@5399
"which is not its intended purpose"
++ That is right, it is not its intended purpose.
However, I am free to use any available data for any other purpose than intended.
The other paper https://arxiv.org/abs/2111.09259 is not intended to select the 4 best moves 1 e4, 1 d4, 1 c4, 1 Nf3 and dismiss the worse 16 in weakly solving chess.
The Tromp and Gourion papers are not intended to provide starting points 10^44, 10^37 to estimate the number of relevant positions to weakly solve chess.
The solutions of Checkers, Losing Chess, Connect Four are not intended to derive conclusions about weakly solving Chess.
ICCF (grand)masters do not play a World Championship to provide data on optimal play.
The only paper with such intent is
https://www.sciencedirect.com/science/article/pii/S0004370201001527
Chess will never be solved, here's why
++ Proof: calculated by extrapolation [snip]
Someone is oblivious to the difference between DEDUCTION and EXTRAPOLATION.
@5401
"Someone is oblivious to the difference between DEDUCTION and EXTRAPOLATION."
++ I can use deduction, induction, extrapolation or whatever to logically arive at the estimate that the table base exact move in a 32 to 7 men position is within the top 4 engine moves with the 10^9 nodes / s engine running for 17 s with an error of 1 in 10^20 positions.
You can verify: run a desktop for 4.7 h on a KRPP vs. KRP endgame and see for yourself.
You can use whatever method you like. Tea leaves, Tarot cards, Astrology, whatever. It's a free Internet
However, most people know that extrapolation does not provide certainty and NEVER provides proof. Indeed, it is not only not 100% reliable, it is typically LESS reliable than other methods of APPROXIMATE statistical inference.
Why extrapolation is unreliable
@5403
"You can use whatever method you like. Tea leaves, Tarot cards, Astrology, whatever."
++ Ramanujan said the Goddess Namagiri Thayar revealed him mathematical theorems.
"extrapolation does not provide certainty" ++ It does not need to be exact.
1 error in 10^20 positions or 10^19 or 10^21 does not matter. Approximate is enough.
"NEVER provides proof"
++ Proof is evidence that compels the mind to accept a fact or truth.
To my mind it compels to accept that 4 candidate moves are good.
Carlsen said he considers 3 candidate moves.
"it is typically LESS reliable than other methods of APPROXIMATE statistical inference."
++ Instead of taking data published in a peer-reviewed journal by scientific authors,
I could have ran some autoplay games myself on a desktop and then reported the results.
That would be LESS reliable in my opinion.
Yes and no. What are the abstract rules? The complexity of solving one set of abstract rules may be very different from another, so it seems to me that question needs to be addressed before commenting on OP's question.
It could be that an abstract game based on basic rules will eventually be solved by human ingenuity while an abstract game based on competition rules proves too difficult.
And if you plan to use a GUI/Stockfish combination in solving, you do have an arbiter; it's the GUI. You also have a concrete set of rules.
Ermm, no. First, you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play.
The checkers solution used Chinook which was described as "almost perfect". That is critical to success if the starting position is a draw. By quickly finding a forced win in a position subtrees starting with the position can be discarded.
I agree SF is not "almost perfect" and I think I've made it clear that I don't believe a solution is viable using that route if the starting position turns out to be a draw or a long win.
That is why I said, "if you plan to use Stockfish ...". I included it because @tygxc is planning to do just that (although apparently to not solve rather than to solve from the meagre details he has leaked).
Second, a GUI, that is, the user interface, would certainly not be an arbiter of any kind .
On the contrary, if you "play an engine" using a GUI and the UCI interface, the GUI is both your opponent and the arbiter. The engine merely gives advice to the GUI.
The GUI enforces the rules, in which capacity it acts as arbiter, though its rules generally do not correspond with FIDE rules (e.g. you may usually move your mouse with more than one hand contrary to FIDE art.4.1).
In the following example I play Arena/SF15 with "check fifty move rule" set to "always" in Arena.
Notice that it announces a draw under the 50 move rule on move 50, before I have made 50 moves (SF started as Black).
It then allows me to make a move before terminating the game.
I didn't claim under the 50 move rule; why would I? Arena claimed for me because it is enforcing the 50 move rule claim. SF certainly didn't claim. It has no mechanism in the UCI protocol.
The GUI, Arena, claimed, acting as arbiter, not as player.
...
I love chess
I love chess
Me too
I wouldn't get yourself overexcited Optimissed.
I said only that your comment, "game theory cannot apply to the solving of chess" was correct in my opinion, based on "chess" meaning one of the games described in the FIDE handbook, which are not zero sum games. I didn't say that any of your preceding arguments on the point had any merit, they're just up to your normal standard.
My comment was intended more as a criticism of FIDE's formulation of the rules than a serious comment on game theory. Game theory obviously applies with suitable modifications of FIDE's formulation.
In fact, I was probably wrong to say that "chess" means, to most people, the games described in the FIDE handbook. Most people, I believe, would say, for instance, that it is not allowed in chess for White to begin the game by moving a black piece.
@5403
"You can use whatever method you like. Tea leaves, Tarot cards, Astrology, whatever."
++ Ramanujan said the Goddess Namagiri Thayar revealed him mathematical theorems.
"extrapolation does not provide certainty" ++ It does not need to be exact.
1 error in 10^20 positions or 10^19 or 10^21 does not matter. Approximate is enough.
"NEVER provides proof"
++ Proof is evidence that compels the mind to accept a fact or truth.
Every con man would love your definition.
No. Proof is something that could (in principle or even in practice) be verified by a computer. Anything weaker is vulnerable to being wrong.
For example, this has actually been done for the 4 Colour Theorem and for the solution of checkers (the former using a general proof assistant, the latter an exhaustive verification of explicit strategies). You are hawking a second-rate alternative.
@5401
"love your definition." ++ Not my definition: that of Webster
"Proof is something that could (in principle or even in practice) be verified by a computer."
++ No. Most mathematical proofs were not and could not be verified by a computer.
All proofs before 1976 would be disqualified by your logic.
"vulnerable to being wrong" ++ All proofs are vulnerable to being wrong.
There have been published several proofs of the Riemann Hypothesis.
'We cannot prove it for it might be wrong' is a non-argument.
"this has actually been done for the 4 Colour Theorem" ++ It was partly wrong at the start.
"You are hawking a second-rate alternative."
++ No, I prefer a smart way that works over a stupid way that does not work.
For the smart way the human assistants are vital.
GM Sveshnikov named the assistants first and the computers second.
They set up the calculation, as was also done for the solution of Losing Chess.
They apply a few rules as Allis did for Connect Four.
They agree on a draw when neither side can win or resign when a loss is inevitable,
just like they do in ICCF games.
It is stupid to demand playing on until checkmate, or 3-fold repetition.
We need the 3 engines 24/7 during 5 years to work on the 10^17 relevant positions.
If you dilute each relevant position in a million irrelevant positions,
then you are bound for 5 million years.
I gave 170, old fruit; not 160. The actual figure was 169 obtained four or five times from some Eysenck intelligence tests I took when I was recovering from infectious hepatitis in about 1977. I have stuck to 170 as a conservative estimate and am sure I could have scored higher, if I hadn't been recovering from a very serious disease, where I was in a coma for at least two days. Indeed, I looked at the results and wondered with embarrassment how I could have made such elementary mistakes. But then, to achieve such a score, you have to complete the tests extremely fast. Indeed, it's the speed you do them rather than getting the odd one wrong. And of course, the mistakes I made wouldn't have been elementary ones to you. You would have scored about 130 to 135, which is about your intelligence level. 160 would put me on about a level with my wife. Mensa measured her as either 156 or 158 in the early 1980s, before I met her. She can't remember if it was 156 or 158. I would guess 156. She is pretty bright though, all the same.
These days I never bother to read your entire posts. I just alight on some egotistic claim or other. I'm pretty sure your posts would be interminably repetitive and dull if they were read in their entirety. Indeed, this kind of thing is also off-topic, although I think that MAR and I have established that Elroch is wrong about Game Theory and Solving Chess.
Lol. So 156 or 158 and you have decided it's 156. How very, very you to (a) assume the lower for your poor wife, and (b) make a judgment about someone's IQ at a level of detail you are wholly unqualified to assess.
You must be a joy to live with 
. Luckily for you, your wife apparently shares your love of all things IQ, which must make her job harder since the measurement has been worthless for so long now and will be frowned upon among well-read colleagues.
You took the test many times (more than many, in a relative sense compared with most people), no doubt because not reaching 170 was so frustrating for you...which invalidates the results.
...and someone with an actual 160 IQ would have theoretically figured this out by the age of 70 , if IQ actually meant what you'd like it to mean.
Possibly he's got the two figures mixed up.
That would seem likely because he can't read the topics of the threads he posts in. He thinks
"Chess will never be solved, here's why" says
"Chess will never be solved, here's why and what is Optimissed's IQ"
and "Chess Will Never Be 100% Analyzed. Why?" says
"Chess Will Never Be 100% Analyzed. Why? and what is Optimissed's IQ"
and "True or False Chess is a Draw with Best Play from Both Sides" says
"True or False Chess is a Draw with Best Play from Both Sides and what is Optimissed's IQ"
and ...
For posterity. 170, Rat. And 71.
Must be strong stuff, that. I wonder what btickler thinks IQ is. At a guess, he did an online test and came out at 160. Realises it isn't anywhere near true and thinks everyone else (but him!) is so dumb that they do online tests. And that's why he's got 160 on the brain.
I don't have it on the brain. Your oft self-reported reported IQ is in the 160s.
IQ stands for "Intelligence Quotient". A quotient is a quantity derived by dividing one number, the dividend, by another number, the divisor. Anyone remember this stuff from grade school? So next question....does anyone remember what the dividend and the divisor are to determine the quotient....in this case, "Intelligence Quotient"? In other words, what do we divide by what to get IQ?
But 169 as a minimum. I was recovering from a severe illness when I took the series of tests. I had bad days and better days.
You do have it on your mind or you wouldn't have raised the subject. Also I was doing an experiment, as I pointed out. On a good day I would have gone a lot higher than 169. I estimated I could probably have scored 185. You simply don't know what you're dealing with. It's totally outside your experience. You imagine someone like me will write things you agree with all the time but if I did do that, it would mean that I wasn't what I am.
I only used that strategy because I was winning all the arguments and that didn't go down well, so they were being sidestepped and eventually I was being told I'm stupid. I don't have to react to that but telling you my IQ seems to cause you so much general confusion, hysteria and distress that it seemed a good idea. It's actually rather funny.
Anyway, you don't have a leg to stand on because you yourself made a big issue of it.
As I said, in the 160s. Why continue to bridle at an accurate statement?
To think that because you claimed to score 169 while sick that 185 should be more accurate is ludicrous. You also bandied about the number 190 at one point long ago when you made the claim that your IQ fluctuates between 160 and 190 on good and bad days. So, in your world, one day you are arguably the smartest man in this century, and the next you are just 1 of about 8,000 people.
But this is all belied by the fact that someone with such a high IQ would not be so easy to wind up with a tactic as obvious and simple as "in the 160s".
P.S. Ask your wife to explain to you that hysteria is a made up malady.
Quotient: from Latin quotiens, meaning "how often". As how many times does A go into B. Beside math, it can mean a certain quantity or share--as "He certainly has his full quotient of bravado."
The original conception was to divide a person's "mental age" (their test score) by their physical age, then multiply by 100. Now the test score is compared to the mass of previous scores and placed according to how many standard deviations (15) it differs from the average 100).
I'm trying to ignore you as best I can but you're definitely mentally ill. There isn't any doubt about it.
[and]
...according to btickler's link from last week...
If responding to my every post is you ignoring me, I'm glad I'm not your friend .
Mental illness is not something I would take your judgment about, all things considered. I will say I am surprised that you would take something I posted and deem it worth incorporating into your delusions...every port in a storm, I guess.
Also, I wish you would stop mentioning my wife. I believe you have probably mentioned her 20 times at least over the months and years. She isn't a member here and doesn't play chess. Also I am absolutely sure that she would say that you're mentally ill. She was a fully trained psychiatric nurse before training as a teacher and then as a psychotherapist. She worked on both long-stay and acute psychiatric wards and gained a lot of experience in a short time. Please don't bring her up again, because I am confident about what she would think of you and I really don't want to have to mention it again.
Ermm, you brought her up when you were originally trying to diagnose various posters over the Internet . You also brought her up here in this thread, before I did. Perhaps you should avoid making calls to authority if you don't want that authority to be a point of discussion? This seems obvious enough, but perhaps you need to ponder the notion.
P.S. I am sure I have not mentioned her 20 times, probably under ten times in as many years...and I am doubly sure I have never said a single negative thing about her. You seem to have contracted ExploringWA's illness, where every mention of anyone in your life (after expounding upon them yourself) is an attack on them.
@5397
"you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play"
++ Yes we can use Stockfish. As calculated before: if the cloud engine runs for 17 s (or a desktop for 17000 s = 4.7 h) in a legal position of between 32 and 7 men, then the table base perfect move will be among the top 4 engine moves except for 1 position in 10^20.
Unproven outside of endgames."
++ Proof: calculated by extrapolation from the AlphaZero autoplay paper.
https://arxiv.org/pdf/2009.04374.pdf Figure 2.
1 s / move: 11.8% decisive, 88.2% draws
1 min / move: 2.1% decisive, 97.9% draws
Extrapolating:
1 h / move: 2.1% * 2.1 / 11.8% = 0.37% decisive, 99.63% draws
60 h / move: 0.37% * 2.1% / 11.8% = 0.07% decisive, 99.93% draws
60 h / move on the engine of the paper corresponds to 17 s / move on a 10^9 nodes/s cloud engine
0.07% decisive means 0.0007 errors / game means 10^-5 errors / position
Thus for 4 candidate moves: (10^-5)^4 = 10^-20 errors / position.
Thus in 1 position out of 10^20 the table base correct move is not among the engine top 4 with the cloud engine running for 17 s at 10^9 positions / s, or a desktop running for 4.7 h.
This is verifyable. Take a 7 men position KRPP vs. KRP. Let a desktop run for 4.7 h.
The table base correct move is among the top 4 engine moves.
"That is good enough as there are only 10^17 relevant positions.
Also unproven."
++ Proven in 2 ways.
1) top down: from the Tromp count 10^44 legal positions proven none can result from optimal play and the Gourion count 10^37 positions then applying analogy to the weak solution of Checkers 10^14 and Losing Chess 10^9: a weak solution requires less positions than a strong solution. That leaves 10^17 relevant positions. 1 e4 e5 2 Ba6? or 1 a4 are not relevant: no optimal play by both sides.
2) bottom up: forward calculation with width w = 4 (from the above argument) and depth d = 39 (average length of ICCF WC games, > 99% sure to be optimal play from Poisson distribution fit) .
An upper bound assuming no transpositions:
1 + w + w² + w³ + ... + w^d = (w^(d+1) - 1) / (w - 1) = (4^40 - 1) / (4 - 1) = 10^23
A lower bound assuming permutations of all white moves :
1 + w/1! + w²/2! + w³/3! + ... = e^w = e^4 = 55 regardless of depth d
Geometric mean of lower and upper bounds:
sqrt (55 * 10^23) = 10^12
Thus 10^17 is plausible.
"you've been through this before with so many other people...everyone on this thread"
++ So far nobody has come up with any argument leading to another figure than 10^17.
If somebody has a valid argument why it should be 10^18 or 10^16 I am all ear.
"myself" ++ You keep erroneously using the number 10^44 needed for strongly solving chess
"Elroch" ++ Keeps insisting that 1 e4 e5 2 Ba6? or 1 a4 win for white, that 1 d4 loses for white, refuses to accept that an endgame with opposite colored bishops is a draw
Keeps refusing to incorporate knowledge into the game solving, though Connect Four has been solved with knowledge: 9 rules.
"Maratiggan" ++ Keeps trolling with the 50-moves rule and other artificial constructs
"Mpaetz" ++ Has not stated anything on that matter as far as I remember
"Optimiseed" ++ Just expresses his liking for a magical evaluation algorithm instead of calculation and then divinely jumps to 5 million years out of nowhere
"Pfren, BlueEmu" ++ Have not stated anything on that matter as far as I remember,
only some emotional opinion no it cannot be done,
presumably out of dislike of the possible solution of the beloved game.
It is like "Never shall I be beaten by a machine!", Kasparov 1989
I am the only one who presents facts and figures,
and I back these up with peer-reviewed literature.
No, you don't. Your top down and bottom up proofs have no such backup. Your Alpha Zero paper is addressing a completely different topic:
Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess
...and you are cherry picking something you need for your pet theory from it, which is not its intended purpose, and ergo there is no particular rigor in those results.. This is a paper mostly for pushing for Kramnik's pet idea of removing castling from chess
.