@4966
This thread is about solving chess, not about transfinite numbers or the continuum hypothesis.
Chess will never be solved, here's why
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Sep 18, 2022
0
#3904
tygxc wrote:
@4966
This thread is about solving chess, not about transfinite numbers or the continuum hypothesis.
But none of your posts are relevant to solving chess either.
@4969
"none of your posts are relevant to solving chess either"
++ I beg your pardon. All of my posts are relevant to solving chess.
I have calculated how long it takes to weakly solve chess: 5 years. I have shown how to do it.
Others troll with off topic.
Sep 18, 2022
0
#3906
tygxc wrote:
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
@4973
"There's no output strategy" ++ The output are the 3 alternative lines per white move.
"there's nothing to say how you determine what they are"
++ The top 4 moves of the cloud engine running for 17 s, (or a desktop running for 4.7 h). As previously shown the real good move is always among the top 4 moves with 1 error in 10^20.
"When you look for the sub function "Do they draw too?" it isn't there."
++ Either a table base draw, or a 3 fold repetition, or a humanly known draw, adjudicated by the good assistants.
"No mention of a computer" ++ Of course the 3 computers serve to do that. 1 computer looks at 1 e4, 1 computer at 1 d4, and a 3rd computer at 1 c4 and 1 Nf3 lines that do not transpose.
Sep 18, 2022
0
#3908
Elroch wrote:
There is no solution that involves two-fold repetitions being involved on the path to anywhere but a draw.
It is like in real play. A player fishing for a solution gets to a two-fold repetition and realises he needs to change his strategy from that point. When the strategies are final, this no longer occurs - two strategies that reach a two-fold repetition will reach an n-fold repetition because they are fixed.
Perfectly understood.
But a solution is not the same as a process for finding a solution. The tablebase approach avoids any problems by associating any position with on ordered pair (b,n) where b is a basic rules position and n is an increasing distance from some objective and never repeating a "b".
SF doesn't. It happily moves into repeated positions whether it evaluates its position as positive or otherwise and whether it is actually winning or otherwise (which it doesn't know). So a process for solving chess using SF with a twofold repetition rule would not produce the same results as a process using a threefold repetition rule. The GUI is arbiter and would terminate games under a twofold repetition rule that would continue under a threefold repetition rule. SF has a triple rule avoidance routine that will fire in many circumstances.
@4976
"SF has a triple rule avoidance routine that will fire in many circumstances."
++ Yes that is right. It might be modified to 2-fold. It may also be left 3-fold, when some 2-fold repetitions may get into the lines, but that does not harm.
Sep 18, 2022
0
#3910
tygxc wrote:
@4973
"There's no output strategy" ++ The output are the 3 alternative lines per white move.
Which is not a strategy, so according to your definition(s) not a solution. What is it exactly that you are posting?
"there's nothing to say how you determine what they are"
++ The top 4 moves of the cloud engine running for 17 s, (or a desktop running for 4.7 h).-Which? It could affect any timescale.-As previously shown the real good move is always among the top 4 moves with 1 error in 10^20.
Well you didn't say that. When are you going to produce a usable description of your method?
But cloud engines don't produce moves; you need software, e.g. an engine and a GUI. And which cloud computer anyway?
When you say "previously shown" were you referring to my post here (I reproduce the screenshot) or one of the other half dozen examples I posted where SF blows half a point with all its top 4 moves?
"When you look for the sub function "Do they draw too?" it isn't there."
++ Either a table base draw, or a 3 fold repetition, or a humanly known draw, adjudicated by the good assistants.
Well you didn't say that. When are you going to produce a usable description of your method?
You don't appear to have fixed which ICCF game we're talking about yet, you say, "Take an ICCF WC Finals drawn game e.g. this one. [my italics]
https://www.iccf.com/game?id=1164259".
When do you expect to decide on a definite first step? Will that be within five years?
But mainly you say, "do they draw too?". Your example appears to be an agreed draw, so the alternatives will draw too if you assume an agreed draw will follow. Are you just intending to prove that any moves will draw if a draw is agreed? I think you should be able to do that without too much investment.
"No mention of a computer" ++ Of course the 3 computers serve to do that. 1 computer looks at 1 e4, 1 computer at 1 d4, and a 3rd computer at 1 c4 and 1 Nf3 lines that do not transpose.
The last 3 are going to be a bit stuck if they're trying to follow your explanations with the example game you've given. And I could have sworn White has more first moves.
Sep 18, 2022
0
#3911
Optimissed wrote:
MARattigan wrote:
tygxc wrote:
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
The entire idea of strategy as applied here and in those definitions is incorrect and "strategy" is referred to because it seems classy and also it refers to the definitions and seems to support them.
"A different move" is the non-obfuscatory way to refer to the procedure, not that anyone here, who is on the wrong side of a discussion, is interested in being non-obfuscatory.
A model of clarity I must say. How the hell can "a different move" refer to a procedure?
I'm using the word "strategy" because that's exactly the word that @tygxc has used in his definitions. I don't have any problem with the word; try a dictionary.
@4980
" that's exactly the word that @tygxc has used in his definitions"
Those are neither my definitions, nor those of wikipedia.
It are the definitions of Prof. Em. van den Herik, a prominence in the field.
https://www.sciencedirect.com/science/article/pii/S0004370201001527
'Strategy' can refer to a set of moves, but also to a set of rules, or a combination of both.
@4979
"What is it exactly that you are posting?"
++ The output is the analysis of the succesive moves until a table base draw, or a prior 3-fold repetition or known draw. Look at the games as trunks of trees and the output are the branches.
"Which? It could affect any timescale." ++ The intent is to use 3 cloud engines of 10^9 nodes/s running 17 s/move. This would be equivalent to 3000 desktops of 10^6 nodes/s.
"cloud engines don't produce moves" ++ They do, just like an engine on a desktop does, but 1000 time faster.
"you need software" ++ E.g. Stockfish
"which cloud computer anyway?" ++ The one selected during procurement of the rental service during 5 years. It should be able to process 10^9 nodes/s. It is a matter of price, availability etc.
"When you say "previously shown" were you referring to my post"
++ No I was referring to my own calculation from AlphaZero autoplay.
"examples I posted where SF blows half a point with all its top 4 moves?"
++ Those are irrelevant KNN vs. KP that would be looked up in the table base long before they even appear. Besides you did not run your desktop for 4.7 h. If you want to test the result, then try a KRPP vs. KRP on your desktop and see for yourself that the table base exact move is always among the top 4 engine moves.
"When are you going to produce a usable description of your method?"
++ I have given it several times. Take an ICCF WC draw. Consider 3 alternatives to the last white move. Calculate these to either a table base draw, or a 3-fold repetition, or a known draw. The latter requires some human supervision but is not essential, it just saves time.
"You don't appear to have fixed which ICCF game we're talking about yet"
++ The good assistants take the set of all ICCF WC Finals draws and pick those that correspond to a certain repertoire. E.g. against 1 e4: 1...e5 2 Nf3 Nc6. Then games with 2...Nf6 or 1...c5 can be left out. Then those games are treated one after the other.
"When do you expect to decide on a definite first step? Will that be within five years?"
++ I do not know. It would cost 3 million $. That is the obstacle.
"Your example appears to be an agreed draw" ++ In a known drawn position: opposite colored bishop endgame, no chance to win for either side.
"so the alternatives will draw too" ++ Probably, but maybe there are ways to avoid the drawn opposite colored bishop endgame.
"No mention of a computer" ++ Of course the 3 computers serve to do that. 1 computer looks at 1 e4, 1 computer at 1 d4, and a 3rd computer at 1 c4 and 1 Nf3 lines that do not transpose.
"I could have sworn White has more first moves."
++ There are 20 first moves. I look at the 4 that oppose most to the draw. If they draw, then the 16 that oppose less to the draw will draw or lose as well.
Sep 18, 2022
0
#3914
MARattigan wrote:
Elroch wrote:
There is no solution that involves two-fold repetitions being involved on the path to anywhere but a draw.
It is like in real play. A player fishing for a solution gets to a two-fold repetition and realises he needs to change his strategy from that point. When the strategies are final, this no longer occurs - two strategies that reach a two-fold repetition will reach an n-fold repetition because they are fixed.
Perfectly understood.
But a solution is not the same as a process for finding a solution. The tablebase approach avoids any problems by associating any position with on ordered pair (b,n) where b is a basic rules position and n is an increasing distance from some objective and never repeating a "b".
SF doesn't. It happily moves into repeated positions whether it evaluates its position as positive or otherwise and whether it is actually winning or otherwise (which it doesn't know). So a process for solving chess using SF with a twofold repetition rule would not produce the same results as a process using a threefold repetition rule. The GUI is arbiter and would terminate games under a twofold repetition rule that would continue under a threefold repetition rule. SF has a triple rule avoidance routine that will fire in many circumstances.
This is correct, but I think we all understand a valid way to a solution (apart from practicality of resources) is to use heuristics (eg Stockfish evaluations based on incomplete analysis) to arrive a strategy. We both understand that this strategy has to deal with every legal move that the opposing side to a strategy could play.
While I haven't been completely precise, my notion is that we can ignore moves by the opponent that lead to a position that has already been dealt with nearer to the starting position. This is rather like the reverse of generating a tablebase.
To be more precise, at first pass, the strategy generates all positions that can be reached in a single ply by applying the strategy (i.e. it picks a first move). The second pass is to add all positions that are reachable by legal moves by the opponent. This repeats with the strategy picking a single move and the opponent adding all legal moves except that, at later opponent passes, we don't need to look at moves that return to a position reached at an earlier pass, since such a move cannot help show the strategy does not draw.
You are right to point out that when developing a strategy, we can't tell the heuristics will work. If they don't, it's back to square one to develop better heuristics and start going through the passes from the starting position once again.
The way in which @tygxc misses the point is by thinking that by confidently believing some of the opponent moves are bad based on generalisation of imprecise rules that are known to sometimes fail, they can be ignored. This sort of "solution" is for players, not researchers. He also fails to justify a belief that the solution is small. The opponent being able to play large numbers of moves completely freely generates enormous numbers of positions. There is no guarantee it is as few as the square root of the number of legal positions, since it may take the first player many moves to get an irreversible move played, and there can be hundreds of irreversible moves. Long games can explore a lot of positions even with a small exponential factor (eg 2^100 is bigger than the number of legal positions).
It's also worth noting that the combination of all balanced positions and all positions where one side is winning is more than half of all legal positions.
Sep 18, 2022
0
#3915
tygxc wrote:
++ There are 20 first moves. I look at the 4 that oppose most to the draw. If they draw, then the 16 that oppose less to the draw will draw or lose as well.
Now it's all clear. You didn't mention previously that you had access to a chess oracle with perfect knowledge of the 32-piece tablebase that tells you which moves "oppose the draw best".
If only you had mentioned this before, no-one would have pointed out you are wrong.
@4986
"a chess oracle with perfect knowledge of the 32-piece tablebase that tells you which moves oppose the draw best"
++ That is accumulated human knowledge over centuries of play and analysis, logic, and corroborated by independent calculation with no other input but the Laws of Chess.
https://arxiv.org/abs/2111.09259
Figure 5 and figure 31.
It is logical that
1 a4 does not oppose more to the draw than 1 e4 or 1 d4.
1 Nh3 does not oppose more to the draw than 1 Nf3.
@4985
"this strategy has to deal with every legal move that the opposing side to a strategy could play"
The move must oppose to the draw. 1 e4 e5 2 Ba6 does not oppose. 1 e4 e5 2 Nf3 Nc6 and now neither 1 Nd4, 1 Nxe5, Ng5, Nh4, or Ng1 opposes to the draw.
"when developing a strategy, we can't tell the heuristics will work."
We know some heuristics and when they work and when not. That is one task of the good assistants. When in doubt, calculate? When no doubt, adjudicate a win (like a rook down with no compensation) or a draw (like an opposite colored bishop ending with no prospect to win).
If they don't, it's back to square one to develop better heuristics and start going through the passes from the starting position once again.
"This sort of "solution" is for players, not researchers."
This research paper recognises the use of knowledge as beneficial.
https://www.sciencedirect.com/science/article/pii/S0004370201001527
"The opponent being able to play large numbers of moves completely freely" ++ Not completely freely: he must oppose to the draw or to a loss.
"it may take the first player many moves to get an irreversible move played" ++ ICCF games show otherwise: there is always a compelling reason to (re)capture or move a pawn.
"the combination of all balanced positions and all positions where one side is winning is more than half of all legal positions." ++ Only reachable drawn positions are of interest. Each pawn move and each capture renders huge numbers of positions unreachable. Most of the legal positions can never be reached by optimal play. E.g. the 3 random samples
https://github.com/tromp/ChessPositionRanking
tygxc wrote:
@4949
10^17 is a huge number, but it is finite. Chess is finite.
It is a huge number, but it doesn't relate to solving chess.
Sep 18, 2022
0
#3919
tygxc wrote:
@4986
"a chess oracle with perfect knowledge of the 32-piece tablebase that tells you which moves oppose the draw best"
++ That is accumulated human knowledge over centuries of play and analysis, logic, and corroborated by independent calculation with no other input but the Laws of Chess.
https://arxiv.org/abs/2111.09259
Figure 5 and figure 31.
It is logical that
1 a4 does not oppose more to the draw than 1 e4 or 1 d4.
1 Nh3 does not oppose more to the draw than 1 Nf3.
No, it is not "logical". It is inductive from incomplete evidence that is definitely not adequate to justify certainty.
Your permanent problem is that you don't understand that there is an enormous difference between a very high degree of confidence and logical certainty. The former can be wrong. The latter cannot.
Let me give you an example. Suppose you get a set of binary data from some sort of generator. It has as many digits as every position ever looked at in the game of chess. All of the digits are ones. How sure can you be that more of the data has no zeros?
If you say "certain", you haven't learnt to reason correctly.
Yes. But it's worth remembering that whether these cardinals exist is not a given. You can do almost all of mathematics with ZFC set theory. The first inaccessible cardinal is bigger than all the cardinals that can be proven to exist in this model of mathematics: it has to be added via another axiom.
It is not provable that the existence of this cardinal is consistent with ZFC (but it is believed to be, like it is independently believed that ZFC is consistent).