Pursuit question: Be3 then ...Ng4

This common situation is really bothering me because I've never seen how masters resolve this situation in the opening, and I've never seen it in an opening book, yet it happens to me all the time...

The most common specific moves that I encounter are: I play Be3 as White to protect my pawn at d4, but Black has a knight at f6 so he attacks that bishop with ...Ng4. Now what should I do?

This situation invites "pursuit," which is where one piece endlessly attacks another, until a draw by repetition occurs. In this case pursuit could happen by Be3 ...Ng4 Bc1 ...Nf6 Be3 ...Ng4 Bc1 ...Nf6, etc. I am usually happy to draw in this manner but I'd like to know what I'm supposed to do, in case I feel like playing for a win sometime.

Here are all the possibilities (I believe):

o First prevent ...Ng4 by h3 or f3, before playing Be3.

o Allow ...Ng4 and retreat my bishop, because the knight will just get chased away in the next move with h3 or f3, so White gets a free move. (h3 or f3) Unfortunately, sometimes Black also has a nice freeing or attacking move during that pause in play as I retreat my bishop.

o Allow ...Ng4 and don't retreat my bishop: allow ...Nxe3.

o It doesn't make any difference because the time versus material exchange is perfectly even.

o Draw by pursuit.

o It depends on the specific position, especially as to whether Black can squeeze in a good attacking move during that one-move pause in regular play.

Which is the answer?

Below are some specific examples of this situation (I assume there's no name for it) I've encountered in the opening while playing against Chess Titans. More generally, the situation could apply to either queenside or kingside, or could happen to White or Black.

You might be right, but I'm not yet convinced. Thanks for your opinion at least.

Any other opinions? I forgot where I read recently (I think it was by Nigel Short) that this issue of bishop versus knight can be critically important because it's one of those small advantages/disadvantages that can accumulate to produce a win/loss, so one should be careful about whether that exchange is going to be advantageous/disadvantageous in any way.

In the first one, just play Bg1 and kick the knight.

Usually they play moves like Ng4 because they want the bishop pair. Whether it's 'worth the trouble' depends on the position and tactics. I don't think there is any universal rule for this. The obvious way to avoid getting kicked is to simply not allow it to happen with a move like h3 or have something else in the position to make the move not desirable. You could also just avoid moving it in the first place. The bishop on c1 in particular can stay on c1 for a while in lots of positions. 

In the first game the bishop could go to g1 but I wonder if you can just play 6.e5 and try other things. 

In the second game 14.h3 looks fine. Otherwise Black gets the bishop pair for free in an endgame. The bishop pair can be unusually good in the endgame.

In the 3rd game the bishop doesn't belong on g5 at all because Black can simply prepare some kind of knight move that prepares the move ...f5 and provokes a trade of dark-squared bishops which would be in his favor. White could be the one losing a tempo. If the bishop on c1 moves at all it probably needs to be on e3 with the move h3 kicked in to prevent ...Ng4 stuff. 

But yeah it depends...

It looks like you're right on that first example. I just found on 365chess that first position (why I didn't find that position before is a long story...), and the only two responses shown for White are 7. Qd2 (3 games out of 4) and 7. Bg1 (1 game out of 4). I also noticed that 6. Be3 is only the third most popular 6th move for White, maybe because of the knight harassment problem, so the situation could have been avoided earlier.

You're also right that I'm probably trying to overgeneralize by three rather different examples: in the first one the bishop can retreat to a new square, in the second one the bishop can retreat to only its old square, and in the third one the bishop can't retreat at all. Still, I'm pretty sure there must exist some applicable heuristics, like maybe "If your bishop can't retreat after threatened by ...Ng4, then don't play Be3, otherwise keep developing and let it be captured," so to just say "It depends" just delays the question by forcing it to be more specific about which case it is.

Thanks for your information. With that 365chess example at least I have some documented examples of what players have actually done, although not all those games were master games. I'll have to digest the rest of all this info for a while.

In the mean time, here's another example from my own games against the computer...

It's not so great to generalise because Ng4 isn't always something that needs to be avoided. The bishop pair isn't great in every position and you may have tactical reasons that make such a move dangerous. I guess you can think about moves like h3 when you need to avoid such moves.

In the last game 9.Nd5 is stronger with the idea of Bg5 being a possibility. If Black castles the pin will be hard to break. The bishop can go to e3 in those positions too but then you probably will have to play a move like h3.

just let him take your bishop. You just develop pieces instead of wasting a whole move\

In bobbin il systems ，( are u still wondering), I'd just let him take the bishop and work on f file play and the d5 outpost. The doubled pawns are quite useful as the e3 pawn covers the d4 square

The problem then is your light squared bishop... Maybe someone higher level has an idea?

Botvinnik*... Automcorrect