This is my favorite variation against Black in the King's Indian. It has proven highly successful with me, and I have won some nice games with it:
Which King's Indian Variation?

You'll probably get several different opinions. Personally, I'm fond of the Classical Variation, Bayonet Attack. I've had much success with it.
The idea behind that variation is that if the d-pawn is attacked (by c5 or e5 pawn breaks) the pawn can simply advance and lock up the center; also preventing the Queen's Knight from getting too far. Also, the d3-Bishop protects the c and e-pawns from Black's Knights and further strengthens the center.
I like it because it gives White a lot of early space and can develop into some smashing attacks. (Like one game I posted in the Showcase forum.)

I think the Bayonet Attack is the actual trend and it's objectively difficult to play against.
But since KID players are usually aggressive and love to start an attack against the enemy king, I'd suggest White to aim to closing the position or preventing kingside attacks with the London System or the Fianchetto Variation.

But since KID players are usually aggressive and love to start an attack against the enemy king, I'd suggest White to aim to closing the position or preventing kingside attacks with the London System or the Fianchetto Variation.
I think most White players also love to attack. Besides, the KID is borderline unsound. Bayonet attack for the win!

King's indian is hard to attack but from my experince taking your queen out early game really helps. As it gives you a high amount of material for white and sometimes with pins and forks if the knight is teamed up with the queen it leads to middlegame checkmates

IMO "when we're playing Black which is annoying" :
a : First of all it's important for me to inform the existence of this variant which can annoy 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 4) e4 d6 5) Nf3 o-o 6) Be2 e5 so far everything is normal then coming the exchange variant which generally is not really a problem (because the opening remains interesting to play even without the Queens) 7) dxe5 dxe5 and now "the completely unexpected move" 8) Qc2 our 0-0 attack strategy seems wrong because "the game is open with Queens still in play" and currently we have our dark square Bishop who is blocked and in short is weak.
b : 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 4) e4 d6 5) Nf3 o-o 6) Be2 e5 and then 7) Be3 a move that tends to irritate because if the center doesn't close we can't really make "our strategic KID attack plan" 7)...Ng4 8) Bg5 f6 9) Bh4
c : 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 and then 4) g3 o-o 5) Bg2 d6 6) Nf3
d : 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 4) e4 d6 5) Nf3 o-o 6) Be2 e5 and then directly 7) d5 at first we can't see the problem then 7)...a5 8) Bg5 this move can annoy
e : 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 4) e4 d6 5) Nf3 o-o and then 6) h3 we have the impression of "a clown move without any real idea" but actually no 6)...e5 7) d5 Nh5 8) Nh2 and then "it's no longer funny at all" because 8)...f5 9) exf5 and if 9...Bxf5 10. g4
Afterwards normaly these variants are not strictly speaking the strongest but they are more problematic IMAO

the Averbahk for white is nothing to sneeze at. Black has to play c5 instead of e5 and it is not the normal KID Black knows and loves.
the Saemich endgames can be pretty rough for black too.
This is what Kasparov made abandon the King's Indian Defence:
https://www.chessgames.com/perl/chessgame?gid=1070932

IMO "when we're playing Black which is annoying" :
a : First of all it's important for me to inform the existence of this variant which can annoy 1) d4 Nf6 2) c4 g6 3) Nc3 Bg7 4) e4 d6 5) Nf3 o-o 6) Be2 e5 so far everything is normal then coming the exchange variant which generally is not really a problem (because the opening remains interesting to play even without the Queens) 7) dxe5 dxe5 and now "the completely unexpected move" 8) Qc2 our 0-0 attack strategy seems wrong because "the game is open with Queens still in play" and currently we have our dark square Bishop who is blocked and in short is weak.
For the record, it was the bot.Rusty from the Chessmaster program which inflicted a terrible defeat on me with this variant and I am currently watching https://youtu.be/1G2VNOY7Ln0?list=PLAwlxGCJB4NfgPJBNicg3jGq6NkCKwTM2 1h18 I can see that Etienne Bacrot with Black is playing the same kind of opening with the same idea :
IMO I find interesting to see how Anish Giri will play this same kind of opening
My opinion is Averbackh or Bayonet.
Fianchetto for white is the kind of position where a computer can squeeze black to death but a human player can easily make 1 slip and black's position becomes super active, like in the famous Reshevsky-Bronstein game.
all just my opinion, Bill

The idea behind that variation is that if the d-pawn is attacked (by c5 or e5 pawn breaks) the pawn can simply advance and lock up the center; also preventing the Queen's Knight from getting too far. Also, the d3-Bishop protects the c and e-pawns from Black's Knights and further strengthens the center.
I like it because it gives White a lot of early space and can develop into some smashing attacks. (Like one game I posted in the Showcase forum.)
Nc5 seems to come with a tempo now

the sämish and averbakh are decent options agianst the kings indian. however, i believe that the c5 advance by black can really kill any of the sharp attacking white usually wants when he plays the sämish or averbakh. in the averbakh the Bg5 pin can often be extremely annoying because often black cant do anything about it
the 4 pawns attack is the best of the 3 listed. blacks best option is c5 where he transposes to a benoni. the difference between the 3 is that white often gets a kingside attack in this position
The fianchetto variation is also a good choice if you like to take advantage of space and win slowly. this variation at the higher levels often fizzles into a draw but is perfectly playable at the club level for a win.
there are many other little sidelines for white.all of which are typically not very threatening.
what really scares black most is the main line bayonet attack. no other variation makes black struggle this hard to get something out of the position
Which king's indian defense variation is best and most successful for white?