...
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.
I'm asserting that anything other than an inductive understanding of a "chess solution" is impossible. I think that's completely incontrovertible.
Yes, we all think it's impossible with current technology, and the humankind might very well be extincted before it is possible, without a breakthrough in technology, or in our understanding of the game. You wondered why people seem fixated wiith a mathematical solution, then. To me it's not that, but exact solutions have been found for other games, so it's natural to take that as a reference. We already use inductive reasoning to play better and better, so it's completely fine, but it is not correct to call it an exact solution, a theorem, like someone (not you) does: chess is still too complex for that. Inductive reasoning cannot fully generalize, so its conclusions are, strictly speaking, only probable, while mathematical induction is a special case, where it can be proven that the generalization is full, i.e. exhaustive. That's still impossible for chess, without a complete mathematical representation of the game, as you noted.
Just going over an old thread. I think I took issue with you, over your claim that mathematical induction is a special case which, somehow, can be exact.
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.
It's been mentioned to him, by a few people. I don't expect he'll do it again.
#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.
#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.
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.
#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.
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.
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.
Yes indeed.
It's like homeopathy: the argument becoming ever more diluted, every time it's used.
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.
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 .
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..
#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.
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.
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 imprecise 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 knew 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.
I give buy lopez a try