Chess will never be solved, here's why

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tygxc

@7133

"the computers and programs of the year 2100 will far outclass those of the present"
++ Yes, they will make fewer mistakes for the same time per move.
That does not change anything, it will only go faster.

"punch large holes in the analyses that the Sveshnikov five year plan"
++ Because the plan of Sveshnikov to 'bring all openings to technical endgames' depends on the 7-men endgame table base and you cannot punch holes into that.

"unanalyzed lines the human experts judge to be unworthy of consideration"
++ 1 e4 e5 2 Ba6? is unworthy of consideration and will stay so.

"possibilities that exist following opening moves that the plan will never examine"
++ If 1 e4 & 1 d4 are calculated to 7-men endgame table base draws, then 1 a4 is not relevant.
If 1 Nf3 is calculated to a 7-men endgame table base draw, then 1 Nh3 is not relevant.
Likewise 1 f3 and 1 g4? are not relevant.
If the best moves cannot win for white, then the worst move cannot win for white either.

tygxc

@7139

"not a way to solve chess"
++ It is a way to weakly solve Chess, just like done for Checkers, Losing Chess, Connect Four

"person involved in peer-reviewed research on the subject"
++ Prof. van den Herik, authority on the subject: 'it is beneficial to incorporate game knowledge into game solving'. Schaeffer used best first heuristic and pruning in solving Checkers.
Allis solved Connect Four with knowledge rules only.
There is no reason why weakly solving Chess should be subject to more stringent restrictions than weakly solving Checkers, Losing Chess, Connect Four, Nine Men's Morris etc.
Chess is 1000 times more complex than Checkers to weakly solve.
You need not invent additional complications.

BoardMonkey

How long would it take to solve chess with an unlimited supply of stubby pencils? Sorry about your insanity tygxc. I do okay living with mine.

tygxc

@7146

"Chess is not checker!"
++ No, Chess is not Checkers. Chess is 1000 times more complicated to weakly solve than Checkers: 10^17 relevant positions instead of 10^14.

"1. Could not play a game of chess.
2 Could not beat any human at chess.
3. Could not give a refutation on any chess positions.
4. Could not play a perfect game of chess.
5. Could not give any kind of analysis."
++ None of these are part of weakly solving Chess.
Please re-read the definition of weakly solving a game.
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
A strategy can be a set of moves, like Checkers, or a set of rules like Connect Four, or a combination of both.

"And no more useful then a opening book of moves we already have as best."
++ Oh yes, as it gives a path from the initial position to a 7-men endgame table base no matter what white tries. It will never end with 'white is slightly better' or +=, or +0.50, it will only end in 7-men endgame table base draws.

"Your opening book can give no more answers, or give any other moves."
++ All relevant white tries are included.

"Chess is not a forcing game like checkers"
++ Nine Men's Morris is not a forcing game either and has been solved to a draw as well.

MARattigan
tygxc wrote:

...

"unanalyzed lines the human experts judge to be unworthy of consideration"
++ 1 e4 e5 2 Ba6? is unworthy of consideration and will stay so.

...

Your stance is that the line is unworthy of consideration but you still can't win it as Black against Stockfish.

If you actually had a solution you might even be able to win it against Stockfish.

That's what solutions are for.

That's just one of the reasons why your proposal is to spend 5 years not solving chess.

MARattigan

And 4.82 x 10^44 is the estimated number of positions in basic rules chess, which is a drop in the ocean compared with the number of positions in competition rules chess.

Elroch

The difference is huge for a strong solution of chess, but not for a weak solution which merely has to achieve the optimal result of the starting position, not to successfully take advantage of blunders by the opponent.

The reason is that if you have been following an optimal strategy in a game, you need not fear a repetition of a position you have already been in changing the value of the position, regardless of the value of the opening position. If the value of the opening position was a win to you, your strategy will never permit the opponent to return to a position (if it did, they could go round in circles so your strategy does not win). If the value of the opening position is a draw, repetitions do no harm to getting the theoretical result.

tygxc

@7150

"What path to a 7 man position"
++ For example this one: in 57 moves from the initial position to a 7-men endgame table base draw https://www.iccf.com/game?id=1164344

"you would not need to use other peoples work that does solve chess with 7 man or less"
++ Schaeffer had to create his own table base for Checkers. For Chess it already is there.

"why would you even need the table base" ++ Because only the table base provides the exact evaluation draw / win / loss. Nothing else can. 

"you can not force me as the other player to play one of your book moves"
++ All reasonable white moves are covered, black draws.

"Chess is not a forcing game like checkers."
++ Nine Men's Morris is no forcing game either and has been solved to a draw.

Elroch
tygxc wrote:

@7150

"What path to a 7 man position"
++ For example this one: in 57 moves from the initial position to a 7-men endgame table base draw https://www.iccf.com/game?id=1164344

Kudos on finding a game where every move by one side is forced!

[EDIT: just checked, and you seem to have missed some legal moves, making your statement false]

Elroch
tygxc wrote:

@7146

"Chess is not checker!"
++ No, Chess is not Checkers. Chess is 1000 times more complicated to weakly solve than Checkers: 10^17 relevant positions instead of 10^14.

"1000"

tygxc

@7156

"a game where every move by one side is forced"
++ 'For example' means there are many perfect games.
In ICCF WC Finals alone there are > 1000 perfect games.
Nobody said any moves were forced.
If white plays differently, then black draws differently.
How is the subject of weakly solving Chess.

tygxc

@7157

"1000"
++ 10^17 / 10^14 = 1000.

Elroch

10^15 / 10^14 =10

So I can fail to solve chess more quickly than you.

tygxc

@7160

Again explained

Positions                                                             Strongly solving          Weakly solving
All legal moves                                                   10^44                          10^22
Underpromotions to captured pieces only        10^38                          10^19
Reasonable moves only                                      10^34                          10^17

The difference between weakly and strongly solving is a square root
w^d = Sqrt (w^(2d))
w = width, d = depth

10^44 comes from the Tromp paper
10^38 comes from the Gourion paper multiplied by 10 to include 3-4 queens
Reasonable comes from the random sample of 10,000 Gourion positions
If you doubt that, then take any of the 10,000 randomly sampled FEN and try to construct a reasonable game from the initial position that leads to it. You will fail to do so.

Elroch

You can reduce it even further by not including minor pieces.

llama36

You could solve it for the dark squares (just don't include any of the light ones).

Then solve it for the light squares.

Put the two solutions together and you've solved chess.

QED (quite easily done)

Elroch
llama36 wrote:

You could solve it for the dark squares (just don't include any of the light ones).

Then solve it for the light squares.

Put the two solutions together and you've solved chess.

QED (quite easily done)

With a bit of help from me and you, @tygxc should be able to solve chess with less computation than checkers. 

charmquark314
MARattigan wrote:
charmquark314 wrote:

That's not why. Solving chess, at least in the sense of strongly solving chess, would be to provide an algorithm that evaluates every legal position to "white mates with perfect play", "black mates with perfect play", or "draw", and provide a move that does not change that evaluation. (Since chess games have a finite length, said algorithm can consistently win any winning position, and force a draw in any drawn position.)

"Chess" denotes several different games each with its own set of solutions. Of the FIDE versions only games played according to the post 2017 competition rules are limited to a finite length. Games played under post 2017 basic rules or all pre 2017 rules are not.

That means that for the unlimited games simply providing a move that doesn't change the evaluation is not enough. E.g. for a position with this diagram (with the White king on one of the two squares shown) and White to play ...

an algorithm that recommends moving the king to the other square doesn't change the evaluation but also doesn't solve the position.

And strictly speaking the evaluation is necessary at most for drawn positions in the unlimited games. Just a move will do.

 No chess engine we have right now can do that. Such an engine's self-play would result in either consistent wins from one side, or consistent draws.

True, which is not to say a consistent result indicates perfect play. It may be the case that SF15 would draw against itself no matter how many attempts it made with less than geological think time per move from this Black winning position, for example.

 

(As opposed to a random legal move generator v SF15 which would probably achieve the mate in far fewer attempts than a monkey on a typewriter would need etc.) 

Yes, that does mean we have solved chess with up to 7 pieces on the board (an algorithm for that is available on this website).

'Fraid not. For example it doesn't do the final position in this competition rules game which is a mate in 16.

(Try using the top move it shows against the computer in "Analysis".)

 

Fair enough, I was referring to the current FIDE rules.

You aren't taking the 50-move rule into account. If you shuffle your king in the position you mentioned, you'd at some point be unable to mate within the 50-move rule, thus changing the evaluation from "white mates" to "draw". Hence my hypothetical algorithm would force mate in less that 50 moves in your given position to prevent a draw, which changes the evaluation. Using the website, you similarly have to take the 50-move rule into account.

No, a consistent result does not indicate perfect play, but perfect play requires a consistent result.

MARattigan
Elroch wrote:

The difference is huge for a strong solution of chess, but not for a weak solution which merely has to achieve the optimal result of the starting position, not to successfully take advantage of blunders by the opponent. ...

1. That depends on the weak solution. The fact that there are weak solutions that include no repetitions doesn't imply that all weak solutions include no repetitions. I think most would (though there would exist a reduced solution for each that didn't). Nothing in what @tygxc has said so far includes any steps to eliminate either repetitions or blunders.

2. The difference may not be huge for many weak solutions, but that doesn't mean that it's not huge for any process for finding those solutions. A perfectly accurate player (both perfect and accurate) would not repeat a position that is winning for him. Stockfish will not only repeat winning positions but also repeat positions it thinks are winning (it does't know one way or the other of course). 

Here is a recent game I ran, Arena/SF15 v Arena/Rybka/Nalimov from a ply count 0 mate in 46 position.

SF15 has already blown it on move 9 under the 50 move rule.

Exercise for @tygxc: could he still win if the 50 move rule "didn't matter" but the triple repetition rule "did matter".

As you said earlier, @tygxc doesn't understand the difference between basic rules positions and competition rules positions. I'll have another go at explaining.

So @tygxc:

ARE YOU LISTENING?

I give two examples, both from the KR v K endgame to keep it simple.

In the above game the FEN in the final position is the same as the FEN in the initial position with the exception of the ply count and move number. Under FIDE basic rules chess since 2017 the remaining fields are sufficient to determine the possible continuations and hence the theoretical value of the positions .

The remaining fields are in fact all Tromp takes into account in arriving at his estimate of 4.82 x 10^44 legal positions, so he counts the two positions as the same.

Under FIDE basic rules since 2017 that is OK; both positions are a forced win for White and the positions can be counted as the same.

Under FIDE competition rules however, the initial position is a forced win but the final position is a draw because after 49...Kb1 White has no checkmate and Black can claim under the 50 move rule. Under those rules the positions must be counted as different. (If you don't know how to mate from the initial position you are safe to follow Syzygy, because there are no pairs of previous positions considered the same under art.9.2.)

The above shows a game and variation. If you check the FENs in the final position of both they are identical in all fields. Tromp also counts these two positions as the same.

Under FIDE basic rules since 2017, White is winning in both positions.

Under FIDE competition rules, however the final position in the main line is drawn by triple repetition after 4...Ka1, whereas the final position in the variation is winning for White (again you can follow Syzygy if you have difficulty). So again under FIDE competition rules the positions must be counted as different.

Notice also that if you're playing under competition rules and ask Syzygy for advice as Black in the final position of the mainline, it will tell you to play 4...Kc1 which loses rather than 4...Ka1 which draws. That's why you should stop insisting that Syzygy is a strong solution of 7 man positions under FIDE competition rules. It's not.

Of course, ICCF rules are something altogether different again.

Final exercise for @tygxc:: Find the smallest upper bound you can for the number of positions in the KR v K endgame under FIDE competition rules.

 

 

MARattigan
charmquark314 wrote:
MARattigan wrote:
charmquark314 wrote:

That's not why. Solving chess, at least in the sense of strongly solving chess, would be to provide an algorithm that evaluates every legal position to "white mates with perfect play", "black mates with perfect play", or "draw", and provide a move that does not change that evaluation. (Since chess games have a finite length, said algorithm can consistently win any winning position, and force a draw in any drawn position.)

"Chess" denotes several different games each with its own set of solutions. Of the FIDE versions only games played according to the post 2017 competition rules are limited to a finite length. Games played under post 2017 basic rules or all pre 2017 rules are not.

That means that for the unlimited games simply providing a move that doesn't change the evaluation is not enough. E.g. for a position with this diagram (with the White king on one of the two squares shown) and White to play ...

an algorithm that recommends moving the king to the other square doesn't change the evaluation but also doesn't solve the position.

And strictly speaking the evaluation is necessary at most for drawn positions in the unlimited games. Just a move will do.

 No chess engine we have right now can do that. Such an engine's self-play would result in either consistent wins from one side, or consistent draws.

True, which is not to say a consistent result indicates perfect play. It may be the case that SF15 would draw against itself no matter how many attempts it made with less than geological think time per move from this Black winning position, for example.

 

(As opposed to a random legal move generator v SF15 which would probably achieve the mate in far fewer attempts than a monkey on a typewriter would need etc.) 

Yes, that does mean we have solved chess with up to 7 pieces on the board (an algorithm for that is available on this website).

'Fraid not. For example it doesn't do the final position in this competition rules game which is a mate in 16.

(Try using the top move it shows against the computer in "Analysis".)

 

Fair enough, I was referring to the current FIDE rules.

You aren't taking the 50-move rule into account. If you shuffle your king in the position you mentioned, you'd at some point be unable to mate within the 50-move rule, thus changing the evaluation from "white mates" to "draw". Hence my hypothetical algorithm would force mate in less that 50 moves in your given position to prevent a draw, which changes the evaluation.

Exactly why I said, "for the unlimited games", meaning games without the 50 move or triple repetition rules, e.g. FIDE basic rules chess since 2017. Under those rules you never reach a point at which the moves change the evaluation, so the moves are always perfect.

But the result isn't.

Using the website, you similarly have to take the 50-move rule into account.

Under FIDE competition rules that's true, but it still wouldn't be any use. E.g. starting with the king on h8, after ...

the site's top move (https://syzygy-tables.info/?fen=6K1/6R1/8/8/3k4/8/8/8_b_-_-_9_5) is 5...Kc5 which loses for Black when he could draw by 5...Ke5.

In that case it's easy to say at what point White's moves cease to be perfect (5.Kg8).

No, a consistent result does not indicate perfect play, but perfect play requires a consistent result. 

We're agreed on that. My comment wasn't intended to contradict what you said; just an observation.