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The same question applies to Black where the dark-squared bishop is considered Black's best bishop.
This was from the book "Logical Chess Move by Move" by Irving Chernev where he quotes Siegbert Tarrasch as saying the King's Bishop is the greatest attacking piece, so I guess it does pertain to mainly one player with one school of thought. I found it interesting how Tarrasch at times would not even move his King's Bishop during a whole game.
The black king, will occupy e8 and g8 (before and after castling, respectively), both of which are white squares. Also, the weakest point on the black kingside is f7, again a white square. Because of this, if you are trying to attack the king, the white bishop can often be more valuable.
Perhaps someone else can add some more deeper reasons, but this has been my experience.
Added: Also worth noting, attacks on h7 can often threaten mate, another white square. Furthermore, just having the bishop on the diagonal attacking f7 would pin the pawn to a castled king.
Neither bishop is inherently better than the other. Depending on your choice of opening, white's dark-squared bishop can be far more valuable to him.
White's light (king's) squared bishop stands on squares of the color occupied by the enemy king. This is true of his initial position, e8, and his likely castled positions, mostly g8, occasionally c8.
Also, the light squared bishop attacks important squares around the enemy king. This includes f7 and d7 for both the original and castled positions (on the king and queen side respectively) plus h7 (king's side castling), or b7 (queen's side castling).
I would say the values of the light-squared bishop vs the dark-squared bishop is negligible, but in any given opening, one is likely to end up more valuable. It may be that if you average over -all- openings, the bishop that can attack f7 and h7 would be more valuable, but such averages are next to meaningless and counterproductive if you end in on of the 'exceptions' that happens 40% of the time.
For example, when black plays the French opening one of his bishops usually ends up being quite terrible, at least for a while.
I would not call it "white's better bishop", but it is considered crucial to a king-side attack in most cases. Without it, black can defend his king-side a lot more easily.
You have to consider that "Logical Chess Move by Move" is a very beginning-level book and is meant to show clear games, often between players of significantly different strengths, and many of the games are very old, from a time when king-side attacks were more commonly allowed. We simply do not think the same way today as defense is a lot better, but it is hard to get an attack on the black king without it...in general.
I only answered to post that rule of thumb about the light-squared bishop usually being crucial to an attack on the black king-side.
In the mainline King's Indian Defense, where the center locks and white and black attack on opposite wings, black's dark square bishop is very bad, and the light square bishop is nearly essential for a successful attack.
This generalization seems to be useless at best.
There are not such stats. Komodo did some tests, showing better relative performance when the c1(dark-square) bishop is off the board, rather than removing the f1(light-square) bishop. But the difference was rather insignificant. So it depends very much on the type of chess positions played. I am not certain about attacking(never checked that, but in many positions the dark-square bishop is definitely stronger), but what concerns general chess play, kingside fianchetto(g3 and Bg2) is almost always the best possible opening setup, in a very wide range of openings, so keeping this bishop should be good. The reason is of course such a bishop strengthens the king shelter, while at the same time x-ray-attacking a number of opponent pieces along the long diagonal(Nc6, Ra8, etc.) In comparison, a bishop fianchettoed on the queen side(Bb2) does attack opponent pieces on the long diagonal, but does not provide shelter to the friendly king, so it performs less convincingly.
Which bishop will be stronger very much depends on which opening is played and the position of pawns in the center and around your king. For instance, if you play the French Defense, the light-squared bishop is generally your weakest piece, and it's often a good idea to exchange it off with something like b6, Ba6, BxBd3, etc. This is because there are black pawns on e6 and d5. On the other hand, if you're playing the Ruy Lopez, then you will have the pawns on e5 and d6. Now your light squares are open, that bishop is a fantastic piece and I'd want to avoid exchanging it. I hope that helps!
The White bishop is whites best piece after the queen as it’s the active bishop, and can also fianchetto the king side. In which case can be worth up to 4.5points. Also, Fischer has elected to capture a bishop rather than a rook, such is its strength esp at defending the king. Likewise with the black side, the white bishop is often referred to as the problem bishop often getting blocked in or not being developed to a good square. A lot depends a lot of a lot of things, I'm a very open player, and I protect my white bishop, its worth more than a knight, bishops are like my children and the white one my favourite. ;-) watch some of Fischer's games, he is the main exponent of the white bishop and has even traded his queen for the opponents bishop!
