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.
so tygxc, why are you discussing irrelevant stuff when you havent addressed the fact that ive brought your arguments to multiple math professors and all of them found the same errors that ive pointed out to you?
do you think that by ignoring this fact it'll go away?
hey tygxc, since you seem soooo interested in trying to inform people about your fantasy, why dont you just update the "obsolete" wiki article so you can reach the most people possible?
im sure they wont find all of the same errors that i, my math professors, and everyone else on the forum pointed out.
surely they wont pay attention to how you assign one node to each position where you assume perfect play, where by your own calculations would require over a billion nodes per position.
tygxc you cannot find a single comment by me on this thread that is wrong that i have not already acknowledged as such.
btw tygxc, ive presented your arguments to some friends, and there's currently a division, not whether you're right or not, but whether you are trolling or not.
@tygxc would do well to discuss things with one of the best AIs (Claude 3.5 Sonnet, ChatGPT 4o / Bing AI Chat) to clarify some points, since he does not believe humans who have more knowledge than him. Remember, these models are trained on a large subset of all human knowledge. While they are not 100% reliable supplementary questions usually resolve any initial inaccuracies (for full disclosure, there were examples of this in the raw output for this query). Don't use AIs as encyclopedias, use them for intellectual stimulation!
Here is the sort of thing I mean (edited for compactness and quality)
Me >: Hallo Claude. Is it necessary for a weak solution of a game to deal with every legal opponent move or just some subset of these?
Claude >: A weak solution of a game refers to a strategy that guarantees a player the best possible outcome
A weak solution must deal with every legal opponent move, not just a subset. Here's why:
1. Completeness requirement: The weak solution must provide a strategy that works against any possible sequence of opponent moves, as long as the player following the solution plays optimally. If it only covered a subset of opponent moves, it wouldn't be a true solution.
2.Tree structure: Conceptually, a weak solution can be thought of as a decision tree that covers all possible game paths resulting from optimal play. Each node in this tree must account for all legal opponent moves at that point.
3. It's important to note that while a weak solution must account for all legal opponent moves, it doesn't necessarily provide the optimal counter for every possible game state - only those that can arise from optimal play by both sides. This is what makes it "weak" compared to a strong solution, which would provide optimal moves for every possible game state, including those arising from suboptimal play.
=========================================================================
The point at the end is an interesting nicety. A drawing strategy in a weak solution does not have to play accurately against bad opponent moves because it only has the objective of achieving a draw. For example, the opponent can blunder mate in 1 and the strategy can just play to achieve a draw and still meet the definition. But to have no way of finding out what move to play is NOT compatible with the definition.
@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
Right. Silly me, I was thinking promotions to queens and knights are a perfectly normal aspect of chess (with large numbers of multiple promotions in the tiny less than 10^7 games master chess dataset) and often optimal (proponent ) or legal (opponent) regardless of any previous promotions. But I now see you have taken the tygxc-logical move to generalize bishops and rooks to queens and knights.
Masterful!
nah bro yall are ganging up an tygxc
because he's literally just spouting BS. the longer you stay on this thread the more you realize how much tygxc deserves to be clowned on.
@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?