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Saddest Ending

I think you played well against someone significantly higher rated than you.
Nice game! 15. Rh1 would have been a killer move! The Black Queen would only have g2 and then 16. Bxh7+ Kh8 17. Be4+ and your winning the Black Queen!
First thought :
Even if you don't study openings, when you play 2.Nf3, your purpose is to attack the e5 pawn. When Black replies 2...Bc5, the only consistent follow-up is 3.Nxe5. If you don't feel like playing this capture, then find an alternative to 2.Nf3 (or to 1.e4).

For your information, even if Black gets the pawn back after 3.Nxe5 Qe7 4.Nf3 Qxe4+, your position is close to winning because 5.Be2 Bb6 6.0-0 threatens Re1 and a bishop move (pinning the queen on the black king). Black needs to move his queen immediately again, and you have a big advantage in development, which is the Holy Grail of the 1.e4 player. You don't need to see this during the course of the game, of course, but during analysis it's useful to notice it for the next opportunity.

Second thought :
With castles on opposite sides, you aim at getting your rooks on the same files as the ennemy King. Here Black cooperates with Qxg2 and later Qxh2. Even if you don't notice the tactics, you can play 15.Rh1 Qg2 16.Rdg1 purely on general grounds (play both rooks to the ideal open files). No computation is required, play it and get the new position on the board. After 16...Qf3, the most consistent move is 17.Bxh7+, using the accumulated firepower to destroy the black king's pawn wall. Again, don't compute anything, simply play it. After 17...Kh8 (forced), the battery (Rh1,Bh7) is in place for a discovered check. Is there a valuable target on a white square (your bishop on h7 is a white square bishop) ? Yes : the black queen on f3 ! You win it with 18.Be4+, and so on.

Tactical play is not necessarily linked with complicated computations. Here it is based on a sequence of simple visual patterns : rooks on open files, exposing the king, a battery for a discovered check, a target on a white square.

Third thought :
What is the common issue between the first and second theme ? Consistency ! A move like Nf3 or Bd3 is a direct attacking move, you aim at a target (e5 or h7). Grab the target if the opponent does not defend it (Nxe5). Attack the target with more pieces if it is poorly defended (Rh1, Bxh7+). Otherwise what was the point of the attacking move ?

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