Is there a reason for MC's second move? In this game, Magnus Carlsen made an unusual poor first move Nh3. Presumably, it was to throw off his opponent, especially since the game was under fast time controls, so that is understandable. But I cannot understand why he played another poor move after that. Why f4? Why not d4 or g3 (with their obvious benefits)? Is 1. Nh3 Nh6 so frequently used that he needs to make two poor moves in a row to make sure his opponent has no preparation? More concretely, is there any potential positional gain by f4? As far as I can tell, f4 only serves to expose the king and delay development of all the pieces...

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1. Nh3 Nh6 2. f4 d5 3. Nf2 Ng4 4. e3 Nxf2 5. Kxf2 c5 6. b3 Nc6 7. Bb5 Bd7 8. Bb2 a6 9. Bd3 Qc7 10. Nc3 e6 11. Qh5 Be7 12. Rhf1 Bf6 13. Kg1 Nb4 14. Rac1 Nxa2 15. Rce1 Nb4 16. f5 e5 17. e4 c4 18. Nxd5 Nxd5 19. Bxc4 Nb4 20. c3 Nc6 21. Qxf7+ Kd8 22. Ba3 Be8 23. Qd5+ Qd7 24. Bd6 Be7 25. Bxe7+ Kxe7 26. Qc5+ Qd6 27. Qb6 Bd7 28. d4 Nd8 29. Qa5 Nc6 30. Qa2 Kd8 31. Rd1 Kc7 32. Qf2 Rad8 33. b4 Rhf8 34. b5 axb5 35. Bxb5 g6 36. f6 Kb8 37. Bc4 Bc8 38. Bd5 Be6 39. Bxe6 Qxe6 40. d5 Qd6 41. Ra1 Kc7 42. dxc6 Qxc6 43. Ra5 Kb8 44. Qa7+
2.f4 is a poor move, just like 1.Nh3 was. 1.Nh3 puts White at roughly -0.50; then, after 1...Nh6 White comes back to around 0.3. If Carlsen had played 2.d4, like you said, he would have maintained this evaluation. Instead, 2.f4 brings things down to -0.4ish.

A reason behind 2.f4 is to bring the knight back to f2, but it's still a bad move. As I mentioned in the previous question on this game, Carlsen was clearly just having fun in an online rapid game. There was no deep strategy involved. If he wanted to play some deceptive variation with the sole intention of winning, you would have seen something far more impressive than this from the world champion.

If you want to analyze Carlsen's games in order to learn from them, please take a look at ones he's played in serious super-GM tournaments. Trying to glean knowledge from an online game in the PRO league isn't worthwhile (especially when 1.Nh3 is the first move).