Notice that black's last check is pushing the white king one row away from their passed e-pawn. Once black promotes the b-pawn, white will have to give up the rook for it. After which white's king is simply not in position to cover the advance of the e-pawn and therefore additional tempi will have to be spent with king moves to try and reach ...
In short, the plan you proposed is possible, but it is just too slow, even if black allows it, which is not mandatory. If black permits it, here is a simple win that, although I checked it with a computer, I could see it in my head fairly easily, which means those two could see it that much more easily.
[FEN "8/8/1R4p1/4P1P1/2r2K1p/7P/1p6/2k5 w - - 0 1"]
Let's note the following: 1.Rxc2 and 1.Kxf4 and 1.Rd8+ are equally good, since they all draw. If we ignore 1.Rd8+ for now, 1.Rxc2 is clearly at least as good as 1.Kxf4 in the position, since it drives black's king back one square, meaning that black will at some point have to 'waste' a move with the king to get to white's remaining pawns (the option of 1.Rd8+...
My plan was to keep the Black rook on the 5th or 4th rank to cutoff
the White king and advance the h and g pawns. But then what?
Your plan is a bad one.
The general rule in rook and pawn endgames is:
Your king protects your pawns
Your rook attacks your opponent's pawns
You can add another one:
Push your passed pawns
As you can see your passed pawns are ...
This answer is intended to expand upon my comments, and give some concrete lines. Let's discuss the position as I (mistakenly) first thought it was presented:
[fen "R7/6p1/P3p1k1/7p/8/6PP/r7/4K3 w - - 0 1"]
This position is a draw, no matter who is to move. If White doesn't play a7, then Black's rook will have the option to pick off one of White's ...
After Rxc2 Kxc2 Kxf4 we reach the below position, which is a tablebase draw.
The plan for White is really simple: queen the h-pawn (White can give up the rest of the pawns).
Black king is too far away to help, that is why it is a draw (there are winning techniques for Black, but they require kings to be in close proximity).
Feel free to test my claims with ...
So just why is that f7-g6-h5 setup so important?
Compare the two pawn structures below, one on the kingside where Black has achieved the f7-g6-h5 structure and one on the queenside where White has achieved an advanced equivalent pawn structure.
[FEN "8/p4p2/Pp3Pp1/1Pp3Pp/2P4P/8/8/8 b - - 0 23"]
Now imagine kings on the board and one minor piece, say a ...
While it may appear that White can whisk around Black's rook and promote, there is a indeed problem that you have missed: Black can promote first!
White's king is currently in check from Black's rook, so the monarch must be moved to either the f3 or e3, cutting the king off from half of the board.
Since White lost a tempo moving their king, Black now ...
With such an overwhelming pawn advantage it should be easy enough to win.
What you said is definitely a good plan. You can push h5 and g5 to push the king back.
[fen "8/R4ppp/4pk2/1r6/8/5K2/6PP/8 b - - 4 38"]
1... h5 2. Ra4 g5 3. h3 Ke5 4. Ra2 f5
We can see here that black has an easy win. g4 is coming and once the pawns are traded, Black's two ...
They may as well try, since Q vs R is extremely difficult to win (even disregarding skewer tactics). The example of RB vs R is a great similar example, as it is a theoretical draw, but extraordinarily difficult to draw. There are numerous examples of top grandmasters being unable to convert Q vs R. As to a computer vs human- this was tested in 1978 in a ...
Is it possible to win this endgame(either white or black)?
Of course either black or white could win this endgame. All it takes is one blunder by either side.
If what you meant to ask if either side can force a win, then the answer is "No". Black is a pawn up but white has a much more active rook and the black king is cut off on one side of the ...
This is a very common rook endgame at higher levels, and it is considered very important to know how to defend it at the 2000-rating level and above, and maybe even a little lower.
The answer as to why the f7-g6-h5 formation is so important is that it combines a relatively safe pawn structure for hiding the black king, and it makes it almost impossible with ...
After the move 43... Rc2, White should have played 44. Kh3 instead of 44. Kxg3, and played the below sequence.
[FEN "5k2/8/8/4p3/R3P1PP/6p1/2r3K1/8 w - - 0 1"]
1. Kh3 g2 2. Ra1 Re2 3. Rg1 Rxe4 4. h5 Re3+ 5. Kxg2
There is a mate in 39 moves afterward according to the Lomonosov tablebases.
Imagine there'd be no other pawns on the board, except for the b2 pawn and the e5 pawn. Then ask yourself the question: is black's position won? If the answer is yes, there is no need for calculation, right?
The answer is yes, because of an elementary (yet crucial) manoeuvre: keeping the black rook on the fourth rank, thereby cutting off the enemy king. ...
The position very much looks to be a draw. The white king can't advance easily as the black rook stays on the third rank. All the maneuvers to bring back the white rook to help advance don't seem to work as both f4 and d4 can be weak. Furthermore the black king can stay on the d file to cover the e7 and c7 square while always having Kd7 if White attacks the ...
The old joke is "all pawn endings are wins, all rook endings are draws, all queen endings are draws by perpetual check".
Black is better. In the old days, before a possible adjournment, the director would ask both players what they were aiming for. If both players said they were playing for a draw, the director might settle things at once.
In this ...