In the Opening the Bishop is Stronger than the Rook
(Joban wa hisha yori kaku.)

Vocabulary: joban=opening, wa=as for, hisha=Rook, ...yori=than..., be preferable to..., kaku=Bishop

White in hand: P 
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN  * wG  * wK  * wN wL |a
| * wR  *  *  * wS wG  *  * |b
|wP  *  * wP wS wP  * wP wP |c
| * wP wP  *  *  * wP  *  * |d
| *  *  *  * wB  *  *  *  * |e
| *  * bP bP  *  *  *  *  * |f
|bP bP bS bG  * bP bP bP bP |g
| * bB bG  *  * bS  * bR  * |h
|bL bN  *  * bK  *  * bN bL |i
+---------------------------+
Black in hand: P 
Diagram 1. Up to Bx5e.
Diagram 1 is from a Yagura opening where White has just exchanged Pawns on 5e.

Here White has, roughly speaking, two ways to deploy his pieces, depending on where the Bishop is placed.

Plan A

K-6i    S-5d    
P-2f    B-2b    
P-2e    P-6d
Plan A aims at attacking the King's head directly, with the Bishop back on 2b.

Plan B
K-6i    S-5d    
P-2f    R-5b    
P-2e    B-7c
In Plan B, White pulls the Bishop to 7c, aiming to deploy forces in the central area while applying pressure on Black's base.

In the opening stage, where to move the Bishop is very important in deciding which strategy to take. Whether your strategy is offense-oriented or defense-oriented determines where the Bishop should be placed.

Another example to show you how vital the Bishop's position can be when you are about to move into the middlegame. 

White in hand: nothing
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN  *  *  *  * wK wN wL |a
| *  *  *  * wR  * wG  *  * |b
|wP  * wB wP wS wG wS wP wP |c
| *  * wP  * wP wP wP  *  * |d
| * wP  *  *  *  *  * bP  * |e
| *  * bP bP bP bS bP  *  * |f
|bP bP bS bG  * bP bN  * bP |g
| * bK bG bB  *  *  * bR  * |h
|bL bN  *  *  *  *  *  * bL |i
+---------------------------+
Black in hand: nothing
Diagram 2. Up to B-7c.
In diagram 2, White has just played B7c, giving priority to defense. The Bishop here is for restricting Black's offensive formation.

On the other hand, the Bishop pulled to 4b (Diagram 3) is for applying pressure on Black's King, therefore an offensive move.

White in hand: nothing
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN  *  *  *  *  * wN wL |a
| * wR  *  *  * wB wG wK  * |b
|wP  *  * wP  * wG wS wP wP |c
| * wS wP  * wP wP wP  *  * |d
| * wP  *  *  *  *  *  *  * |e
| *  * bP bP bP bS bP bP  * |f
|bP bP bS bG  * bP bN  * bP |g
| * bK bG bB  *  *  * bR  * |h
|bL bN  *  *  *  *  *  * bL |i
+---------------------------+
Black in hand: nothing
Diagram 3. Up to S-8d.
In either case, remember that the Bishop plays a central role in deciding your major plan in the middlegame.

(2)

At a very early stage of the game where your Golds and Silvers are still in their original positions, the Bishop can count more than the Rook does.

Diagram 1 shows where White has just opened the way for the opening called Masuda-style Ishida-ryu opening.

White in hand: nothing
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN wS wG wK wG wS wN wL |a
| *  *  *  *  *  * wR wB  * |b
|wP wP wP wP wP wP  * wP wP |c
| *  *  *  *  *  *  *  *  * |d
| *  *  *  *  *  * wP bP  * |e
| *  * bP  *  *  *  *  *  * |f
|bP bP  * bP bP bP bP  * bP |g
| * bB  * bK  *  *  * bR  * |h
|bL bN bS bG  * bG bS bN bL |i
+---------------------------+
Black in hand: nothing
Diagram 1. Up to K-6h.
From Diagram 1, White can play P-3f. Then there will be a Bishop-exchange followed by White's B*5e (Diagram 2). You may think White has gained the lead. 

White in hand: nothing
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN wS wG wK wG wS wN wL |a
| *  *  *  *  *  * wR  *  * |b
|wP wP wP wP wP wP  * wP wP |c
| *  *  *  *  *  *  *  *  * |d
| *  *  *  * wB  *  * bP  * |e
| *  * bP  *  *  * bP  *  * |f
|bP bP  * bP bP bP  *  * bP |g
| * bS  * bK  *  *  * bR  * |h
|bL bN  * bG  * bG bS bN bL |i
+---------------------------+
Black in hand: B P 
Diagram 2. Up to B*5e.

Moves from Diagram 2:
B*7g    Bx2h+   
Sx2h    S-2b
B*7g is the move to play here. Black takes a Bishop in exchange for a Rook, which is not a material loss. After White's S-2b, there is a very good move on Black's part, which is...?

B*6e (Diagram 3)

White in hand: R 
  9  8  7  6  5  4  3  2  1
+---------------------------+
|wL wN wS wG wK wG  * wN wL |a
| *  *  *  *  *  * wR wS  * |b
|wP wP wP wP wP wP  * wP wP |c
| *  *  *  *  *  *  *  *  * |d
| *  *  * bB  *  *  * bP  * |e
| *  * bP  *  *  * bP  *  * |f
|bP bP bB bP bP bP  *  * bP |g
| * bS  * bK  *  *  * bS  * |h
|bL bN  * bG  * bG  * bN bL |i
+---------------------------+
Black in hand: P 
Diagram 3. Up to B*6e.
With B*6e, Black is certain to get the Bishop promoted somewhere. White, on the other hand, cannot play Rx3f (Black will play Bx2b+). White cannot drop a Rook in the Black's camp, either.

In the above example, Black gained the lead by a Rook-Bishop exchange, but I should add that generally it is better not to resort to the exchange at an early stage.

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