Mathematics is a lame human made discipline.
For example, there are algebraic transcendental functions which solution can't be written but is possible to draw the solution graphically.
Chess will never be solved, here's why
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@4593
"Humans could vary from say 5ft to 8ft. We have good data on how much they vary to make predictions." ++ We use the Gaussian distribution, though we know it is not exact.
"in chess there are always x amount of lines that maintain current evaluation and avoid an error." ++ Yes, that is right.
"Say that with best play there are 2 available lines that force a win for white.
Once an error happens and evaluation changes from a win to a draw, there are now 19 available lines to force a draw with best play." ++ Yes, that is right. But what does that mean?
Let us assume chess is a draw. In the initial position there are 20 possible white moves. Most of these lead to a draw as well. 1 g4 probably loses by force. So white has say 19 moves that draw.
Now black has 20 responses to each of the 20 white moves. To 1 e4 1...e5 probably draws, 1...c5 probably as well, 1...e6 or 1...c6 maybe too, maybe not, 1...Nf6 probably not, 1...b5 and 1...f5 surely not. So black has a narrower choice of good moves that hold the draw.
It is this phenomenon that explains why white wins more often than black:
white has a broader choice of moves that hold the draw and black has a narrower choice.
"We don't have accurate data on how much "x" varies to make any predictions on errors per game. We could have 136 games where the first error occured in 100% of the games and the second occured in 15% of the games."
++ Statistics on the 136 ICCF WC games show that the 127 draws are > 99% sure to contain no error and the 9 decisive games are > 99% sure to contain exactly 1 error.
"There is no way to reliably make predictions" ++ Yes, there is.
We can even reliably predict what door allows all 8 billion people to walk under it upright.
We do so using the Gaussian distribution, of which we know it does not work exactly.
tygxc wrote:
@4593
"Humans could vary from say 5ft to 8ft. We have good data on how much they vary to make predictions." ++ We use the Gaussian distribution, though we know it is not exact.
"in chess there are always x amount of lines that maintain current evaluation and avoid an error." ++ Yes, that is right.
"Say that with best play there are 2 available lines that force a win for white.
Once an error happens and evaluation changes from a win to a draw, there are now 19 available lines to force a draw with best play." ++ Yes, that is right. But what does that mean?
Let us assume chess is a draw. In the initial position there are 20 possible white moves. Most of these lead to a draw as well. 1 g4 probably loses by force. So white has say 19 moves that draw.
Now black has 20 responses to each of the 20 white moves. To 1 e4 1...e5 probably draws, 1...c5 probably as well, 1...e6 or 1...c6 maybe too, maybe not, 1...Nf6 probably not, 1...b5 and 1...f5 surely not. So black has a narrower choice of good moves that hold the draw.
It is this phenomenon that explains why white wins more often than black:
white has a broader choice of moves that hold the draw and black has a narrower choice.
"We don't have accurate data on how much "x" varies to make any predictions on errors per game. We could have 136 games where the first error occured in 100% of the games and the second occured in 15% of the games."
++ Statistics on the 136 ICCF WC games show that the 127 draws are > 99% sure to contain no error and the 9 decisive games are > 99% sure to contain exactly 1 error.
"There is no way to reliably make predictions" ++ Yes, there is.
We can even reliably predict what door allows all 8 billion people to walk under it upright.
We do so using the Gaussian distribution, of which we know it does not work exactly.
"Yes, that is right. But what does that mean?"
It means your error distributions that are based on probability are not accurate, because each error has a different probability depending on the position that you cant calculate.
@4598
"It means your error distributions that are based on probability are not accurate"
++ It need not be accurate. We know the Gaussian distribution of size of humans is not accurate, and yet it is accurate enough to use it in many practical probems.
Sep 4, 2022
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#3647
tygxc wrote:
@4559
"The only 100% certain way to decide what is or is not an error would be to calculate all lines from that point in the game to the finish--either checkmate or a draw."
++ Yes, but not all lines are needed, only the reasonable lines.
"If we possessed such a mechanism, chess would already be solved."
++ No, we possess such a mechanism:
3 cloud engines or 3000 desktops during 5 years under supervision of 3 (ICCF) (grand)masters.
There is no fundamental difference between solving chess and solving a chess problem. You can convince yourself of the solution of a chess problem, and you may be right (if you are fortunate), but you have not solved it rigorously and with certainty until you have dealt with EVERY LEGAL MOVE BY THE OTHER SIDE. No excuses, even if lack of rigour is your lifetime habit.
@4600
"There is no fundamental difference between solving chess and solving a chess problem."
++ That is right, solving chess is solving 'white to play, black to draw' for the initial position.
"You can convince yourself of the solution of a chess problem"
++ Yes, by looking at all relevant lines.
"you may be right (if you are fortunate)" ++ It has nothing to do with fortune
"you have not solved it rigorously and with certainty until you have dealt with EVERY LEGAL MOVE BY THE OTHER SIDE."
++ This is wrong. You do not have to look at every legal move from the other side only at the reasonable moves. You can rule out some moves by knowledge and logic.
Sep 4, 2022
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#3649
Yes, you can rule out some moves by "knowledge". And in some cases you will be wrong to do so. That is the nature of imprecise inductive knowledge.
If the generation of boredom by repetition of falsehoods based on poor understanding was a valid proof method, you would be well on the way to solving chess.
Sep 4, 2022
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#3650
Kotshmot wrote:
tygxc wrote:
@4591
"Poisson distribution doesn't work here" ++ How do you know?
...
Mainly because the moves in ICCF games are generally SF's moves and we can check whether the blunders that are made by SF correspond with a Poisson process in situations where it's possible to identify the blunders thanks to the production of tablebases.
Also agreed draws and resignations represent possible blunders accounting for most of the results in your sample. These do not occur with a constant probability mass throughout the game but always at the end.
You count a full point blunder as two errors (half point blunders) but why should this correspond with the square of the probability of a half point blunder. Also the full point blunders are clearly not independent. After a full point blunder the chances of another full point blunder before the next half point blunder are greater than after (impossible immediately after).
I invited you to apply your argument to the series of games in this sample where the blunders have been identified, but there was a curious lack of response. There were no agreed draws or resignations (I switched off resignations in Arena who was actually playing both sides) so the above paragraph doesn't apply. The probability of a full point blunder from the starting position is virtually nil. Do the inter-arrival values correspond with a Poisson process? Do the error rates correspond with your calculations?
You only have to look at some of the examples to see quite clearly that the blunders are not independent. E.g.
256 seconds per move
Starting with move 26 there is a series of nine consecutive blunders under basic rules.These all stem from the fact that neither white hat SF or black hat SF "realises" that if the pawn is pushed it leaves the black king in the middle of the drawing zone for the new pawn position. This is because each in evaluating it's position goes through the same process as the other.
On the other hand in a KRK position both SF's would play perfectly and the the probability of a blunder on any given move would be completely different from that in the game shown.
@4603
"Yes, you can rule out some moves by knowledge".
++ That is also what van den Herik wrote: 'Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs.' 5.2 p. 303
https://www.sciencedirect.com/science/article/pii/S0004370201001527
"And in some cases you will be wrong to do so."
++ No, then it is not knowledge. That is why the good assistants need to be (ICCF) (grand)masters. They can simplify and prune, but only if they are certain they are not wrong.
"That is the nature of imprecise inductive knowledge."
++ No, that is the power of precise knowledge and logic.
The 20 first moves have been ranked. The best moves are 1 e4, 1 d4, 1 c4, 1 Nf3.
If the 4 best moves cannot win, then the 16 worse moves cannot win either.
That allows to collapse 20 * 20 = 400 possibilities to 4, e.g. 1 e4 e5, 1 d4 d5, 1 c4 e5, 1 Nf3 d5
1 e4 e5 2 Ba6 can be discarded at once: loses a piece without any compensation.
1 e4 e5 2 Nf3 Nc6 needs to look at 3 Bb5, 3 Bc4, 3 d4, 3 Nc3.
It is again useless to look at 3 Ba6.
It is useless to look at 3 Na3: cannot be better that 3 Nc3.
It is useless to look at 3 b4: loses a pawn without any compensation
It is useless to look at 3 Nxe5: loses a piece without any compensation.
It is useless to look at 3 Ng5 or 3 Nh4: loses a piece without any compensation.
Do not let 'rigour' stand in the way of progress by ignoring knowledge and logic.
Do not confuse 'rigour' and 'stupidity'
@4604
"the moves in ICCF games are generally SF's moves" ++ No, not at all. You do not know ICCF.
"agreed draws and resignations represent possible blunders"
++ No, ICCF (grand)masters are not forum dwellers.
They resign when lost and agree on a draw when it is a draw. They often play on for months in drawn positions hoping in vain for an error (?) by the opponent.
"accounting for most of the results in your sample." ++ All wins are by resignation, draws are by agreement, by 3-fold repetition, or by claiming a 7-men endgame table base draw.
"These do not occur with a constant probability mass throughout the game but always at the end." ++ 127 of 136 games are error-free. When an error is made in 9 out of 136 games, the side who made the error realises this next move and resigns. That is why the few errors usually are at the end.
"You count a full point blunder as two errors (half point blunders) but why should this correspond with the square of the probability of a half point blunder." ++ That is a reasonable assumption. It does not even matter. ICCF has no blunders (??), only 9 errors (?) in 136 games.
"the full point blunders are clearly not independent."
++ There is only one error (?) per game in ICCF, so independent or not does not matter.
After a full point blunder the chances of another full point blunder before the next half point blunder are greater than after (impossible immediately after).
++ Does not matter for ICCF: only 1 error (?) in 9 out of 136 games.
Sep 4, 2022
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#3653
tygxc wrote:
"That is the nature of imprecise inductive knowledge."
++ No, that is the power of precise knowledge and logic.
The 20 first moves have been ranked. The best moves are 1 e4, 1 d4, 1 c4, 1 Nf3.
If the 4 best moves cannot win, then the 16 worse moves cannot win either.
OK put it another way.
I've just ranked them again; 1. g4 2. Nh3 3. f4 4.b4. How does your precise logic prefer the ranking you gave? Stockfish? Look at the examples I referred to in my previous post.
Sep 4, 2022
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#3654
tygxc wrote:
@4604
"the moves in ICCF games are generally SF's moves" ++ No, not at all. You do not know ICCF.
"agreed draws and resignations represent possible blunders"
++ No, ICCF (grand)masters are not forum dwellers.
They resign when lost and agree on a draw when it is a draw. They often play on for months in drawn positions hoping in vain for an error (?) by the opponent.
"accounting for most of the results in your sample." ++ All wins are by resignation, draws are by agreement, by 3-fold repetition, or by claiming a 7-men endgame table base draw.
"These do not occur with a constant probability mass throughout the game but always at the end." ++ 127 of 136 games are error-free. When an error is made in 9 out of 136 games, the side who made the error realises this next move and resigns. That is why the few errors usually are at the end.
"You count a full point blunder as two errors (half point blunders) but why should this correspond with the square of the probability of a half point blunder." ++ That is a reasonable assumption. It does not even matter. ICCF has no blunders (??), only 9 errors (?) in 136 games.
"the full point blunders are clearly not independent."
++ There is only one error (?) per game in ICCF, so independent or not does not matter.
After a full point blunder the chances of another full point blunder before the next half point blunder are greater than after (impossible immediately after).
++ Does not matter for ICCF: only 1 error (?) in 9 out of 136 games.
Total b*llocks. All of that.
@4608
"'I've just ranked them again; 1. g4 2. Nh3 3. f4 4.b4"
++ Now that is 'Total b*llocks'.
I did not give the ranking, but
1) Human knowledge e.g. Capablanca:
'From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop.
Therefore, theoretically one of these two moves must be the best,
as no other first move accomplishes so much.'
2) AlphaZero Figures 5 and 31
https://arxiv.org/abs/2111.09259
The title is chess knowledge, not 'Total b*llocks'
tygxc wrote:
@4598
"It means your error distributions that are based on probability are not accurate"
++ It need not be accurate. We know the Gaussian distribution of size of humans is not accurate, and yet it is accurate enough to use it in many practical probems.
Quoting for posterity.
Finally, the tacit admission that what Tygxc proposes is not a solution for chess at all...it's just modelling better play to "pretend" that chess is solved, Why not just let engines keep improving and call it a day? They will get to the same unsolved threshold anyway without "guidance". This is kind of like the hubris of centaur players that consider themselves equal partners with their engines. They are more like butlers for their engines 
.
@4611
"what Tygxc proposes is not a solution for chess at all"
++ Yes, it is, but you still do not understand.
The estimation of the number of legal, sensible, reachable, relevant positions 10^17 does not need to be accurate, it can be 10^18 or 10^16.
The number of perfect games in the ICCF WC 127 need not be accurate: it can also be 126.
The weak solution of chess must be accurate:
proof how to draw for black against all reasonable white moves.
Sep 4, 2022
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#3658
btickler wrote:
Optimissed wrote:
...
"I know you have lost all patience with me. I suppose you don't like the combination of accuracy, honesty, scepticism and high intelligence.
But I used to be able to see through solid objects. I'm not even joking. I probably could do it still. I can make people better by thinking. ...."
I used to be able to do that as well. Still can. I've got five windows in my flat and I can see through all of them. (Mind you, if I don't get round to cleaning them soon my gift could disappear.)
Optimissed wrote:
I see you like "hubris". That's one of those pretentious words that trolls use a lot innit?
You never use "innit". It's really telling that you are colloquializing your dialogue on purpose in an attempt to make me look bad. Given that being perceived as the most intelligent person alive is your primary goal in life, taking this step shows how angry you are, which in turn shows how accurate my post was. I will address that in a somewhat kinder way in a moment when I respond to your Typewriter reply.
Sep 4, 2022
0
#3660
If I had a book, a physical book, with every possible game of tic tac toe, I would consider that solving tic tac toe. The number of chess games is finite and if I had a book with every possible game of chess that could be played( it might have 10^100 pages or even 10^1000 pages) I would consider that solving chess.
@btickler it doesn't need you to accept it, but the hairs of your head are all numbered.