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How does white cash in on the computer's 3 point advantage?

After 13. Qg3+, white is given a 2.91 point advtg by the computer, with the recommended move being 14. Kd1.

How does white cash in on the advtg though? Tried running it through stockfish and though its line was uncomfortable for black, it doesn't seem possible for white to exploit the pin against the rook and knight and actually pick up a piece.

en.lichess.org/aOQePdKn/white#26

Yes, ke7 was blacks recommended best move after kd1. After that I just don't really see whats justifying a 3 pt advtg for white in the position.

Actually it is not that easy to see this. Looking at some moves after ...Ke7 (the only move to not lose the piece), I would say that the advantage comes from two main factors:
-Black's king is stuck in the center, but he is by far not as safe as the White's king
-after the best move e5 the Bc8 is basically trapped.
So essentially Black is playing without his Bc8 and the rook on a8. Combined with a bad king and the easy development for the white pieces, Black is in trouble.
Not that it is easy to cash in, but the advantage seems justified.

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