""without promotions as a whole" ++ No, the Gourion paper gives 4*10^37 as the an upper bound for the number of chess diagrams without promotion to pieces not previously captured. "
actually it doesnt. try reading it. oh wait that's too much for you.
"Summing over all possibilities yields that the upper bound for the total number of legal chess diagrams without promotion is equal to 3.8521 . . . × 1037 ." (page 7)
@12737
I did not compile the random sample of 10,000 (Tromp did), I only inspected and found none can result from optimal play by both sides. Tromp conjectured only 1 in 1,000,000 could qualify.
That explains the reduction from 10^38 to 10^34 or 10^32.
@12737
I did not compile the random sample of 10,000 (Tromp did), I only inspected and found none can result from optimal play by both sides. Tromp conjectured only 1 in 1,000,000 could qualify.
That explains the reduction from 10^38 to 10^34 or 10^32.
You still have yet to produce a link to said conjecture.
@12738
"without promotion" means without promotion to a piece not previously captured, or without an obvious promotion. If 1 queen is on the board and 7 or less pawns, then you cannot tell if the queen is original or promoted. So for the Gourion number it counts as without promotion, even if the queen is promoted.
@12735
Dear MEGACHE3SE, as you are right for a change, I am happy to admit that and I have replaced the illegal position by another position from the Sample of 10,000 positions without promotions to pieces not previously captured
Here is another:
(this position requires a promotion btw)
That explains the reduction from 10^38 to 10^34 or 10^32.
a single position explains a reduction thats completely uncited and unjustified., yeah, perfect logic.
@12734
I cannot really reply to your vague statement about 12 strawmen. If you had said: 'I have submitted <quote1> to <title><first name><last name> of <university name> and he responded <quote2> then I could reply to that. Even better if he made an account and replied here in this thread. As far as I know laughing or insulting are no valid ways of proof.
I insult you because after you get proven wrong repeatedly, you make no effort of self correction.
@12733
"check wikipedia" ++ Wikipedia is not reliable: anybody can edit it. The article is obsolete. lmfao which is why theres not a single instance of anybody editing it along the lines of your claims? the people you cite your claims of are decades old. claiming that the article is obsolete is laughable.
@12732
"without promotions as a whole" ++ No, the Gourion paper gives 4*10^37 as the an upper bound for the number of chess diagrams without promotion to pieces not previously captured. The last 3 words are omitted from the title for brevity and as it is obvious.
maybe you should try reading the actual paper instead of just twisting it to your own definitions.
"Summing over all possibilities yields that the upper bound for the total number of legal chess diagrams without promotion is equal to 3.8521 . . . × 1037"
in addition, reading the actual paper shows that no such calculations are made 'for previously captured"
If 1 queen, 1-2 rooks, bishops or knights are on the board with 7 or less pawns,
then it is impossible to tell if those pieces are original or promoted. 5 seconds of critical thinking would have figured out the solution to this: since the positions can be reached without promotion, it is completely unnecessary to compile the separate promoted figure.
still requires promotion to reach this position, BTW.
you blame tromp's data, but the reality is that you are completely misinterpreting what the data set is to begin with.
its hilarious that tygxc is now blaming tromp for the fact that the positions dont line up with his claims. no you moron, its that you are completely misrepresenting what the position set is. those arent a legal positions set LMFAO.
you are on your 4th position, and it STILL doesnt meet the criteria that you claim your position is. there's two dark squared black bishops in your 3rd, and both kings are in check in your 4th.
@12738
"without promotion" means without promotion to a piece not previously captured, or without an obvious promotion. If 1 queen is on the board and 7 or less pawns, then you cannot tell if the queen is original or promoted. So for the Gourion number it counts as without promotion, even if the queen is promoted.
tygxc why do you continue to dodge the fact that i brought your arguments to multiple math professors and all of them found the same errors that I (and others) point out to you?
@12737
I did not compile the random sample of 10,000 (Tromp did), I only inspected and found none can result from optimal play by both sides. Tromp conjectured only 1 in 1,000,000 could qualify.
That explains the reduction from 10^38 to 10^34 or 10^32.
why are you making a claim based on a set that you are actively lying about?
I wonder how many direct counterexamples in a row it's going to take for tygxc to admit that his sample isnt what he claims it is. so far, the FOUR EXAMPLES provided are ALL illegal positions or require a promotion, and tygxc claims that his sample is of legal positions without promotion.
correction: turns out that the last one was illegal too. you cant have 8 pawns and bishops on the same color square.
what tygxc doesnt understand is that the 10,000 positions that he's citing as "legal positions without promotion' are the 10k 'possibly legal' piece arrangements that tromp used to narrow down to the 10^45 legal positions number.
i wonder how long its going to take before tygxc realizes this.
@12742
"blame tromp's data" ++ No, I do not blame the data.
Tromp found (4.82 +- 0.03) * 10^44 legal positions, but as the 3 random samples show the vast majority of those legal positions have multiple promotions from both sides and thus cannot result from optimal play by both sides and thus are irrelevant to weakly solving Chess.
Thus the Gourion number upper bound 3.8521 * 10^37 is a better starting point.
It is a bit too restrictive, as positions with 3 or 4 queens do occur in perfect games with optimal play by both sides, thus multiply by 10 to include those, giving 10^37*10 = 10^38 positions.
However, inspection of a random sample of 10,000 positions shows none can result from optimal play by both sides either. Some of the 10,000 are indeed illegal. That is how Tromp worked: he first sampled 1,000,000 positions and then eliminated illegal ones.
@12742
"blame tromp's data" ++ No, I do not blame the data.
you claimed that you were citing only legal positions, when you werent. then when called out on that, you said "im only using tromp's data". which is blaming tromp.
Tromp found (4.82 +- 0.03) * 10^44 legal positions, but as the 3 random samples show the vast majority of those legal positions have multiple promotions from both sides and thus cannot result from optimal play by both sides and thus are irrelavant to weakly solving Chess.
Thus the Gourion number upper bound 3.8521 * 10^37 is a better starting point.
It is a bit too restrictive, as positions with 3 or 4 queens do occur in perfect games with optimal play by both sides, thus multiply by 10 to include those, giving 10^37*10 = 10^38 positions.
However, inspection of a random sample of 10,000 positions shows none can result from optimal play by both sides either. Some of the 10,000 are indeed illegal. That is how Tromp worked: he first sampled 1,000,000 positions and then eliminated illegal ones.
i love how you are not just linking the positions directly anymore since you cant find them LMFAO. give the data set of legal positions.
so tygxc, why arent you addressing the fact that ive brought your "arguments" to multiple math professors and they all found the same errors that ive pointed out to you?
I wonder how many direct counterexamples in a row it's going to take for tygxc to admit that his sample isnt what he claims it is. so far, the FOUR EXAMPLES provided are ALL illegal positions or require a promotion, and tygxc claims that his sample is of legal positions without promotion.
correction: turns out that the last one was illegal too. you cant have 8 pawns and bishops on the same color square.
He's stubborn, but he does eventually respond to challenges like this, at least that was the case in the past.
no, there's been a half dozen outright falsehoods that have been called out that tygxc has refused to even recognize for months.
tygxc, i know you've read the comment, so why arent you addressing the fact that ive brought your "arguments" to multiple math professors and they all found the same errors that ive pointed out to you?
given the couple years of psychology that ive taken, tygxc seems to be one of those types that sees arguments like this in the form of "if they disagree they're wrong" it connects to a) the way that tygxc is so comfortable leaving factual rebuttals to his claims unaddressed ('theyre wrong anyways, so why should i care') in addition to the complete lack of care that tygxc has for any sort of logical coherency or intellectual integrity.
@12755
The key argument are the 110 draws out of 110 games.
https://www.iccf.com/event?id=100104
thats not a key argument at all lmfao. in fact it has LITERALLY ZERO BEARING. unverified moves mean nothing in terms of solving a game, which is a rigorous mathematical proof.
@12735
Dear MEGACHE3SE, as you are right for a change, I am happy to admit that and I have replaced the illegal position by another position from the Sample of 10,000 positions without promotions to pieces not previously captured
Here is another:
That explains the reduction from 10^38 to 10^34 or 10^32.
@12734
I cannot really reply to your vague statement about 12 strawmen. If you had said: 'I have submitted <quote1> to <title><first name><last name> of <university name> and he responded <quote2> then I could reply to that. Even better if he made an account and replied here in this thread. As far as I know laughing or insulting are no valid ways of proof.
@12733
"check wikipedia" ++ Wikipedia is not reliable: can be edited by anybody. The article is obsolete.
@12732
"without promotions as a whole" ++ No, the Gourion paper gives 4*10^37 as the an upper bound for the number of chess diagrams without promotion to pieces not previously captured. The last 3 words are omitted from the title for brevity and as it is obvious. If 1 queen, 1-2 rooks, bishops or knights are on the board with 7 or less pawns, then it is impossible to tell if those pieces are original or promoted.
Both kings are in check...
Lol, you edited that in a hurry. At least you figured it out this time.