How do I break the 4 for 5 obsession? B for R?

If you are saying the bishop is 3 points in my example then the question is even more relevant. So, either 4 for 5 or 3 for 5, the question primarily focuses on the bishops when they are aiming at the opponent's king. I am talking mostly about kingside castling, but I think the same question could be applied to the queenside. Fischer's famous bishop blunder was on the queenside wasn't it? Perhaps there are different goals and reasons, but the idea is the same.

The bishop is initially zeroing in on a rook. Also, they are protecting their opposite side rook. This could be a Ruy Lopez where B is on b7, or white could have their B on b2. With a concentration of pieces around the queenside rook, it is hard to get the rook out of danger. Ra7 and Rb8 are common ways for black as well as Rc1 for white. Likewise if the a file is open, then you can trade. The second player will have their bishop on their back rank. 

My question is generally, what is the role of a bishop on the long diagonal? Yes, it covers more squares. Yes, it can attack the center and eyeball the king on g8 or g1. But am I the only one who wants to get a rook for that bishop? 

In the following part of a game I got rook obsessed. I wanted to find a way to play Bxh1 (meaning BxR) without trading queens. Perhaps this is the wrong thinking. Should we be looking at things like the bishop pair, pins/forks, or simply defending another piece and trade off that bishop later for something like a knight?

It depends on context but I am wondering what the general consensus is in the top level play. I see a lot of Be6 and white takes the bishop with theirs on c4. In this case, is this more prevalent? Just wait to trade off bishops when you feel you can get a positional advantage? Don't look for more. 

When I started learning QGD and read about Slav lines, I also looked at the Tartakower variation. I didn't want to play Ba6 at that point. Bb7 got my bishop trapped, and I lost plenty of games with this. So, I stopped playing Bb7. Perhaps my question can shed light on this opening as well.

I know there are books on openings, but are there also books, games, or other sources which address individual pieces on prominent squares like b7, b2, g7, and g2? As for the KIA and Catalan, I just hate the idea of pointing my king's bishop away from all the action. I almost never venture into that territory as white. Are there common elements here regarding the bishop we can use? 

Here is the start position but each subsequent position I think could be looked at with the question, what role does the bishop have?

The f1 rook is hanging.

My question is not about the exact position. My question is about bishops. Stop trying to solve it like it's a puzzle. Look at it in terms of bishop placement.

Read the text I typed, don't just look at the FEN. Try to understand before you type (think before you speak).

Why "without trading Queens"?

24. ... Qxh1 wins a whole Rook, after which trading Queens is the simplest and clearest path to the win.

When you are ahead by a significant amount of material (a whole Rook, in this case), exchanging pieces... especially Queens... deprives your opponent of counter-play and makes your win easier.

Why keep the Queens on the board, when you have an easy win in the endgame. A Rook up, you don't need to win the game all over again. It's won already, as long as you prevent counter-play.

THE QUESTION IS ABOUT BISHOP PLACEMENT. I AM NOT GOING TO WAIT 100 YEARS TO GET THE EXACT POSITION SO YOU CAN TRY TO "SOLVE" IT. I MERELY GAVE AN EXAMPLE POSITION WHERE THE LSB WAS LOCKED IN. IF YOU READ MY QUESTION YOU CAN SEE THERE WAS MORE TO IT.

Regarding the development of Black's Bishop to b7 in the Slav, remember that the c6-Pawn can always advance again, to c5... opening the Bishop's diagonal and challenging White's d4 Pawn.

In fact, there is a technique called "the Nest method" whereby... if the immediate move b7-b6 would weaken the light squares too much... Black first plays the solid c7-c6, then later on plays b7-b6 (creating a nest for the Bishop), Bb7, possibly Rc8 and finally advances c6-c5 freeing the Bishop and challenging White's central d4 Pawn.

"remember that the c6-Pawn can always advance again, to c5... opening the Bishop's diagonal and challenging White's d4 Pawn."

So, you are saying to not look at Bb7 as a way to attack along the long diagonal, but rather be a defensive piece for other pieces? This is counterintuitive to use a higher valued piece to protect a lesser valued piece. If the bishop is in front diagonal to a pawn, then both can protect each other. See below examples.

I was going to mention something about B getting to c6, but that's too obscure I think and I found a master game which is more pertinent here. The c5 move you are mentioning cannot be played here, and the only way to avoid a trade is c6. A quick Stockfish evaluation shows white goes up a point. So, I conclude that you don't want the bishop to be behind the pawn and if it were white pawns along the diagonal, then you would be more blockaded.

This is the problem I am having with Bb7, Bg7, Bb2, and I haven't even experimented with Bg2 yet. The bishop gets trapped.

So, I am wondering if there are structures which enable black to actually keep the LSB on the board and use it to attack instead of being traded off on these "2x2" squares.

Otherwise, if you want to keep the bishop pair and not lose the LSB in a trade, then a bishop move to d7, e6, f5, g4, and h3 when possible is better. Like in this game.

Here is a Master game illustrating that "Nest method followed by ... c5" that I mentioned above.

In the So vs Caruana game you gave above, White's 13. Bf3 did exchange off the b7-Bishop, but allowed Black an easy equality. At the super-GM level, equalizing completely by move 20 or so is perfectly acceptable for Black.

Very good, now go play in the sandbox, dig deeper. Make sure to bury your head in the sand and an adult will come after to give you a PBJ sandwich. 

"If anyone took your advice then the KID, QID and Catalan would not be played, the idea of the kid is that you play either d6 e6 and then push e5 reroute the bishop to h6 and then g5 and attack the kingside"

Yes, I agree. Bh6 sidesteps the question. It is like Ba6 in the QGD. I don't know about Ba3 and Bh3 as a motif, but that is possible too. Don't know if it is good. Sometimes in the Ruy Lopez I see white playing Bb3 after the a6, b5 push. Then if Na5 is played white keeps the bishop with Bb2.

I am referring to games like this one. 

And before you say that was a decade ago, look at this game.

Yes, in the Ruy Lopez the White Bishop on b3 can become tremendously strong if the position opens up.

Example:

The focus of the question is bishop placement on b2, b7, g7, and g2. Not anywhere else like in this game. It's the funny one where Nakamura got his bishop caged in. This is what happens when I go to one of the four squares usually.

The Bishop on the long diagonal (g2 / b2 / g7 or b7) can play a few different roles.

1) Pressure on the enemy center:

Is there a current masters game like the skittles one (without the Qh4 trickery), a game where the bishop is making the win with the bishop still on the long diagonal?

Possibly... I don't own a games database.

Not sure why you would want a current Master game. They are much, much harder to follow than games by the old masters... Alekhine, Capablanca, Nimzovich, Reti, Tarrasch, etc. They might be more technically correct at the 2700 level, but that's worthless to a 1500 player (or, for that matter, to a 2350 player), and the older games have far more pedagogical utility because the themes are more clearly presented.

"Not sure why you would want a current Master game."

Is there an old master game which is backed up by Stockfish? I would think established lines by the dead greats of the past are repeated by current masters (2500+, not just 2700+).

Which one is you?