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

Again, that's not something I can easily check, since I don't own an engine.

If you want to look at grandmaster games involving fianchettoed Bishops, then Bronstein, Boleslavsky, Konstantinopolsky, Fischer, Tal, Kasparov, Geller, Nunn, Gligoric, Uhlmann and several others have all been major contributors to King's Indian Defense theory and praxis.

So far no game with an attacking win, but I did find one with the Bc6 idea. Is this any good?

Here's a nice one. Dubov doesn't trade the bishops and makes headway into what I am trying to find out about.

I like the Dubov game.

Note that an attack doesn't have to be directed against the King in order to be effective.

In fact, an attack against the opposite wing (instead of aiming at the castled King) is often more effective, since the enemy King isn't there to defend the Pawns on the attacked flank.

This can be especially effective if the attacking side is willing to sacrifice a Rook for the opposing Bishop, leaving the fianchettoed Bishop free to run amok.

Pachman vs Bronstein, Prague 1946

Zita vs Bronstein, Moscow 1946

its 3 for 5 btw

So, you don't value a bishop stronger when it is on the long diagonal?

Bishops should be valued at 3.5 when the center is open and there are unbalanced Pawns on both wings... eg: 3 vs 2 on the Q-side and 3 vs 4 on the K-side.

Knights should be valued at 3.5 when the Pawns in the center are locked... eg: Pawns at c4 / d5 / e4 vs Pawns at c7 / d6 / e5.

"unbalanced Pawns"

Not sure what you mean. This is based on which side's perspective? If white has 3 and black has 2, does that mean white can say it has 3.5?

I play tactically, with a bit of positional calculation built in. I would take it, be up the piece and win. 

Unbalanced Pawns just means that one player has a Pawn advantage on one flank, while the opponent has a Pawn advantage on the opposite flank. Overall, Pawns are equal. 

It's also called "opposing majorities".

Like this:

Note that at depth 30, Stockfish gives White an advantage of almost exactly half a Pawn... echoing my claim that the Bishop should be counted as 3.5 in this sort of position.

Ok, because white has three white pawns, black has two pawns, what is the conclusion? Can you spell out the example and say what the value of the bishop is?

I don't see a bishop other than the bishop on e3, does that mean it is 3 or 3.5?

Count the Pawns. White has 6. Black has 6. But they aren't distributed symmetrically... White has a Pawn advantage on the Queen's wing (3 vs 2), while Black has a Pawn advantage on the King's wing (4 vs 3).

This is the sort of position in which a Bishop is usually better than a Knight, and the Bishop can be counted as 3-and-a-half while the Knight only counts as 3.

Why? Because the Bishop is a long-range piece and can influence play on both wings PROVIDED THAT the center is open (so that the Bishop can observe both wings) AND THAT there is in fact play happening on both wings... hence, the requirement that the Pawns should be distributed in an unbalanced manner.

The Knight meanwhile can typically only influence play on one flank.

I do.

"This is the sort of position in which a Bishop is usually better than a Knight"

I would say that is the real reason, not that there is some pawn majority.

In this position, black is much better than the knight position.

Yes, exactly. We were discussing WHEN a Bishop was worth more than 3 points.

Now let's try balancing the Pawns (3 vs 3) and retaining the Bishop-for-Knight. and see if Stockfish still thinks White is +0.53

Note: all I've changed is to move the e5-Pawn to c7.

EDIT:

Cool - that reduced White's advantage by nearly half (from +0.53 to +0.28).

So, as I said, the Bishop vs Knight gains in strength when the center is open AND the Pawns are distributed in an unbalanced manner... in opposing majorities rather than a symmetrical arrangement.

The question is not "Is a bishop worth more than a knight?" I don't understand why you are putting in knights into these examples.

The question is purely about the bishops and their value, NOT relative to knights, rooks, or queens. If black has a bishop, white has a bishop (let's say same colored square to start with), are there times one bishop is worth 3 and the other times it is worth 3.5? Then, you could ask the same question with bishops of opposite colored squares (the consensus I hear commentators say is that it is more often equal).

The guess I have is that bishops on same colored squares might change (3 or 3.5) depending on position, but bishops on opposite colored squares are more likely to be equal (3) throughout the game.

Yes. If your Bishop travels on the same color as your own center Pawns, it is considered "a bad Bishop" (that's a technical term) and is devalued compared to a Bishop that travels on the color opposite to your center Pawns.

Example: White's Bishop is "good", Black's Bishop is "bad".

Stockfish at depth 30 rates this as +0.53

Having said that... I must point out that the Bishop vs Knight case is simply more relevant than the Bishop vs Bishop case.

IMO.

So, then the next thing is what I am asking about in the OP. How do you know to go Bb7 as opposed to a move like Bd7 -  Bc6 (the Wei Yi game)? Or, how do you keep the pawns out of the way (the Nakamura game)?

When there is no bad bishop or good bishop, and it is just two bishops duking it out like the Dubov game, how can you evaluate 3.5 vs. 3?

Also, the bad bishop example is a strawman because in essence it would be less than 3. I am talking about bishops valued only 3 or 3.5 (if you don't want to say it is 4).

In the Dubov - Wei Yi game, Black played 8. ... Bd7 then 9. ... Bc6 for tactical reasons... if he had played the Pawn b7-b6 instead, then 9. Ne5 (discovering an attack by the g2 Bishop on the a8 Rook) would have given White a strong pull... about +0.87 according to Stockfish.

The Bc8-d7-c6 maneuver was played to avoid the weakness on the long light-squared diagonal.

"When there is no bad bishop or good bishop, and it is just two bishops duking it out like the Dubov game, how can you evaluate 3.5 vs. 3?"

If there are no strong positional cues to differentiate the opposing Bishops, then why would one be worth any more than the other? In the Dubov game, Black equalized fairly quickly (before move 25), so there is no reason to think that one player's Bishop was worth dramatically more than the other.

"Black played 8. ... Bd7 then 9. ... Bc6 for tactical reasons... if he had played the Pawn b7-b6 instead, then 9. Ne5 (discovering an attack by the g2 Bishop on the a8 Rook) would have given White a strong pull... about +0.87 according to Stockfish."

You are too close to the trees to see the forest. YES, I know at that position, you could come to that conclusion. But before the game starts, you got to be doing some prep. It's not like Wei Yi sat there for 20 minutes deciding to play Bd7 or Bb7. He had to have committed himself to NOT playing Bb7 earlier on in the game. 

So, the question is if you played differently before, would it have made a difference? Should he have opted for a different idea?

There aren't many Bd7-Bc6 games compared to Bb7 or B along the c8-h3 diagonal. Was it wise to go down the path he did? Another way to ask this is, did white miss a chance in the game?