiku]
"there are no reliable evaluations" ++ There are: at the end of the game it is draw/win/loss per the 7-men endgame table base or a prior 3-fold repetition. "
solving all the way to the 7man is by definition unreliable LMFAO
Reliable in principle, utterly impossible to do thoroughly in practice!
I wonder for how Few pieces the tablebases have actually solved for !
Even to 'solve' for how many possible positions (not whether they're wins or not) with just two Kings and one piece or pawn on the board - isn't that straightforward for a human being.
Its going to take you some time to allow for the fact that the Kings can't be adjacent and that either or both Kings might take a square or two from a pawn of either color.
But if you've taken care of that - all such positions of three men are legal apparently.
Not so with four. Which would start to get really involved for a human.
Could take quite a while.
Hours and hours perhaps just to calculate the total possible legal positions.
Let alone solve them.
Some positions are illegal because there was no legal means to get there.
But it may take a lot of men for that.
Still - the computers will have to check for that too ...
There's no essential need to exclude unreachable positions. They are just not as useful.
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.
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.)
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.
@MARattigan
Martin -
now a more direct reply by me.
You're saying that the tablebases haven't even Rigorously solved for three pieces on the board?
Quote from your post:
"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."
I would think it would be easy for three pieces.
Try this Martin - as long as Kings aren't adjacent and pawns are on any of their 48 squares - then all positions of three pieces with either side to move are all legal and legally reachable. Can you show an exception to the forum?
You don't need to worry about the starting position there.
There's your 'algorithm' right there.
This is easy enough for a human being that I would think that computers could easily handle four - and five with time. Time they've more than had.
But six pieces - that's something else.
The 500 multipliers begin to 'cut in'.
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Plus people thinking 'only legal positions need be considered' are missing the point that to find all legal positions you need to find and 'exclude' all the illegal ones.
Plus if you're doing that anyway in the project there's no reason to exclude the illegal positions from cataloguing.
A position is punched in ...
computer responds: 'Cannot be solved because its illegal.'
Or - 'Is not solved here because its legally unrecheable - see side project for further cataloguing of 'solutions' of unreachable positions that are otherwise legal. ' (maybe no 'funding' for that one)
@10328
"It's too bad there isn't a fifty-move rule for Internet arguments."
Repetitio mater studiorum.
Repetition is the mother of study.
Many here still do not understand that it is not necessary to strongly solve a game to weakly solve it and that it is not necessary to weakly solve a game to ultra-weakly solve it.
"Many here still do not understand that it is not necessary to strongly solve a game to weakly solve it"
Many here do not understand that it is necessary to strongly solve a game to solve it.
Anyway if the pseudo-solving gets those people their funding then that's an approach in 'their context' to 'necessary'.
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As I thought - tygxc wants to get right off that subject of for how many pieces chess has Really been solved for.
Martin seems to have suggested its not 'solved' for anything beyond two Kings.
But I'm saying it is 'solved' for three pieces because its obvious.
@10341
"how many pieces chess has Really been solved for"
++ Chess is strongly solved for all positions of 7 men or less and for some 8-men positions.
Chess is at least in part weakly solved by the 106 ICCF WC Finals Draws.
For all practical purpose Chess is ultra-weakly solved: the initial position is a draw.
"Chess is strongly solved for all positions of 7 men or less and for some 8-men positions."
No it isn't.
Haven't you admitted they couldn't include castling?
If so - shows they're Struggling.
Whatever it is they're doing - they've been hung up between 7 and 8 for quite a while.
Based on what I suggested about 500-multipliers - they might never reach even 11 men.
I repeat - I doubt they've genuinely solved even for six men.
tygxc - suggest you read Martin's recent posts so you know what it is I'm replying to.
But whether you do or not - you're doing OK.
interesting