When following the ongoing 2024 FIDE Candidates Tournament, I notice that Black often plays the Two Knights Defense in response to the Italian, but White goes for a quiet Giuoco Piano line instead of 4. Ng5. Why?
Example games are Firouzja vs. Nakamura, Vidit vs. Gukesh, Vidit vs. Nakamura.
Against a well-prepared player, 4.Ng5 generally isn't as challenging as 4.d3. With 4.Ng5, if Black knows his theory in and out, White can't hope for an advantage. But with 4.d3, Black can know his theory and get a perfectly good game, but White still retains long-term chances to play for a win (it's just a normal game). That isn't to say 4.Ng5 doesn't have its place, and it can be quite dangerous if you play it occasionally. I myself used it in the final round of a tournament 2 years ago to beat an FM in 17 moves! And recently, I lost on the Black side of it to a kid rated many hundreds of points lower than me in a rapid game...
4.Ng5 was even played in Firouzja-Caruana (Sinquefield Cup, Nov 2023), which was a long time control. To me at least, it seemed this game put the move a bit more into the current fashion, and I've noticed myself facing 4.Ng5 as Black more often on lichess.
In recent years, White players have struggled to play for advantage in the 4.Ng5 lines. The main line goes:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6
In olden times people tried 8. Be2 here, however, Black appears to have excellent compensation for the pawn after for example:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6 8. Be2 h6 9. Nf3 e4 10. Ne5 Bc5
Because of this, in the last 10-15 years the move 8. Bd3 has become more fashionable. The idea being, to be able to retreat the knight to e4 after a possible h6 kick.
However, among other Black options, 11... f5 has shown itself to give Black very good play in this variation:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6 8. Bd3 Nd5 9. Nf3 Bd6 10. O-O O-O 11. Re1 f5! 12. Nxe5 Qf6 13. Nf3 g5 14. g3 f4 15. Nc3 fxg3 16. hxg3 Qxf3 17. Qxf3 Rxf3 18. Be4 Rf7 19. Nxd5 cxd5 20. Bxd5 Bb7 21.Bxf7+ Kxf7 22. d4 g4
I have gotten this endgame with either colour in some online games and from my experience it is White who has to be careful and who should look to make a draw, rather than Black. So this is no good to play for advantage with White.
Finally, there is one more thing White can try:
[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6 8. Bd3 Nd5 9. Nf3 Bd6 10. O-O O-O 11. Re1 f5! 12. Nxe5 Qf6 13. Nf3 g5 14. c4! Nf4 15. Bf1 g4 16. d4 gxf3 17. Qxf3
In the resulting position, White has three pawns for a piece and the position is an absolute mess. Either side can lose very quickly if they do not know the theory, however, as far as I am aware, it is supposed to be roughly equal. At the lower levels this is likely a good attempt. But at the top level everyone playing 3...Nf6 will be aware of the theory here so White is unlikely to have much success unless they can find a fresh idea.
Why is 4. Ng5 in the Two Knights not common in current (2024) top-level chess?
You see Nakamura offering it. He is know as a tactical attacking player, so you shouldn't assume top-players avoid Ng5 in general, but certainly against Nakamura they are going to choose positional ideas instead of letting him sac a pawn and attack.
In general, the "Slow Two Knights" still offers White a chance to an enduring slight advantage so players choose to keep two outcomes of win or draw this way. Of course Vidit still lost in the game you provided but the strategy is win/draw as white...
Additionally, if the White player isn't expecting a two-knights then he will avoid it. Only if he knows it is very likely then he might prepare something.
