White wins 47.7%
Black wins 23.6%
Draws 28.7%

Diagram

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Rxh6! Nxh6
Qxh6+ Kf7
Qh7+ Kf8
Bd1 Nf7
Bh5 Bxd5
Nc3 Ng5
Qh6+ Kg8
Bxe8 Qxe8
Ng4 Nh7
Nxd5 ....

Against Bg4, White has other potential counters, such as developing Nge2 rather than Nf3; from e2, the Knight still has a number of reasonable futures (if White plays O-O-O, Ng3 is good, supporting the h-pawn advance as well as a potential g-file opening sac via g4 and Nf5; if he plays O-O, there is always Nc1-b3 to support the frequent Queen's side advance with c5).

On the other hand, there's little else to do about Ng4 but prevent the move entirely. Where can the Bishop really develop other than e3?

* Bd2 (or b3 and Bb2) don't contribute anything to the major White strategic plans.

* Bf4 will simply result in the B being driven off in most variations, as Black plays e5 at some future point. Thus, it is virtually a waste of a tempo, and does not ultimately solve the problem of the White Bishop.

* Bg5 has little merit, unless White's intent for the Bishop is to trade it for Black's via Qd2 and Bh6 (in which case, Be3 is just as suitable a preliminary, moreover, White will possibly have to play h3 anyhow, else Ng4, once the pin is broken, prevents Bh6). The pin simply isn't that strong against the fianchetto, as Black can move the Queen away from the pin without pain, answering Bxf6 simply with Bxf6. (By contrast, in openings where Black does not fianchetto, this pin is very strong because Black must often simply suffer from it, as the Queen's overriding duty becomes to be able to recapture on f6 to save Black from a major and frequently fatal Kingside weakening that would occur otherwise after Bxf6 gxf6, and this duty cannot usually be maintained without remaining in the pin) Nor can White usually reinforce the pin well, because in most KID lines the center tends to become blocked, depriving White of e4 and d5 for a Knight; the only square a Knight can reinforce the pin from thus being the awkward g4.

The upshot is that Bg5 seems to give very little benefit besides delaying Black's eventual ... f5 a few moves, as he must first move the Queen before removing the Knight.

* Ba3 (after b3) is potentially good, *if* the usual blocked Pawn center occurs. If it does, this may even be superior to Be3, since from a3 the Bishop directly pressures Black's base (d6) and thus combines very well with the Pawn advance c5. Otherwise, the Bishop is probably misplaced here.

King's Indian, Makagonov System (5.h3)
1.d4 ♘f6 2.c4 g6 3.♘c3 ♗g7 4.e4 d6 5.h3

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5.Nf3 50,868 <42.6%> 27,771 <39.8%>

5.f3 25,895 <43.4%> 12,103 <40.5%>

5.Be2 21,083 <43.8%> 12,056 <41.0%>

5.f4 7,593 <43.4%> 3,108 <40.4%>

<5.h3> 5,816 <48.3%> 3.212 <46.5%>

5.Bd3 3,418 <43.2%> 1,829 <41.2%>

5.Nge2 2,646 <43.0%> 1,311 <40.0%>

5.Bg5 1,425 <44.3%> 687 <41.2%>

And the corresponding numbers for White winning percentages when all first moves and 1.d4 are considered are:

1.(any) 3,931,442 <38.6%> 1,860,057 <35.0%>

1.d4 1,333,171 <38.7%> 673,352 <35.3%>

3...Bg7 108,753 <41.8%> 56,102 <40.0%>

As i recall, back in the 1960s and 70s probably ..c5 was the better center break but later on people would start playing stuff like ..Na6 and ..e5 with decent results. The early ..e5 often led to crushing attacks by White involving the advance of g- and h-pawns (Larsen vs H Westerinen, 1969).

It should be:

"Mak-o-gonov" as in the player:

Vladimir Makogonov