According to Houdini and Chess.com’s computer analysis, I clearly didn't understand the position after 1.d4 Nf6 2.Nc3 d5 3.e3 Nc6 4.Bd3. I played 4...Bg4(?!), but both chess engines were quite clear that THE move to play was 4...e5.

Why is 4…e5 seen as the best move? How does the exchange of center pawns after 5.dxe5 Nxe5 favor Black?

My idea was to play 4...Bg4(?!) first, in order to get my light squared bishop outside of the future pawn chain of f7, e6, d5. After 4…Bg4, Houdini shows 5.f3 as strong,  kicking Bg4. But 5.f3 looks wrong to me, perhaps weakening White’s castled position, with Black given the chance to open the g-file in some variations after White castles with …something x f3, exposing White’s king.

Would you play 5.f3 after Black plays 4…Bg4?

Notice how black has a pawn on the fifth rank and white only has a pawn on the third rank? Black will have a bit more space to maneuver. White's dark squared bishop is also looking kind of lame staring at his own pawn and a knight. That is why black has a slight advantage.

5. f3 kicks the bishop back and looks to get some more space since white is losing some space in the centre. I personally wouldn't play it so I guess I don't fully understand the benefits vs the risks of the hole and more exposed king.

Play in the center is almost always stronger... but this is not so important : 4...Bg4 is playable and I think you rely too much on engine's analysis, which may be confusing for you.

The game wasn't won or lost at this point, was it ?

I won the game by spotting a few simple tactics, not by placing my pawns on the best squares as seen by chess engines.

I just found it interesting how strongly the chess engines said to play 4...e5. It got my positional chess mind thinking.

Oh...you sent me a link with a picture of Yoda and a great article. Thank you!

"Pawn break in the center, stronger is !"