Rookie question.

Hi, I'm just starting off here in the chess community and had a question for really anyone willing to offer feedback.  I recently found myself in a mid-game situation where I wondered if exchanging a Rook and a Bishop for both my opponents Bishops is a good or bad idea.  The reasoning behind thinking it may be viable was the fact that it would parilyze my opponent's diagonal coverage while still leaving me with having one of each piece.  Thanks for your time and consideration.

In general rooks are more valuable than bishops. Of course, it's impossible to say for sure what the right choice was without seeing the exact position.

If pawns are equal to 1, then a rule of thumb is:

Knights = 3

Bishops = 3

Rooks = 5

Queen = 9

Study has been done to try to find more precise values. Knights and Bishops are probably a shade over 3 and Bishops are just slightly more valuable than Knights, something like N = 3.15, B = 3.25. Rooks my be slightly less than 5 (4.75 perhaps).

But these are just rules of thumb. It tells you that in general you don't want to give up a rook for a bishop. But in particular games it might be wise (see this blog post for example).

 As a general principle, exchanging Rook and Bishop for the Bishop pair is a bad idea.

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(As Loomis pointed out, in specific situations things can of course change... you must always think about the specifics of a postion...)

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But your question is a very interesting sort of strategic question. You can impair your opponent's diagonal coverage by removing both bishops, but is this worth a bishop and rook?  This seems to me a very advanced sort of strategic thinking even if the conclusion is bad.  Why bad?  The best way to analyze this is to think about an endgame after your exchange.

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Imagine White has: Bishop and Rook and say a pawn -- vs Black with: Two Rooks and a pawn.   

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In an ending like that Black will almost certainly quickly gain the upper hand (so long as White doesn't have some immediate tactical win)... First, the two rooks coordinate with each other naturally and powerfully, easily forming a battery that can dominate a rank or file. In contrast, the Bishop and Rook are awkward together and struggle to combine forces. Most importantly, while the Rooks can roam over the entire board and combine to attack all squares, the Bishop travels on one set of colored squares or the other... the bishop is non-existent on half the board! The rooks work wonderfully with the pawn too. Black can set up his rooks behind his pawn as though pushing it down the board to Queen. The rooks' force flows along the board along the same channel the pawn travels... but the poor Bishop can only support a pawn on half the squares the pawn travels, and it can't both support the pawn and protect it into the next square, something the rooks do easily.

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Finally, a lone bishop can't mate, a lone rook can (easily). This gives black powerful sac options --- in our example ending, black could trade both rooks for rook and pawn and have a guaranteed draw. White would have no such option.  

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The valuation of pieces is a fascinating thing. Andrew Soltis has written a book about it, (looks great, haven't read it all)... where he explains that the valuation of a piece is dynamic! It changes depending upon what stage of the game one is in. This is why, (apologies to Loomis), no single static numerical value, however precise, gives the value of a piece through out a game.  Knights shine in crowded postions, and tend to be most valuable in the opening and steadily decrease in value as the board clears.  For rooks it is the opposite... shut-ins in the opening, they are late bloomers who dominate the endgame. The value of a bishop is heavily dependent on how things stand on it's particular color...  Given all this, it is amazing actually how well the pawns = 1, bishops and knights =3 etc. scheme holds up. 

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Your question though, really asks about the coordination of pieces -- their power together.   What is the bishop pair worth? (I'll bet Soltis discusses it at some point...)  The underlying idea is to assess one's pieces as they work with each other, not in isolation... I think that idea really takes one quite far....farther than a patzer like me has gone!  I think, before one gets into things like the value of the bishop pair, I think the first thing is to ask...: how are my pieces coordinating with the pawn structure.  A strong player will see that a bishop or knight can be made good or bad for a long time by assessing the bishop or knight in relation to the pawns.  A strong player will try make the interaction of pawns and pieces as favorable to himself as possible.  

Some of the finer points of piece valuation (like the value of the bishop pair) don't really matter IMO unless one is playing very strong accurate chess, Expert or Master level. 

Phew, that's my two cents... by the way, just because I went on at length doesn't mean I actually know anything... I am a rather poor chess-player LOL. (But I've  read a lot of books, ok? ;)

amazing writeup .. you seem spot on.

Piece values can change from colour to colour too.. for example.. the black queen in a traxler (fully accepted) is probably worth 3 times what the opponents queen (usually unable to move much) is.

IN the dutch, I find that the f6 knight is usually worth a rook and sometimes I will sac the exchange just to avoid the powerful attack / limit it's defensive values!

Takes experience to know what's worth what but in general the 9 5 3 3 1 is good. 

I would just like to add a further comment on a quote from Josh Waitzkin that was brought to my attention, "A pair of bishops is generally considered more valuable than the combination of a knight and bishop."  Which still didn't much address my original question, but brought me closer to an answer.  So I continued to do research and discovered this link:

http://www.chesshere.com/chess_strategy.php

 It highlights several interesting ideas regarding the dual bishop use.  Some quotes are, 

"In open positions, bishops are usually considered slightly better than knights, especially toward the end of the game when many of the pieces have been captured." (This information is a bit obvious but I'll use it in illustrating a point later on)

"It is particularly good chess strategy to retain both bishops to act as a weapon, especially if the opponent has lost one or both of his bishops."

Really the only question this leaves me with is, exactly how powerful does the dual bishop become end-game?  Knights generally decrease in value as the board opens up, and bishops increase in value. Furthermore the dual bishops are considered a more powerful weapon than either a bishop and knight combination or a knight knight combination.  How much more valuable does the bishop become in his ideal end-game and paired situation?