How close can we come to proving that white draws?

[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.

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!

Hence why I said "slightly different problem" (see above quoted text).

My OPINION is that if, as I think likely, it's not possible to force the win of material from the opening position, then it's also impossible to force a checkmate.

There are probably other ways to prove that chess is a draw as well: this method is just something I came up with during the "Is Chess Solved" thread: I don't claim it to be the only way, the fastest way, or anything else. But it is a fact that other games have been solved without generating the entire game tree.

[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!

Hence why I said "slightly different problem" (see above quoted text).

My OPINION is that if, as I think likely, it's not possible to force the win of material from the opening position, then it's also impossible to force a checkmate.

There are probably other ways to prove that chess is a draw as well: this method is just something I came up with during the "Is Chess Solved" thread: I don't claim it to be the only way, the fastest way, or anything else. But it is a fact that other games have been solved without generating the entire game tree.

It is not an opinion to dispute proven facts. It is just nutty. You don't need to win material to win a game, or draw a game of chess.

Do you know the rules of chess.

[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.

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!

Hence why I said "slightly different problem" (see above quoted text).

My OPINION is that if, as I think likely, it's not possible to force the win of material from the opening position, then it's also impossible to force a checkmate.

There are probably other ways to prove that chess is a draw as well: this method is just something I came up with during the "Is Chess Solved" thread: I don't claim it to be the only way, the fastest way, or anything else. But it is a fact that other games have been solved without generating the entire game tree.

It is not an opinion to dispute proven facts. It is just nutty. You don't need to win material to win a game, or draw a game of chess.

Do you know the rules of chess.

You might be correct, but equally the loss of the king might be a type of loss of material.

[Uri Blass]

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.

How do you know that no draw searcher can answer the question?
It is possible that you can prove by brute force that white needs only 20 moves to force a draw.

I believe that white need more moves for it and probably needs some hundrends of moves but I have no proof.
I suggest to have a game when the target of white is to win by checkmate or simply to survive n plies without a draw when the target of black is to force a mate or draw in less than n plies and based on the value of n when white get practically 50% in engine-engine games we can have a guess how many plies white needs for a draw.


Engines authors will have to change their engine to play this type of game well and they will need to build at least draw searcher(something that for some reason nobody is interested to do without this type of game).

[Albert Silver]

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?

Not really sure about the need for this. If you follow elite correspondence chess of last few years, it is now well over 90% draws, and entire events are decided by a single win. Most wins and losses are actually not due to the chess, but technicalities such as time losses. The writing is on the wall.

[Dann Corbit]

Coming close to proving means not proving.
Something is proven or it isn't.
We have good educated guesses (most think the game is drawn).
But to prove something means that there is no doubt left whatsoever.

[Uri Blass]

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?

I suggest first to try to solve some easier problems.

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

rnb1kbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

Can we prove with the hardware of today that white does not lose and if yes then what is the distance to mate or repetition.

Note that I am practically sure that white is winning but no engine can see a forced mate.
Can engine see at least a forced draw for white(Note that you need to change the search to prove at least a forced draw because engines are not programmed to evaluate repetition of the position as a win for themselves and if you change them to evaluate repetition as a win you need to change the way that they use the hash tables because the question if you can force a repetition is dependent on the history of the game.


what about the following position

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

4k1n1/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQ - 0 1

How many nodes do engines need to search to see a forced mate and how many nodes they need to search to see at least a forced draw for white?

[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.

How do you know that no draw searcher can answer the question?
It is possible that you can prove by brute force that white needs only 20 moves to force a draw.

I believe that white need more moves for it and probably needs some hundrends of moves but I have no proof.
I suggest to have a game when the target of white is to win by checkmate or simply to survive n plies without a draw when the target of black is to force a mate or draw in less than n plies and based on the value of n when white get practically 50% in engine-engine games we can have a guess how many plies white needs for a draw.


Engines authors will have to change their engine to play this type of game well and they will need to build at least draw searcher(something that for some reason nobody is interested to do without this type of game).

A minimax could do this in theory. But there is no such thing as a draw searcher engine.
But I suggest you get started right away. As the universe will suffer heat death in only trillions of years.

[jefk]

how close are we to prove the earth is not flat ?

this thread almost looks like a joke to me;
happy Friday 13th anyway

In the game chess (besides GM's from Steinitz to Carlsen)
there have been now six serious attempts to find
the best advantage for White in chess,
1)
Chessbase
besides statistics (1.Nf3!) they have a 'live book' now for many years
https://en.chessbase.com/post/livebook- ... ing-oracle
(uhm forgot to mention this above coz they never bothered
to 'backsolve' the stuff, knowing ofcourse that such is very
dependent on the engine eval and nowadays they show
engine evals for different engines (apparently it never got
in F Friedels mind or so to combine an average engine eval
with statistics (incl corresp and engine games) and then
backsolve the whole lot, but guess what the result is draw
(tip from me: include 'sharpness' to make a repertoire ;
see the PS3 below

2) Arshah
now defunct, but here's still an old glimp
https://chessacademy.am/static/article/32?lang=en
https://about.me/arshah
and it was on FB
https://www.facebook.com/ArShah-Chess-A ... 037964114/
they found chess is a draw, whether you play d4 or e4

3) zipproth (no clarification needed for the geeks)
brainfisch etc. , the Cerebellum book

4) chessdb.cn
only displaying xiangchi chess now again
(they found chess is a draw)

5) Larry Kaufman (Komodo, chess advantage new repertoire etc );
with all respect, but with Dragon LK but you now may have to update
your repertoire again, (and then again ad infinitum ?) Lol
Anyway LK with all respect is senior GM and confirms White
cannot win, considering the drawing margins etc
hey ask him, he's still on this forum , you know
As is still old dr Bob and as far as i know he's one of
the rare chess geeks (besides late ex corresp world chamo
Hans Berliner) who thinks (or thought) that White might win

6) yours truly
www.superchess.blogspot.com
the BB download doesnt work anymore, i may
update this soon but it's only a small book, my personal
book was quite big (20 million positions or so) and
clearly indicated White cannot win.
Ergo (as the topic of this thread, ofcourse White
avoid a loss, ergo White can draw, obviously

As physicist, i prefer the Copernican model above
the Ptolemaeus model, and we're not the center
of the universe. And White cannot win in chess.
If you need a more stringent math proof for that,
is a philosophical question (there's no need for
brute force calcs as 32 tb or so for that imho)

Conclusion, from 1-6 proof ? as the English
say, the proof is in the pudding.



PS with transpositions the nr of moves in chess becomes less
than (some) people think; and when we discount positions with
score < 4 or so (tactical mistakes) then such a tree becomes even smaller
and strongly hints to the conjecture that white cannot win ergo chess = draw
PS2 ever heard of 'game theory' Repeating myself, but here is Zermelo
https://en.wikipedia.org/wiki/Zermelo%2 ... me_theory)
If there is no winning strategy for White, than the game is a draw.
(some math freaks or slightly brain damaged Trump supporters
may for trillions more generations may dispute this, but then i'm sure
some Nash type of guy will stand up (eg using network theory) and
may write a paper to show that there's no strategic advantage
in chess (or some similar) games to get a White advantage ergo *draw*
(hey, maybe i will write such a paper, while i'm still alive;
not that some chess nuts will then ever cite that if they think
White can win with 1.b3 best by (their) test(s) or whatever
PS3 chess indeed is a (to a large extent) a tactical game, depending on
your opponent you may like to go for sharp or positional lines;
maybe the multi-pv option with Kom-mcts (or simply) Stockfish can
indicate (with the eval differences between 1,2,3rd lines can
indicate 'sharpness' of a position. What i would like to see as
human player, is a database not only with eval (and backsolving)
but also the option of sharpness to 'backsolve' a repertoire
from that. Some nice work for the programmers

[mmt]

I suggest first to try to solve some easier problems.

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

rnb1kbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

Can we prove with the hardware of today that white does not lose and if yes then what is the distance to mate or repetition.

Yes, it would be good to try such positions since we have no draw searchers. What I proposed in #1 is not all that much harder and it would be interesting to find out what percentage of such positions is drawn or won by white.

what about the following position

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

4k1n1/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQ - 0 1

How many nodes do engines need to search to see a forced mate and how many nodes they need to search to see at least a forced draw for white?

I once solved a little harder position (with a rook for black) and it took a while but it found a mate. I ran positions with a queen or two rooks for black for pretty long and it couldn't find a mate.