How close can we come to proving that white draws?

[mmt]

We can make an opening book with only one choice for white but all possible moves for black. The moves for white could be chosen based on the current opening theory with a preference for captures and pawn moves. After 9 plies we'll have about 1.5 million starting positions (35^4) minus transpositions.

Now there are two questions that we can estimate:
1. For how many of these positions can we prove a draw for white now or with future hardware improvements? We could use current mate solvers to show there is no mate for black but it would be better to make a specialized draw searcher program. It will be much easier than looking for mates but still probably hard. We could try to estimate how much faster hardware will help by looking at what percentage gets solved with increasing time limits.

2. What percentage of the ~10^42 total (ignoring the 50-move rule) legal EGTB positions will be reachable from remaining positions? Starting with 1. d4 we don't need to consider any positions with white pawns on d2 etc. It will be quicker to create an 8-piece EGTB. Maybe a 9-piece EGTB is not out of the question?

Any estimates or other ideas about how to go about this?

[Alayan]

What makes this trickier is that although the final proof tree will only require one white move for each position in the book, to know which move to pick it may be necessary to explore multiple white moves. Is 1. e4 or 1. d4 giving the smallest proof tree ? Who knows ?

A specialized draw searcher program is not so easy. To prove a position is drawn, you need to show that all black moves either draw or lose. To prove a quick forced 3-fold is indeed forced, you might have to search a huge tree where black is losing surely but slowly and solve it all the way to mate or a drawn TB position. And solving such a tree is computationally hard. Even something as bad like 1. g4 d5 2. f3 e5 3. Kf2 Qh4+ 4. Ke3 d4+ 5. Kd3 e4+ 6. Kxd4, which has four horrible moves, takes significant time to solve to mate.

Building specialized endgame tables that remove some moved pawns as possibilities would reduce their size and speedup their generation, but because of promotions, pawnless endgames remain problematic. Also, depending on black moves, the EGTB positions you might rule out for sure will vary.

Proving that white draws or wins is easier than proving that white draws and black draws, as white's starting advantage means that black has less ways to prolong the game, but it's still very hard.

And when it comes to hardware improvement, massive breakthroughs would be needed. 10x more CPU perf, RAM and storage wouldn't cut it.

If willing to use a high Stockfish eval as a cutoff, the problem becomes much easier, but then it's not a mathematical proof, only overwhelming evidence.

[mwyoung]

We can make an opening book with only one choice for white but all possible moves for black. The moves for white could be chosen based on the current opening theory with a preference for captures and pawn moves. After 9 plies we'll have about 1.5 million starting positions (35^4) minus transpositions.

Now there are two questions that we can estimate:
1. For how many of these positions can we prove a draw for white now or with future hardware improvements? We could use current mate solvers to show there is no mate for black but it would be better to make a specialized draw searcher program. It will be much easier than looking for mates but still probably hard. We could try to estimate how much faster hardware will help by looking at what percentage gets solved with increasing time limits.

2. What percentage of the ~10^42 total (ignoring the 50-move rule) legal EGTB positions will be reachable from remaining positions? Starting with 1. d4 we don't need to consider any positions with white pawns on d2 etc. It will be quicker to create an 8-piece EGTB. Maybe a 9-piece EGTB is not out of the question?

Any estimates or other ideas about how to go about this?

Your method is flawed. There is no trick, mateslover, or fictional draw searcher that could ever answer the question.

Remember chess is a 100 percent tactical game. Wins are not won by material advantage, or another human concept of positional understanding. Chess is won by checkmating the king.

The chess game tree is enormous, and there is no computer advancement, or hidden technology that can get around this fact.

The answer is humans will never know if chess is a forced win or draw.

I still see people here have a hard time understand just how big the game tree in chess truly is and what this means.

[mmt]

Your method is flawed. There is no trick, mateslover, or fictional draw searcher that could ever answer the question.

Huh? You haven't shown that my method is flawed at all. I'm obviously not saying that it can be done now.

[mwyoung]

Your method is flawed. There is no trick, mateslover, or fictional draw searcher that could ever answer the question.

Huh? You haven't shown that my method is flawed at all. I'm obviously not saying that it can be done now.

Yes because you are assuming you need only one move for white. And making a book using human theory only. Again flawed logic, and method.

You are assuming moves like 1d3, 1 a3, 1 nh3.... are no good and could not lead to a win. You can not make such assumptions, and then make any claim that chess is a draw, or if black wins. That chess is a win for black. Because you did not search the forcing moves of the other starting positions.

[Angrim]

Proving a draw is MUCH harder than proving a win. You have to refute every move by both sides. If there is a win, and if it is simpler than most people expect, it might be possible with a few more years of tech advances to prove it. But if it is a draw, there is no way with currently foreseeable tech to prove it before our sun burns out.

[Alayan]

Proving that white draws means proving that white can at least force a draw. It doesn't include proving that white cannot force a win (which would done by proving that black can force a draw, and mmt would have then talked about proving chess is a draw, not that white draws).

Looks like the greater part of the arguments in this forum come from misunderstanding what is being read.

[mwyoung]

Proving that white draws means proving that white can at least force a draw. It doesn't include proving that white cannot force a win (which would done by proving that black can force a draw, and mmt would have then talked about proving chess is a draw, not that white draws).

Looks like the greater part of the arguments in this forum come from misunderstanding what is being read.

Ok...9 ply book is 4 1/2 moves. So how many trillion trillion years will this fantasy draw finding computer need to prove white can force a draw.?

[towforce]

Your method is flawed. There is no trick, mateslover, or fictional draw searcher that could ever answer the question.

Remember chess is a 100 percent tactical game. Wins are not won by material advantage, or another human concept of positional understanding. Chess is won by checkmating the king.

The chess game tree is enormous, and there is no computer advancement, or hidden technology that can get around this fact.

The answer is humans will never know if chess is a forced win or draw.

Once again, I'm not re-running the "Is Chess Solved" thread, where all this is discussed in depth, but, VERY briefly, there's no proof that you need to calculate the entire game tree to solve chess: counter examples exist - other games have been solved without generating the entire game tree.

I gave a possible way to do this for a slightly different problem in the other current thread for a similar question - can you prove that neither side can win material. It might be possible, with today's technology, to work out what conditions must exist in a position for it to be possible to win material, and to then show that these conditions don't exists in the starting position.

I am working on another way.

[mwyoung]

Your method is flawed. There is no trick, mateslover, or fictional draw searcher that could ever answer the question.

Remember chess is a 100 percent tactical game. Wins are not won by material advantage, or another human concept of positional understanding. Chess is won by checkmating the king.

The chess game tree is enormous, and there is no computer advancement, or hidden technology that can get around this fact.

The answer is humans will never know if chess is a forced win or draw.

Once again, I'm not re-running the "Is Chess Solved" thread, where all this is discussed in depth, but, VERY briefly, there's no proof that you need to calculate the entire game tree to solve chess: counter examples exist - other games have been solved without generating the entire game tree.

I gave a possible way to do this for a slightly different problem in the other current thread for a similar question - can you prove that neither side can win material. It might be possible, with today's technology, to work out what conditions must exist in a position for it to be possible to win material, and to then show that these conditions don't exists in the starting position.

I am working on another way.

Again I dress the flaw in your logic. You do not need to win material in chess . To win a game, or draw a game of chess. And it could be to force a draw with perfect play. You need to give up material.

So what is your method proving?

Chess is a 100% tactical game!