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Sometimes World Champions Get Lucky

This was a recent game at the Champions Showdown. Carlsen has just played 46. Bf2. How should black have responded?

8/R3bk2/3p4/2pPp3/2P2p1p/3P1P1r/4KB2/8 b - - 0 1

At first sight I thougt of Rh2.

After a lot of thinking here are the variations I thought about:1... Rh2! 2.Kf1 h3 with the idea of pushing the h-pawn.And on any other king move h3 can be played.On moves like Ra8 , with the idea of stopping the passed h-pawn by playing Rh8,so:1... Rh2! 2.Ra8 h3 3.Rh8?(Better is Ra7) Bf6! 4.Rh5(Rh7+ loses to Kg6) Kg6!!(The rook is trapped!)5.resigns(Rxh3 or some other worse move is forced , actually any other move may led to a mate in 15 ) so,black was acctually winning here.Anyways the main line is (according to me):1... Rh2! 2.Kf1 h3 3.Kg1 Rg2+ 4.Kf1(Kh2 loses severly) and now finnaly my favorite part ( THE ROOOOK SWINGERRRRR!) Rg8(With the idea of briging the rook to h8 and push the pawn ahead)5.Bg1(good move , trying to play Bh2 to stop Rh8 and h2) Now another briliant move: Rg3(forcing the king to move away to protect the pawn on f3 and the common move Bf2 trying to get a draw here miserabely fails to :h2 and it will be a mate in 25-30 perhaps)and know 6.Kf2 Rg2+ 7.Kf1 Rd2 and white has had enough he is in a lost endgame and cannot protect his pawns and if he does the h2 pawn is unnstoppable 8. Resigns!!!! 0-1 thay is what I see his king is not as safe as black's king and white bishop will be stuck forever to stop the h2 move and black's bishop is quite good black's rook is much more active and black's pawns are quite nicely protected(except the pawn on h3 which cannot be attacked).

Nice game though..........!!!!!!!!!!!!!!!

By the way 1 . Bf2 Rh1 (is also winning )

I saw the first move quickly too. I liked this variation.

2.d4 exd4
3.Kf1 h3
4.Bh4 Rh1+
5.Ke2 Rb1
6.Rxe7+ Kg6
7.Re6+ Kh5
8.Bf2 h2
9.Re8 h1=Q
10.Rh8+ Kg5
11.Rxh1 Rxh1
12.Kd3 Rh2
13.Be1 Ra2
14.Bd2 Kf5
15.Be1 Ra3+
16.Ke2 d3+
17.Kd2 Ke5
18.Bh4 Kd4
19.Bf6+ Kxc4
20.Ke1 Kb3
21.Bg5 Kc2
22.Bxf4 Ra1+
23.Kf2 d2
24.Bxd2 Kxd2

It's a good puzzle

Arein, 1. ....Rh1 probably wins, too, and in a similar way eventually, however, it gives white time to play 2.Bxc5 which is probably the move that Liren was worried about when he played 1. ....Kf6? which led to a draw.