Adam Hair wrote:Here is some data from high Elo, longer time control engine matches, using similar criteria Larry used in his material imbalance study:
I am not totally sure, but I think that as he mentioned the logistic function, the equivalent from scores to centipawns is something like this (using his data with the reference point at centipawns = 100):
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
Ajedrecista wrote:
May I give a link about a recently published material imbalance study by Antonio Torrecillas (the author of Rocinante and Simplex IIRC):
I am not totally sure, but I think that as he mentioned the logistic function, the equivalent from scores to centipawns is something like this (using his data with the reference point at centipawns = 100):
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
I found that it is dependent on the number of pawns. The difference fades away as the number of pawns on the board decreases.
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
I found that it is dependent on the number of pawns. The difference fades away as the number of pawns on the board decreases.
Are you saying that BN vs NN is always better than B vs N, but by a decreasing amount as the pawns come off, or does it "cross over" at some point beyond which BN vs NN is inferior to B vs N?
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
I found that it is dependent on the number of pawns. The difference fades away as the number of pawns on the board decreases.
Are you saying that BN vs NN is always better than B vs N, but by a decreasing amount as the pawns come off, or does it "cross over" at some point beyond which BN vs NN is inferior to B vs N?
From my data, it appears to me that there is a point where there is no measurable difference between the two (possibly when there is only 2 to 3 pawns for each side):
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
I found that it is dependent on the number of pawns. The difference fades away as the number of pawns on the board decreases.
Are you saying that BN vs NN is always better than B vs N, but by a decreasing amount as the pawns come off, or does it "cross over" at some point beyond which BN vs NN is inferior to B vs N?
From my data, it appears to me that there is a point where there is no measurable difference between the two (possibly when there is only 2 to 3 pawns for each side):
I do not believe that BN vs NN becomes worse than B vs N.
Thanks. I think where you say "centipawns" you mean "elo difference". It appears to me from your data that the effect is much more noticeable with queens off than with queens on, which makes good sense. I think we'll have to try this term again, perhaps modified as indicated by your data.
Could you print the similar comparison table for BBN vs BNN compared to BB vs BN? It's not at all obvious which is better, and I recall that the answer also depends significantly on the number of pawns present. Thanks.
hgm wrote:This raises some questions about the B-N difference (for Larry!). This has been shown to corrlate with the number of Pawns present. But, as we all know, correlation does not necessarily mean a causal relationship. The number of Pawns correlates also quite well with total material. If we suppose the bare value of the (lone) Bishop is higher than that of Knight, the presence of opponent Knight(s) pulls its value down to Knight level, as it is doomed to be traded. But the later the game stage, the more likely it is that the number of Knights it faces is reduced, making it suffer less danger it will have to be traded for one. So that it is more likely to rise to its bare value.
So my question is: does the value of a B-N imbalance correlate in any way with the presence of the second Knight?
The general belief among chess masters is that BN vs NN is better than B vs N, since the bishop "needs" a knight more than a knight does. I was not able to substantiate that to any meaningful degree in my initial study. In Rybka we did make that distinction based on weak evidence. We're not making it in Komodo now but perhaps I'll revisit the evidence on this point. It's definitely not a major effect.
I found that it is dependent on the number of pawns. The difference fades away as the number of pawns on the board decreases.
Are you saying that BN vs NN is always better than B vs N, but by a decreasing amount as the pawns come off, or does it "cross over" at some point beyond which BN vs NN is inferior to B vs N?
From my data, it appears to me that there is a point where there is no measurable difference between the two (possibly when there is only 2 to 3 pawns for each side):
I do not believe that BN vs NN becomes worse than B vs N.
Thanks. I think where you say "centipawns" you mean "elo difference". It appears to me from your data that the effect is much more noticeable with queens off than with queens on, which makes good sense. I think we'll have to try this term again, perhaps modified as indicated by your data.
Could you print the similar comparison table for BBN vs BNN compared to BB vs BN? It's not at all obvious which is better, and I recall that the answer also depends significantly on the number of pawns present. Thanks.
Well, I did mean centipawns due to the approximate relation 1 Elo = 1 centipawn. But Elo difference is correct.
All of the bishop data is located a little earlier in the thread.
Adam Hair wrote:
Well, I did mean centipawns due to the approximate relation 1 Elo = 1 centipawn. But Elo difference is correct.
All of the bishop data is located a little earlier in the thread.
OK, I found it. It seems from your data that having both knights is bad when no one has the bishop pair, but good when one player does have it. That's probably why my initial study showed no significant plus or minus to having the knight pair. Maybe the underlying principle is that an unpaired bishop needs knights to cover the other color, and two is better than one, while with the bishop pair there is less need for knights.
Given the number of items involved the error should be around 8 cp if not more.
Being the values so similar to the error, I would not take too far into consideration.
The difference (-10) probably comes from the mobility and is not affected appreciably by the phase.(removing queens 2 or 4 cp)
The only interesting configurations are queen and knight vs queen and bishop,
and bishop against knight when each side has 6 or more pawns.Here the Knight has enough compensation to match the slight advantage of the bishop.
Interestingly, the bishop pair loses half of its strength by the presence of a bishop on the side of the knight.