piece weight and importance

Originally posted by Ragnorak
coquette
"but two bishops or two knights are worth more than a bishop and knight together because the pieces "work better" together"
Rubbish! If there was only your opponents king against your two minor pieces, are you saying you'd want the two knights? With which you can't (forcibly) checkmate your opponent.[/b]

Yes, the reason why the bishop pair is worth about a half pawn (based on the study linked earlier) bonus is that the bishops don't duplicate each other's coverage. Any other combination of pieces gives you some duplication of coverage, which diminishes the value of the combo. So, in reality, the bishop pair isn't worth more; the other combos are worth a little less. But it's easier to think of the bishop pair as worth more.

Quoting the article: "Why is the bishop pair so valuable? One explanation is that the bishop is really a more valuable piece than the knight due to its greater average mobility, but unless you have both bishops the opponent can play so as to take advantage of the fact that the bishop can only attack squares of one color. In my opinion, another reason is that any other pair of pieces suffers from redundancy. Two knights, two rooks, bishop and knight, or major plus minor piece are all capable of guarding the same squares, and therefore there is apt to be some duplication of function.

With two bishops traveling on opposite colored squares there is no possibility of any duplication of function. So, in theory, rather than giving a bonus to two bishops, we should penalize every other combination of pieces, but it is obviously much easier to reward the bishop pair. It is partly for similar reasons we say to trade pieces when you are ahead; if you have two knights against one (with other pieces balanced), the exchange of knights means that you are trading a partially redundant knight for one that is not redundant."

Also: "The conclusions are clear and consistent: although the average value of a bishop is noticeably higher than the average value value of a knight, this difference is entirely due to the large value of the bishop pair. In other words, an unpaired bishop and knight are of equal value (within 1/50 of a pawn, statistically meaningless), so positional considerations (such as open or closed position, good or bad bishop, etc.) will decide which piece is better."

Originally posted by HolyT
Yes, the reason why the bishop pair is worth about a half pawn (based on the study linked earlier) bonus is that the bishops don't duplicate each other's coverage. Any other combination of pieces gives you some duplication of coverage, which diminishes the value of the combo. So, in reality, the bishop pair isn't worth more; the other combos are worth a litt ...[text shortened]... s open or closed position, good or bad bishop, etc.) will decide which piece is better."

This is true and gives good insight.

Whilst it is a clear advantage to avoid duplication as you point out, there are occasions where the bishop pair are rendered less effective than (say) bishop and knight for this very reason. Afterall, in cases where defence or attack on a key square are required, the bishop pair by their very nature cannot cooperate, as they can never control the same square in unison.
So it really is (as said all along) about the specific position. It is just that statistically, there are slightly more positions where the bishop pair are favourable.

Originally posted by Policestate
This is true and gives good insight.

Whilst it is a clear advantage....

Hah. Whilst. Give it back, it's mine!!!!

Originally posted by Jamin
Hah. Whilst. Give it back, it's mine!!!!

About 50 years ago, when Bobby Fisher was still in diapers, I was taught that a Bishop of the SAME color as the opponent's king is more valuable than the other bishop as it can directly check the king both before and after castle if the king remains on the castled square. I just told my opponent about that, Getting it exactly ass wardsback as I'd mixed it up in the intervening 35-40 years I hadn't played!! Anyone know about this?? I read it in a book in my Jr. High school library.
Whilst is a perfectly good word from the English, MUCH BETTER than the news IDIOTS who (or is it whom) use IMPACTED to mean other than a damn tooth!!!

Originally posted by Gary Thomas
who (or is it whom)

I think it is "who".

The value of a piece is always dependant of the position at hand. Else it is only a 'rule of thumb', nothing else.

Perhaps - if you think your bishop is the stronger one, then it gives you confidence to use it more agressively. Like placebo or something.

Originally posted by Jamin
Hah. Whilst. Give it back, it's mine!!!!

Whilst - now generally obselete; 'while' being the modern usage. Still grammatically correct however. I like a little Olde English sometimes 🙂

Originally posted by Policestate
Whilst - now generally obselete; 'while' being the modern usage. Still grammatically correct however. I like a little Olde English sometimes 🙂

Castles are worth more than horsies.