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The first move is pretty easy to find, in my opinion- it simply has to be Rb4 if white is to have a prayer of winning this. White cannot get the white king off the first rank without the aid of his rook unless black’s rook has to pull other duty, nor can he push the h-pawn immediately to the 4th rank without allowing black to play Rc4 attacking the pawn and drawing immediately. Let’s just illustrate these two ideas with a short analysis, starting with the latter first:
1. h4? Rc4! (likely the only move)
2. Ra1
Here, of course, h5 is met by Rh4 followed by Rxh5. All black need do is repeat moves. Continuing:
2. …..Kb7
3. Rb1 Ka7 and what does white have other than another check from a1? A clear draw.
The other plan of bring the white rook to f1 or g1 and subsequently to f2 or g2 to allow the white king to escape the edge is simply too slow:
1. Rf1 Kb7 (escaping the edge)
2. Kg1 Kc7
And it should be clear that if white tries Rf2, black just exchanges and his king will beat white’s to h8. The same will happen with 1.Rg1/2.Rg2. Also, in this line, it does white no good to play a move like 2.Rf4 since the black king has already been allowed to escape the edge.
Now, let’s consider 1.Rb4:
1. Rb4
The idea behind this move is to delay the entry of the black king long enough to get the pawn advanced, and, as necessary, moving the white rook right and forward to protect the advancing pawn at each step, if the black king advances on white’s rook- eventually, the pawn will queen, or black’s rook will have to leave rank 2. First, let’s look at simple waiting rook moves for black:
1. …..Ra2
2. h4 Rf2
3. h5 Rf8
Here, Rf6 nor Rf5 hold: [3. …Rf6 4.Rh4 Rh6 5.Kg2 Kb7 6.Kg3 Kc6 7.Kg4 Kd6 (7. …Kd5 8.Kg5 Re6 9.h6 Re5 10.Kg6 Re6 11.Kf7 Rd6 12.h7+-) 8.Kg5 Re6 9.h6 Re5 10.Kf4! Re8 11.h7 Rh8 12.Kf5 Ke7 13.Kg6 Kf8 14.Kf6 Ke8 15.Kg7+-]; or [3. …Rf5 4.Rh4 Kb7 5.h6 Rf8 6.h7 Rh8 7.Kg2 Kc7 8.Kg3 Kd7 9.Kg4 Ke7 10.Kg5 Kf7 11.Kh6! Ra8 (11. …Kf8 12.Kg6+-) 12.Rf4! Ke6 13.Kg6 Ke5 14.Rh4 Ra6 15.Kg5+-]. Basically, in these two variations, the black king is just one move too late to support the rook blocking the pawn from either h8, or h6. Continuing:
4. h6
Here, white could play Kh2/g2, or Rh4, but it won’t change the move counts in black’s favor since they will all transpose to the same endings. Continuing:
4. …..Rh8
Here, king moves just lose more tempi, and the rook check is no good since the king attacks from g2 and covers h1. Continuing:
5. Rh4 Kb7
6. Kg2
The first critical point after the first move of white’s. On 6.h7, the black king beats white to the corner and double attacks the pawn. There is no time to waste on further pawn advances until the white king can support it. Continuing:
6. …..Kc7
7. Kg3 Kd7
8. Kg4 Ke7
9. Kh5
I think Kg5 wins too, but is one move longer due to an additional check from black’s rook, but the position eventually transposes anyway. Continuing:
9. …..Ra8
Here, moves like Kf7 and Kf6 lose to Rf4+: [9. …Kf7 10.Rf4 Kg8 11.Ra4! Kf7 (11. …Kh7 12.Ra7 Kg8 13.Kg6; or 11. …Kf8 12.Ra8+-) 12.Ra7 Kf6 13.h7 Re8 14.Kh6 Rc8 15.Ra1 Rb8 16.Rf1 Ke6 17.Kg6 Ke5 18.Rh1 Rb6 19.Kg5+-]. Cont.:
10.Rf4
Here, h7 probably wins, but seems to allow the black king to get more involved, and I see no reason to allow him any closer. Continuing:
10. ….Rf8 (Ra5 11.Kg6 Ra6 12.Kg7)
11.h7!
I tried for a while to avoid a queen vs rook ending (starting at move 10), but I think black can force it one way or another in this line, but I am not sure I have found the cleanest ending, but I am tired and want to get this done before I sleep. Continuing:
11. ….Rf4 (nothing better)
12.h8Q with a winning Q vs R.
The truth is that I see nothing better than this defense for black. It is clear that trying to attack the rook with the king at moves 1 through 3 is just going to cost tempi, and change nothing for the better- so 1.Rb4 wins outright.
Where are the answers?
From twitter @StephenWillms
And thanks for everything you do in chess
1.Rb3 looks promising for White, with the plan 2.h4 and 3.Rh3- this should be winning.
i think, white can win with something like
1. Rb4 Rc5
2. Kg2 Rh5
3. h4 Ka6
4. Kg3 Ka5
5. Kg4 Rh8
6. Rf4 Rg8+
7. Kf3 Rh8
8. Rg5 Kb6
9. h5 Kc6
10.Kg4 Kd6
11.Rg6+ Ke7
12.Kg5 Kf7
13.h6 Ra8
14.h7 Ra5+
15.Kh6 Ra8
16.Rg7+ Kf6
17.Rg8 Ra5
18.h8Q+
of course, i don´t know, if this is the best variation.
greets, jan
This is way too deep for me too analyze right now if I could even do it.
The best chances appear to come from Rb3 or Rb4.
A fair question is, why does Rb4 win when Rb3 doesn’t? It is all in the move count:
1. Rb3 Ra2 (waiting for white)
2. h4 Ra4
3. Rh3 Kb7
And, now, white has a choice of starting to bring the king forward, or push the pawn. We will look at both, but neither can work:
4. h5 Kc7
Here, black could play Ra8 immediately- it won’t matter, it will just be a transposition to what follows:
5. h6 Ra8 (forced, of course)
6. h7 Rh8 (forced)
Now, count the moves. It takes black 4 moves to reach g7 to apply the double attack on h7 to win the pawn. Moving first from this position, in 4 moves white can only reach g5- so the white pawn falls.
If, instead, at move 6 white left the pawn at h6 and started bringing the king forward, it won’t make any winning difference:
6. Kg2 Kd6
Now, count the moves. Any line in which white plays h7 will be a transposition to the previous line arising from 6.h7 after black blocks with Rh8, so we can ignore those. Any rook checks from white just lose tempi as the black king keeps coming kingside. It takes black 4 moves to bring the king to the g-file at g8 or g6, then the rook to h8. It takes white, moving first, three moves to reach rank five, but the black king at f6 will force white’s king to h5, or the black king can head directly to h8. I already know this type of position is a draw, but let’s play it out:
7. Kg3 Ke6 (Ke7 same)
8. Kg4 Kf7
Here, Kf6 also draws: [8. …Kf6 9.Kh5 Kf7 10.Rg3 Ra5 11.Kh4 Ra4 12.Kh3 Ra8 and white can make no progress]. Continuing:
9. Kg5 Ra5
10.Kf4 Ra4
11.Ke5 Ra5
12.Kd4 Ra8
And, having allowed white to attempt to walk the rook down just enough to lure the king away, the rook returns to a8 in order to come to h8 and win the pawn with Kg6. The point is that walking the rook down in this manner only works if the pawn is on the seventh rank and queen on the next move.
Back at move 4, white had the option of leaving the pawn at h4, and bringing the king up immediately, but this will still draw:
4. Kg2 Kc7 (heading for g/h-file)
5. Kg3
If h5, then black’s Kd7 is just a transposition to the lines previously discussed. Kg3, of course is immediately drawn by the forced exchange of rooks:
5. …..Ra3
6. Kg4 Rh3 (only move, now)
7. Kh3 Kd7
And, we can just count the moves here: Black is 3 moves from g8 to control h8, while White is 4 moves from g7 to prevent black’s plan. Let’s finish playing it out:
8. Kg4 Ke7
9. Kg5 Kf7
10.Kh6
Of course, h5 is just met by Kg7 with a clear draw. Continuing:
10. ….Kg8 and white can’t keep the black king out of h8.
Now, to finish, I would like to show the two lines 1.Rb4 and 1.Rb3 side by side to show where white gained that critical tempo to win with the first, but draw with the second:
1. Rb4 Ra2 1. Rb3 Ra2
2. h4 Rf2 2. h4 Ra4
3. h5 Rf8 3. Rh3 Kb7
4. h6 Rh8 4. h5 Kc7
5. Rh4 Kb7 5. h6 Ra8
Compare the two lines- in both, the pawn is on h6, the white rook is behind the pawn supporting it, and the white king is still on h1. However, in the second one, the black king has already reached c7 whereas in the first, he is only on b7. The difference is that white was able to keep the rook on the b-file longer. In this position, it was more important to delay black’s king than it is to delay the rook’s advance to h8- it is important to keep the black king out of the corner, and only 1.Rb4 allows white the time to do so.
In general, you should do a lot of move counting in endings like this. When you have the time to think, finding the lines that give you more tempi on your opponent can almost always be a benefit to you in pawn endings, with or without pieces on the board.
1. Rb3 doesn’t seem to work. 1…Ra2 2. h4 Ra4 3. Rh3 Kb7 4. h5 Ra8 and black’s King gets to g7 before White’s.
Also 1. Rg1 intending Rg2-h2 suffers from the same flaw. It seems to be necessary to keep the Black K on the a-file as long as possible.
Rb4 !! (only) wins. If Black moves, Ka6 or Ra2 or Rd2 or Re2 draws.
1.R-b4 wins
1…… Ka6
2. h4 Ka5
3. Rb3 Ka4
4. Rh3 and White wins!
What about Rb4? seems to win a tempo since white’s pawn will go to h4 and h5
Thanks for this one Susan. I have have been doing about half the puzzles on here for about a year or so. For me this is the most instructive puzzle so far and I think I will remember the point when I play OTB.
Rb3 and Rb4 were the obvious choices. The tempo difference was very instructive 🙂