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I am tempted to play Rf2.
If Rh7+, Kg5, followed by pushing the king till rook can’t give any more checks from 7th rank.
However, I can’t do a detailed analysis like some of the regulars here, so maybe I am missing something important.
1.Rf2 cuts off black K from f file. 1…. Rf7 challenging the R fails after 2.Rxf7 Kxf7 3. Kh5 diagonal opposition wins.
But black R will operate from behind to give more resistance. like 3…. Rh7+ 4.Kg6 Rh1
Yes, you should play 1.Rf2 almost without having to think about it. The importance of keeping the black king from reaching the corner without giving up his rook is paramount- if he does with the rooks still on the board, it will be a draw. As Anup ably points out the win now with the rooks on the board, really, the only hanging issue is what happens if black uses his rook as a shield, but that leads to a won K+P vs K ending:
1. Rf2!
This is definitely the only way to win for white- if black is allowed to play Kf7 or Kf8, the rook ending is a technical draw- though black would have to play carefully, it isn’t a difficult draw in my opinion- a much easier draw than, for example, the one from yesterday! Continuing:
1. ………….Rf7 (to allow Kf8)
2. Rf7!
I put the exclamation point because this is also the only way to win. Should white delay the exchange of rooks by playing 2.Rf5, black will capture at f5 and the resulting K+P vs K ending is also a technical draw. You gotta learn and remember your basic K+P vs K endings! They form a good basis for understanding the issues in more complex situations. Continuing:
2. ………….Kf7
3. Kh5!
Another only move for white to win. Takes the diagonal opposition, and gets the king out in front of the pawn. Had white played 3.Kg5, black takes the direct opposition with Kg7 to set up an almost trivial draw. Since I covered this exact ending a few days back, I will leave the rest as an exercise for those who feel less at home with such endings.
And I see Prof Bhat has already covered 1. …Rf7 while I was writing.
It’s also necessary to understand what happens after 1. Rf2 Rh7+
2. Kg3 is a big mistake, Black plays 2…Rf7 and now the exchange allows Black’s K to get in front of the pawn without allowing white to gain the opposition, for a book draw. Or White can decline to exchange Rooks, and Black’s K gets to g8/h8 with the rooks still on the board, which also draws.
Correct is 2. Kg5 Rg7+ 3. Kh5 Rh7+ 4. Kg6 and Black has no way to hold from here. Black can also try 2…Rh8 but White just plays 3. Rf6 and has an answer for anything that Black may try.