rg2+,kh8,rh2+,kg8,be6+ and thats that.
Carlsen losing?

Can someone explain move 50 where Carlsen sacrificed his rook?
Well, he's either losing the exchange or his bishop.
Doesn't sac the piece, the check is just an intermezzo.
So moves 46-50 are blunders of both sides?
No? Neither could avoid giving up the exchange.

Can someone explain move 50 where Carlsen sacrificed his rook?
Well, he's either losing the exchange or his bishop.
Doesn't sac the piece, the check is just an intermezzo.
So moves 46-50 are blunders of both sides?
Of course not. GM chess isn't backyard baby chess, maybe 1 in a billion moves they miss something so easy as a fork.
Also, I'm sure this whole sequence was seen many moves ahead. They're spending their time evaluating the winning chances of the final position (possibly many moves after the tactics have cleared). They're not sitting there like amateurs do and thinking "oh crap, my rook is pinned, how am I going to get out of this... oh wow, I think I can sacrifice a pawn!"
No... not at all... lol.

Can someone explain move 50 where Carlsen sacrificed his rook?
Well, he's either losing the exchange or his bishop.
Doesn't sac the piece, the check is just an intermezzo.
So moves 46-50 are blunders of both sides?
Of course not. GM chess isn't backyard baby chess, maybe 1 in a billion moves they miss something so easy as a fork.
Also, I'm sure this whole sequence was seen many moves ahead. They're spending their time evaluating the winning chances of the final position (possibly many moves after the tactics have cleared). They're not sitting there like amateurs do and thinking "oh crap, my rook is pinned, how am I going to get out of this... oh wow, I think I can sacrifice a pawn!"
No... not at all... lol.
I was pretty sure I'm missing something. Thanks!

Can someone explain move 50 where Carlsen sacrificed his rook?
Without looking specifically at the moves, sometimes it is better to sacrifice a piece and keep the initiative and/or get a better position, than to fight to keep a material advantage, then end up losing the initiative and positional superiority, only to in turn, surrender a piece. If Makhail Tal was never able to prove material advantage wasn't always important, I am not sure who ever could.

Leave it to Carlsen to sqeeze out a win from an op-colored bishop ending with even material.
How many of us would have offered the draw, and went back to our rooms?

Leave it to Carlsen to sqeeze out a win from an op-colored bishop ending with even material.
How many of us would have offered the draw, and went back to our rooms?
I probably would have.

I probably would have tried too hard to lose, then won.
I've never bothered to try reverse psychology on my opponents....they always catch my blunders...
Yup, over. 1-0