How do you play the K.I.D. when White plays e3 instead of e4?

E.g.,

The point is that Black uses a tactic to get in the move e5 (Nxe4 threat, exposing bishop attack on the e5 knight). But w/o that tactic (since e3 is played instead of e4), Black has to figure out a different way of getting in the move e5.

That's true in the main line of the Classical, but many other lines Black plays Nbd7 then e5 and it's perfectly doable here. Although it seems many players seems to prefer to switch to Grünfeld or Benoni with either d5 or c5, hoping to make e3 looks like a waste or a lack of ambition.

Well, for starters, 4.e3 is almost never played.  If it is, White's position is so passive that Black should have no problems.

FAR more common is 4.Nf3 and 5.Bg5 or 5.Bf4, often followed by 6.e3 (rather than e4).  In these e3-lines, you should have answered your own question about the lack of the ...Nxe4 trick.  The answer is you don't play ...e5.

Let's take the Bg5 line as an example:  After 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.Nf3 O-O (If White hasn't played 4.e4, there is no reason to commit to ...d6, play 4...O-O in these cases) 5.Bg5 c5! and now:

If 6.d5, then 6...d6 with the Bishop opened up for Black and queenside play, OR, you can play in similar fashion to the Benko Gambit with ...b5 and ...a6.

If 6.e3, then 6...cxd4 7.exd4 d5! (all the more reason NOT to commit to ...d6 too early.  If White plays 4.e4, play 4...d6.   Otherwise, castle first.  You aren't "not castling" or castling Queenside here.  After 4.Nf3, there is no Saemisch King's Indian, and about the only line where Black delays castling is in the 5...c6, 6...a6, and 7...b5 line against the Saemisch King's Indian.

So if they do 4.e3, without bringing the Bishop out to g5 or f4, it's even more passive for White.  Strike at the center in similar fashion, an early ...c5 resulting in a Benoni, Benko, or trade and ...d5 type of structure.

1) You should not commit to an opening if your opponent doesn't follow the book moves/variations. Trust me, i tryed. You should only hope to transpose, and that's it. If he goes to a line that you're not familiar with, take your time and a good look in the position.

2) I think after e3 the idea here is to challenge white's center, pushing the pawns like in a normal king's indian, but with a little more enphasis on challenging the center. Developing the pieces should also focus in challenging the center, and the light square bishop should go to g4 and than capture the Knight on f4, forcing the queen to recapture and than put herself in the middle of the battle, where black might gaining tempos by attacking her.

All and all, black's king is really safe and that should be used to transform the K.I.D into a K.I.Attack, after he castles kingside of course. For myself, castling queenside in similar positions do not give you anything good

Semi Classical variation, bit slow, but fine. Pawn to e3, bishop to e2. Probably h3 as well. @pfren knew a master player who had great success with such.

This modest system with e3 and possibly Bd3, Nge2 is intended to drag Black out of KID waters.

Black has a few promising transpositions at his disposal, although none is relevant to the genuine KID where Black typically strikes with his f-pawn.

In short, I gotta learn to play the Benko Gambit.

It's been 5 or 10 years so I don't remember, I think it was Shankland playing a bunch of early e3 setups and doing well against ~2600 crowd for a while.

But yeah, it's not a KID anymore. Others mentioned there are a lot of things that can happen, I'll just throw in that one position I'd enjoy getting personally is a transposition into a Panov attack. This isn't a bad position for white, but I've always felt like black's play is easier to understand.

I put it on lichess' analysis.

After e3, the engine's evaluation went from 0.6 to 0.0

On online games, it was played in 7.2k/192k games, and black won 53% of them.

As for masters, 40 out of 67k+ games have that position, and white won 9 and lost 16.

Personally, i think that the side who deviates from the principles of opening theory is just worse, and that is definelly the case here. No need to reinvent the wheel. That's why i like lichess opening explorer, it shows playerbase stats, giving a more human approach, instead of master's burnout one.

Given the player base and engine's analysis, black's main ideas are d5, d6 and O-O.

In resume, if your opponent leaves opening theory, you'll probably be better, but should forget opening theory as well and analyse the position

It got played by Caruana against Grischuk at the Berlin Candidates 2018 so of course it's a serious idea.

Imo, it's not an objectively good idea. Caruana either tryed to throw Grischuck off the book or had an interesting sharp line. He played one against Ding that blew my mind

It was the Candidates. They don't play trash at the Candidates, they prepare for months and know the opponents well in advance. Caruana also won't spoil a White game in a tournament he needed to win just to get out of the book.

Oh, really? Check out this game. Caruana played 9...e5 as black, and the engine does not really like it. On move 16, he was down two pawns and still playing instantly. FIDE Candidates 2020

Most people have looked at this game in details you know. And that doesn't mean turning on a weak engine at move 9.

What's that supposed to mean? I mean, honest question rlly. Fabi did go for a weaker move "just" to make Ding burn he's time

You are deeply mistaken.

Agree to disagree