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Flashy Greek gifts gone wrong

One sac too far. Can you see why what I played here was wrong, and why white should have lost this game ?
Had to play Ke2 or 0-0-0 before the sac on g7 :) nice try! GG.
15... Rg8 16. Rg1+ Kf8 17. Qh6+ Ke7 18. Qh4+... Kd7!

So black must play 15... Nxe5 16. dxe5 first (16. Rg1+ Ng6), and then the above, I guess ?

... ah no. Oh well.
I too was thinking 15... Rg8, but SF refuted it and showed me the solution.
14.Rxg7+?? was a blunder. Stockfish gives a peculiar way how black can defend. Black can play 15...Rfe8! (Both Rfg8 and Rfh8 seem inferior), then 16.Rg1+ Kf8 17.Qh6+ Ke7 18.Qg5+! Nf6!! (To avoid perpetual) 19.exf6+ Kd6 and white is a rook down for not enough compensation.
It's kind of amazing the quiet 14. O-O-O (or Kd2/Ke2) wins.

Of course 10... Nxe5? is absurd.
Stockfish gives the highest evalution for 14.Kd2, then O-O-O and then Ke2. I don't see why Kd2 is evaluated +15.5 compared to +12 for O-O-O. Of course it's both winning, but why would Kd2 be better?
The only way I can think that the evaluation is higher for Kd2 than 0-0-0 is because centring your king for a potential endgame is a slightly better move. Obviously we assume that black should resign in that position, but the computer continues to think ahead because it doesn't understand those kinds of nuances. It continues to evaluate based on white's winning chances, instead of how bad black's position is.
Winning is winning, there is no more or less so 14 Kd2, 14 o-o-o, and 14 Ke2 are equivalent.
This was a 3+0 game, but both players had 2 minutes left at the end. So it is like if it were 1+0 bullet.
It is remarkable that white played a tempo 14 Rxg7+ followed by the quiet 15 Kd2. I would never sacrifice 14 Rxg7+ without analysis and I would play the safe 14 o-o-o and then calculate if 15 Rxg7+ wins or not.
Another rook sac, now at the other side of the board.
Stockfish gives it two question marks, even though this one turned out to be clearly winning :

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