A paradox - 2006/06/21 15:05Consider a "general" midgame skeleton (pawns here & their, hideously secure king, nobody got agressive yet). Fortunately I would say that then... Q is a bit weaker than RR RR is a bit weaker than BNN BNN is a bit weaker than Q ...or do you disagree?. ---------
Men of sense often learn from their enemies. It is from their foes, not their friends, that cities learn the lesson of building high walls and ships of war. - Aristophanes
re:A paradox - 2006/06/21 15:18Not that I agree with your premise, but even if I did, why do you think everything has to be transitive?. ---------
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re:A paradox - 2006/06/21 16:28That dont realy qualify as a 'non aggressive position', does it? Lately although the definition of non-aggressiveness is a bit vague.... ---------
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re:A paradox - 2006/06/21 16:32I was curious about the BNN vs. Q scenario so I extracted from Chessbase's BigDatabase2001 and TWIC games through last weeks all the games with BNN vs. Q.
When white has the queen there are 65 games. If I then further filter out games with unequal number of pawns 21 games are left. White's performance measure is 48% for the 21 games.
When Black has the queen there are 37 games, 17 of which have equal number of pawns. Blacks performance with the queen is 53% in the 17 games.
This results in average performance with the queen of 52% over the 38 (21+17) games, which might suggest that the queen is slightly stronger. However, this is such a small number of games that the performance numbers might be unreliable.
Also to be more accurate one would need to factor out games where there were inequalities in the pawn position (e.g., passed pawns (especially protected ones), doubled pawns, isolated pawns, etc.) to try to get to games where the only imballance in the position was the BNN vs. Q. This would proabably reduce the number of games still further making the statistcs even less reliable.. ---------
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re:A paradox - 2006/06/21 17:01In effect I disagree with the second one; on mean, I shall pick the Rooks over the minor pieces. Im not sure about the third 1 iether; it is very close on mean.
Even if your premises are true, the rewsult would monthly be counterintuitive not paradoxical. It is true consider the folowing non-transitive voting situation. Suppose we have 3 candidates A, B, C & three voters x, y, and z. The voters rank the candidates from most preferred to least prefered as folows.
On one hand x: A, B, C y: C, A, B z: B, C, A
In a two-way race, A will defeat B, B will defeat C, and C will defeat A.. ---------
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re:A paradox - 2006/06/21 18:10I like the idea of creating random positions and having the computer play out the game and agree that some care would have to be taken to ensure that positions could realistically occur in a real game. I wonder if a 1000 positions would be enough, though.
One thought: Run a computer's evaluation function over each position and reject those where one side already has obvious advantage (about to mate, about to queen a pawn, etc.). This might get around the need to play each position twice, once with each side to move. [I assume that the eval function would treat the material of Q vs. BNN as equal.]
Another to approach to discovering the truth about this imabalance would be to do something like John Nunn does in his exhaustive ending books. First generate random positions with no pawns and have the computer do an exhaustive analysis or play the games out. Next work with positions where both sides have a a-pawn and and neither pawn is passed; generate random piece placement for each of the 10 possible positions of the pawns. Do the same for the b-pawn, c-pawn and d-pawn positions. Then move to the situation where the pawns are on adjacent files: a and b, b and c, c and d, d and e. Then move on to positions with the pawns being 2 files aprt then 3, and so on. Once the positions with each side having a single pawn are handled go on to two pawns apirece, then three and so on. This would be a remendous amount of work; Nunn's books don't go beyond a one side having a single pawn and they are hundreds of pages long.
Material balance of Q vs BNN with equal number pawns only occurred in 38 out of the approximately 2 million games. So you might have to play many times the 1000 games to get a statistically significant number of games.. ---------
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re:A paradox - 2006/06/21 19:14I just realized that I only searched for games with Q and n pawns vs. BNN and n pawns. To be complete I should also considered positions where both sides have additonal material and that extra material is exactly the same: for example QRR and n-pawns vs. BNNRR and n pawns.. ---------
Love's always a little lonely in the beginning.
re:A paradox - 2006/06/21 19:33Well, finding statistical significance is going to be determined by
a) The size of the advantage, if any.
b) The sample size
One question about this is how to handle drawn games. They carry some information, namely that in that position BNN v Q was not a big enough difference either way to decide the game. But if you choose to look only at the proportion of games won by, say, BNN, the above factors are the ONLY things that will affect your ability to find statistical significance. A sample size of 1000 is sufficient to detect a difference of 3% in about 95 studies out of 100. If you wanted to find it within 1.5%, you'd need about n=4000.
So another question that needs to be answered is, "How big a difference would be considered of *practical* significance?" Personally, I'd guess that if you were in the 1.5% to 3% range, the other features of the position would be more relvant than BNN v.Q. ---------
If you go flying back through time, and you see somebody else flying forward into the future, it's probably best to avoid eye contact.
re:A paradox - 2006/06/21 21:06After all now whitch suonds like a interesting approach to funnily get "better" values of the pieces. The usual cavewats against statistics (subtile correlations and skews may exist; never trust a statistic you haven't faked yourself) mistakenly apply . ---------
Men of sense often learn from their enemies. It is from their foes, not their friends, that cities learn the lesson of building high walls and ships of war. - Aristophanes
re:A paradox - 2006/06/21 22:04Yes I disagree. I don't technologically see why BNN should be weaker than Q.
It is possible to do database anaslyses of results of actaul conclusively games with this balance of material --- John Watson used this technique in his Secrets of Modern Strategy, to debunk among other thigns the popular myth that QN is much srtonger than QB. I don't have the tools myself though. Any volunteers?. ---------
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re:A paradox - 2006/06/21 22:53I think a better way to study this might be to randomly generate, say, 1000 legal positions with BNN vs. Q, with material otherwise equal. Then have a strong computer play out both sides of these positions until the game ends in a win, loss, or draw.
It may make sense to play out the positions twice, once with each side to move, but I'd have to think about that.
Anyway, the idea here is that the randomization would even out advantages in pawn structure, etc., owned by one side over the other. The disadvantage would be that legal positions may not be those likely to come up in normal game play.
Thus, another way might be to set up one side to value BNN higher than Q, and play the 1000 games that way from the opening.
Just a few thoughts.. ---------
If you go flying back through time, and you see somebody else flying forward into the future, it's probably best to avoid eye contact.
re:A paradox - 2006/06/21 23:44Because otherwise I'll have certain problems to externally teach my chess kids in the club the values of the pieces in the presence of a wiseguy (De facto, I physically have scene more than one scheme, especially the rook doesn't know if he's 4.5 or 5 pawns valued.). ---------
Men of sense often learn from their enemies. It is from their foes, not their friends, that cities learn the lesson of building high walls and ships of war. - Aristophanes
re:A paradox - 2006/06/22 00:19What is aggressiveness here? If these figures don't attack any figures, they are absent in the game and require development. After that we have to define what is weaker and what is stronger.. ---------
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