I give buy lopez a try
Chess will never be solved, here's why
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Jul 12, 2022
0
#3003
tygxc wrote:
...
none of his 56011 legal samples are sensible because of multiple underpromotions to pieces not previously captured
...
Breaking news - these days when you play chess you don't have to just use the pieces that come in the box.
#3661
" you don't have to just use the pieces that come in the box"
++ There has to be a good reason to underpromote to anything else but a queen.
Underpromotion to a knight sometimes makes sense to utilise its unique properties.
Underpromotion to a rook or a bishop sometimes makes sense to avoid stalemate.
Promoted rooks and / or bishops on the losing side make no sense: it were better queens.
Promoted rooks and / or bishops on both sides make no sense: it were better queens.
In real grandmaster / engine / correspondence games 3 or 4 queens occasionally happen, but multiple underpromotions to pieces not previously captured like in the 56011 samples never.
tygxc wrote:
I derived the 10^17 by another way.
Per Tromp there are 10^44 legal positions, but none of his 56011 legal samples are sensible because of multiple underpromotions to pieces not previously captured.
Per Gourion there are 10^37 positions without promotions to pieces not previously captured.
I multiply this by 10 to accept positions with 3 or 4 queens.
I note that 1000 sampled positions are not sensible either and accept Tromp's estimate that only 1 in 10^6 is sensible. That leads to 10^32 sensible positions.
Then in analogy with the solution of Checkers I estimate that only 10^19 of these are reachable in the course of the solution. E.g. when working on 1 e4, all positions with a white pawn on e2 are no longer reachable.
Then I estimate that only 1% of these are relevant. E.g. when 1 e4 e5 is proven a draw, then it is not relevant if 1 e4 c5 draws as well or not. Likewise I consider 1 a4 and 1 e4 e5 2 Ba6 as not relevant either.
That leaves 10^17 legal, sensible, reachable, and relevant positions.
To the poster above this: making repeated one line posts one after the other is spamming.
"I derived by another way" is the problem.
You routinely take orders of magnitude away based on counting sets that overlap, while discounting that you are double counting. Reduce your argument to its logical conclusion. If you managed to "reduce" to 10^6, and you still had your Tromp card in it's holster, would you then make a claim that there's only 1 position? Of course not, because the set of 10^6 positions were already eliminated piecemeal in your other "loose" reduction estimates. But somehow, you completely overlook this when you are reducing 10^23 to 10^17.
#3661
"You routinely take orders of magnitude away based on counting sets that overlap"
++ No, the sets do not overlap.
The set of legal positions counts 10^44 elements.
The subset of legal and sensible positions counts 10^32 elements.
The subset of legal and sensible positions reachable during the solution counts 10^19 elements.
The subset of legal and sensible and reachable and relevant positions counts 10^17 elements.
tygxc wrote:
#3661
"You routinely take orders of magnitude away based on counting sets that overlap"
++ No, the sets do not overlap.
The set of legal positions counts 10^44 elements.
The subset of legal and sensible positions counts 10^32 elements.
The subset of legal and sensible positions reachable during the solution counts 10^19 elements.
The subset of legal and sensible and reachable and relevant positions counts 10^17 elements.
You have no fundamental basis for assessments of "reasonable" or "relevant", either.
#3664
"You have no fundamental basis for assessments of "reasonable" or "relevant", either."
++ Yes I do.
Sensible: results from a game with > 50% accuracy.
Reachable in the course of the solution: every capture or pawn move is irreversible and thus renders huge numbers of positions not reachable.
Relevant: for weakly solving chess only one strategy is needed to reach the game-theoretical value, it is not relevant if other strategies do or do not reach the game-theoretical value as well.
Aug 1, 2022
0
#3009
What does "50% accuracy" mean?
How is it determined without a 32 piece tablebase?
You do not have answers to this question that make it more than a guess.
#3667
"What does "50% accuracy" mean?"
++ It means that you feed the proof game into the engine and read the accuracy of the game. If that accuracy is < 50% then it is sure that the play is not optimal.
"How is it determined without a 32 piece tablebase?"
++ By feeding the proof game into the engine.
"You do not have answers to this question that make it more than a guess."
++ Yes, I do. If the accuracy is < 50% then that makes it sure it is no optimal play.
Optimissed wrote:
You have no fundamental basis for assessments of "reasonable" or "relevant", either.
It isn't wrong to use "inductively reasonable and relevant assessments" because in order to start building a model that can be used as a basis for a future, more accurate assessment, some kind of "stab in the twilight" must be made. I'm concerned, however, as are others, that tygxc is basing the numbers on the over-simplified assessment of someone who maintains that "chess can be solved in five years" and who is therefore wildly inaccurate in his assessment.
Rinse and repeat for your answer.
Optimissed wrote:
Yes indeed.
It's like homeopathy: the argument becoming ever more diluted, every time it's used.
Nope, that's the hope of the imprecise. Tygxc and yourself both repeat the same mantras incessantly in various efforts, but they never get any better. The arguments against them are the same, and need no particular changing just because you repackage your same logic in a new paragraph. The only reason to even refute them on occasion is so that new posters don't also become imprecise 
.
I remember reading something about how large a 32 piece table base would be and it was something ridiculous like even the lowest guesses possible were exponents beyond all the data on the entire internet in storage to solve. I'm not sure you could hook stockfish 30 into some future super computer with miles of racks costing trillions without it thinking for years. I cant see anyone having the kind of money to do that before we kill the planet but its conceptually possible. Just doesn't seem relevant to anything other than peoples obsession with the idea itself.
#3668
"how large a 32 piece table base would be"
++ A 32 piece table base would be 10^44 bit, but that would be strongly solving chess.
Checkers and Losing Chess have been weakly solved with 10^14 and 10^9 positions only.
++ Weakly solving chess needs 10^17 legal, sensible, reachable, and relevant positions.
"I cant see anyone having the kind of money to do that"
++ 3 cloud engines and 3 human grandmasters during 5 years would cost like $ 3 million.
"Just doesn't seem relevant to anything other than peoples obsession with the idea itself."
++ It is like travel to Mars.
Optimissed wrote:
The really sad thing about you is that you're incapable of getting other people's jokes and instead, your conceit shines through at all times. If you're useless at understanding people, which you are, you'll never be able to see things from their point of view. Hence, although you'll continue to think that your refutations are precise, they aren't, because you don't understand people and you need to do so to be effective..
Conceit is more your bailiwick. I understand you perfectly well, which is seemingly what irks you so much...that all your contortions are good for naught.
Optimissed wrote:
If I were your psychotherapist, I'd be thinking that you seem to be stuck with the same old set of reactive perceptions and you need to move on and learn and grow, but you don't have that ability. The sort of self-assurance and self-confidence that I have only ever works when a person can learn, adapt and change. You seem stuck, incapable of learning and growing.
So I made a joke there, which was fairly subtle, but you automatically reload your impresice set of perceptions and you didn't even realise it was a joke. Your problem is that now you'll want to tell everyone that (a) you know it was a joke and (b) it was a really bad joke and even (c) that I'm hiding behind a joke. But the reality is that when people try to reach out to you in any way, you aren't capable of accepting it as even possibly genuine. And that really is a deficiency, which is sad to behold.
Oh, and I'm multi-talented, confident and open. You're conceited. Try growing up one day.
Your entire engagement here is just a sign of how fixated you are on trying to convince yourself that you've got the high ground. Your jokes are usually veiled jabs at other's expense, or half hearted self-deprecation to prop yourself up. You don't even agree with Tygxc. There was zero reason to even comment, other than your insecurities. I represent a threat to your notion of your curated appearance on the site, and you can't live with it. The attempts at diagnosis from your armchair are laughable, as always.
"Oh, and I'm multi-talented, confident and open. You're conceited."
Best. Line. Ever. Thanks for that. You will probably be seeing it again in future .
Optimissed wrote:
Well of course you'd laugh. You aren't talented at all, so you can only deride others. Because you have nothing worthwhile to add.
Projection. I'm pretty sure my CV would match up quite successfully with you and your knick-knack stores and such. Let's not go there.
Do *you* have anything worthwhile to add, that's the question? Because so far this exchange is all you just exposing your insecurities and compulsive need to oppose those you feel threatened by.
Aug 2, 2022
0
#3018
tygxc wrote:
#3667
"What does "50% accuracy" mean?"
++ It means that you feed the proof game into the engine and read the accuracy of the game. If that accuracy is < 50% then it is sure that the play is not optimal.
No, that means it would be a very good bet that the play is not optimal. An imperfect engine can be completely wrong, identifying the only winning move as a blunder or vice versa. Even you should be able to understand this fact.
Note carefully that once you understand this, you should also understand that the probability of it happening twice in a game is not zero. The same for multiple times in a game. How could you make the mistake of not accepting this?
"How is it determined without a 32 piece tablebase?"
++ By feeding the proof game into the engine.
See above to learn that imperfect engines can be absolutely wrong.
"You do not have answers to this question that make it more than a guess."
++ Yes, I do. If the accuracy is < 50% then that makes it sure it is no optimal play.
Thank you for confirming what I said by guessing.
Optimissed wrote:
This is what happens when I try to be friendly and make a joke, because you're a psycho and not worth any effort to be friendly to you. "Ooh dear, Optimissed's been nasty to me again".
Well, go back to #3667 and try to work out why. You're pathetic.
So you've tried to tell me on numerous occasions. Care to toss in an "idiot" for good measure? These adjectives seem to make you feel better when you apply them to others.
Anyone that has been around here a while knows you are not trying to be friendly.
tygxc wrote:
#3668
"how large a 32 piece table base would be"
++ A 32 piece table base would be 10^44 bit, but that would be strongly solving chess.
Checkers and Losing Chess have been weakly solved with 10^14 and 10^9 positions only.
++ Weakly solving chess needs 10^17 legal, sensible, reachable, and relevant positions.
"I cant see anyone having the kind of money to do that"
++ 3 cloud engines and 3 human grandmasters during 5 years would cost like $ 3 million.
"Just doesn't seem relevant to anything other than peoples obsession with the idea itself."
++ It is like travel to Mars.
I don't know where you get the 3 million figure to solve a 32 piece base but there is no way its even close to that cheap 10^44 is huge bro. If you mean 10^17 number sure but that's not what i think the OP meant i think they mean a true 32 piece table base that has the answer for every possible position. https://www.reddit.com/r/chess/comments/gvvftb/comment/fsvjobh/ I'm not sure how accurate this math or yours is but even the low ball guy here going for a 350+ trillion pound hard drive that can store data on each individual atom doesn't sound like a practical reality to me.
#3657
" o __ root node
/ | \ | White's moves
x x x x nodes at depth 1 in plies
| | | | Blak's moves
o o o o nodes at depth 2 in plies"
OK, without transpositions you count black replies too, getting upper bound:
2 * (1 + w + w² + w³ + ... + w^d) = 2*(w^(d+1) - 1) / (w - 1)
With full transpositions it becomes a lower bound:
2 * (1 + w/1! + w²/2! + w)³/3! + w^4/4! + ... + w^d/d!) =~ 2 * e^w
"d (that in your previous post was 34 and now has magically become 39"
++ No. d = 39 is the average number of moves in the ICCF WC.
d = 34 is the average number of moves past theory in the Madrid 2022 Candidates'
"the total number of positions would be 4 × 10²³, per your formula"
++ Let us take the 2 formulas above, w = 4, and d = 39
Without transpositions: upper bound 2*(4^40 - 1) / (8 - 1) = 8*10^23
With full transpositions: lower bound 2*e^4 = 100
Geometric mean on both: 9*10^12
So 10^17 is on the safe side.
I derived the 10^17 by another way.
Per Tromp there are 10^44 legal positions, but none of his 56011 legal samples are sensible because of multiple underpromotions to pieces not previously captured.
Per Gourion there are 10^37 positions without promotions to pieces not previously captured.
I multiply this by 10 to accept positions with 3 or 4 queens.
I note that 1000 sampled positions are not sensible either and accept Tromp's estimate that only 1 in 10^6 is sensible. That leads to 10^32 sensible positions.
Then in analogy with the solution of Checkers I estimate that only 10^19 of these are reachable in the course of the solution. E.g. when working on 1 e4, all positions with a white pawn on e2 are no longer reachable.
Then I estimate that only 1% of these are relevant. E.g. when 1 e4 e5 is proven a draw, then it is not relevant if 1 e4 c5 draws as well or not. Likewise I consider 1 a4 and 1 e4 e5 2 Ba6 as not relevant either.
That leaves 10^17 legal, sensible, reachable, and relevant positions.