Chess solved?

[jp]

A possible reason to believe some chess position is special is if we see some program that practically does not lose with white or black.
We can suspect that some engine practically solved the position in the meaning that it is unbeatable even with no mathematical proof that the game is a draw.

I'm not even convinced by this suspicion of "practical unproven solution". We should look at tablebase positions and see what happens with engines.

e.g. this position ---

[d]6N1/3n4/3k1b2/8/1r6/5K1Q/8/8 w - - 0 1

Apparently only one move wins. Good luck to all the centaurs. And to all the engines without endgame tables.

I can predict the engines will have many tablebase "blunders" here, but I don't know what the result of all the blundering will be. Can someone please run a few engine games and see? If engines draw all the time, we could suspect that it is a draw, but then we would be wrong.

[Uri Blass]

A possible reason to believe some chess position is special is if we see some program that practically does not lose with white or black.
We can suspect that some engine practically solved the position in the meaning that it is unbeatable even with no mathematical proof that the game is a draw.

I'm not even convinced by this suspicion of "practical unproven solution". We should look at tablebase positions and see what happens with engines.

e.g. this position ---

[d]6N1/3n4/3k1b2/8/1r6/5K1Q/8/8 w - - 0 1

Apparently only one move wins. Good luck to all the centaurs. And to all the engines without endgame tables.

I can predict the engines will have many tablebase "blunders" here, but I don't know what the result of all the blundering will be. Can someone please run a few engine games and see? If engines draw all the time, we could suspect that it is a draw, but then we would be wrong.

50 move rule is part of chess.
This position is a draw.
I do not know what engines see here but it proves nothing because it is possible to have a drawing strategy from the opening position when the players never get this position so you even do not need to evaluate this position.

[jp]

50 move rule is part of chess.
This position is a draw.
I do not know what engines see here but it proves nothing because it is possible to have a drawing strategy from the opening position when the players never get this position so you even do not need to evaluate this position.

This is just one TB position that has been quoted previously by others on this bulletin board. As you know, there are many difficult TB positions that are not "cursed" wins. I can probably find another example from this bulletin board (though the search function on this BB is not the best).

Of course, it proves nothing. Neither does an engine always drawing with either color from the opening position. As you know, the whole concept of looking at engine performance in games abandons all hopes of proof.


What a TB position that is a win but drawn in all engine-engine games would show is this:

you cannot assume that just because the engines get the same result game after game, they have "solved" the position even in an unproven sense.

[jp]

Let me add: If a position is a cursed win, I'd want any unproven "solution" to tell me that. After all, the TBs include that info.


And if engines in game after game get the right result for a position but obviously have no clue what they are doing, then I would not regard that as solved in an unproven sense either.

That is likely to happen in many drawn positions. The engines might have big evals, but presumably if they play games against each other they will stumble their way to a draw by the 50-move rule as long as the defending side does not play completely stupidly.

For example...

[d]8/6pk/7r/8/8/7P/6QP/7K w - - 0 1

Without 7-man endgame tables, Stockfish-dev's (static) evaluation of this position is +4.67. But it's a draw. How many similar positions are there, say with eight or nine men, that Stockfish totally misevaluates?

[towforce]

Another idea: how about... sets of beacon positions, followed by "closing the gap" between the start position and the endgame table base positions?

The analogy I'll use here is the closing of the Mid-Atlantic gap (link) - after the gap closed, Allied shipping losses to Axis submarines fell dramatically, and, correspondingly, Axis submarine losses increased dramatically.

In a typical position, the game tree extends further than can be computed before it hits table bases. Working back from table base positions, "beacon positions" could be found for which the result is known. Beacon positions need not be single positions - they could be a huge number of positions that comply with a rule for which no known exceptions exist (obviously the rule would have to be modified if an exception was found).

Once you have a reasonable set of beacon positions, more beacon positions could be found from these: positions (or position rule sets) for which either side can force the position into another beacon position closer to the endgame.

I have no doubt that using this system, we could massively extend the range of positions for which we think we know the outcome back from the tablebase positions. I wonder how close to the start position we'd be able to get?

At the very least, we'd get a steady increase in the number of times a search hit "known result" positions.

[towforce]

Another idea: how about... sets of beacon positions, followed by "closing the gap" between the start position and the endgame table base positions?

The analogy I'll use here is the closing of the Mid-Atlantic gap (link) - after the gap closed, Allied shipping losses to Axis submarines fell dramatically, and, correspondingly, Axis submarine losses increased dramatically.

In a typical position, the game tree extends further than can be computed before it hits table bases. Working back from table base positions, "beacon positions" could be found for which the result is known. Beacon positions need not be single positions - they could be a huge number of positions that comply with a rule for which no known exceptions exist (obviously the rule would have to be modified if an exception was found).

Once you have a reasonable set of beacon positions, more beacon positions could be found from these: positions (or position rule sets) for which either side can force the position into another beacon position closer to the endgame.

I have no doubt that using this system, we could massively extend the range of positions for which we think we know the outcome back from the tablebase positions. I wonder how close to the start position we'd be able to get?

At the very least, we'd get a steady increase in the number of times a search hit "known result" positions.

Closing the gap from the other end (the start position), there wouldn't, of course, be any "beacons", because you wouldn't know for sure that a given position is safe (because you cannot build the game tree far enough ahead), but thinking about working from the start position, and possible ways to prove that neither side can force the win of material, I came up with this idea:

* what conditions must exist to be able to take a piece without the opponent taking a piece back?

* what conditions must exist for those conditions to exist?

* what conditions must exist for those conditions to exist?

etc.

In this way, it might be possible to prove that it's not possible to force the win of material from the start position, which for me would be very close to proving that the game is a draw (the king is material itself after all).

Looking at a simpler game like tic-tac-toe, it would be reasonably easy to do this exercise: to get three in a row, you must get two rows of two in a row, to get two rows of two... etc, and it would thus be easy to prove that tic-tac-toe is a drawn game.