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My own struggle with Rook versus Two Knights. I had no idea what I was doing. :)
You should've taken the rook with the fork instead of the bishop. I like my chances with single knight vs single bishop much better.
Finally, i'm posting this game. The whole thing is annotated -something i try to do with all my games-, but really, my interest is on the endgame position. Feel free to comment. I don't have the Fritz lines, but i do remember two key points Fritz made, and i'll note them in the annotations. Thanks again for comments.
With Qe2 and d3 white choses one of the most boring lines of the Petrov. But still how it went and if you are good in the endgame... I think after 29... Nfxd4 with the other Knight thus.. then black is allright.
Knight c6 is the best, because it limits rook activity on backrank and seventh rank, so covering e7 and d8 squares and protecting the a7 pawn, this will make it hard for to attack your pawns; Your other knight can come to e7, they protect and coordinated, this will allow you to advance the king in the center. It be impossible to lose this endgame but loose knights can be a target.
You lose because you fail to protect essential squares, one them being a e5, e7 d8 squares, knights need the aid of the king and so you can protect and centralize your king, so setup will be knight onn c6 and e7 and king going to f6. You lost your d5 pawn in two moves thse squares pointed out weren't cover by you knights. Endgame you must make a plan and where you going to place your pieces. This one I immediate realize you must limit the rook scope.