White to move. Is this a win or draw for white?
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1. Ra1
… Kb8 2. Bd6+ wins the rook
… Rh6+ 2. Bd6 wins the exchange leaving a won endgame
… Kd8 2. Ra8#
It isn’t quite this easy. Lenny below is quite right- 1. …Rb2 complicates the issue.
It is won, and Ra1 isn’t the only move that wins here, and I am not even sure it is the shortest way to win.
Win!
… Kb8 2. Bd6+ Kc8 3. Ra8# (why win a rook when it’s mate?)
But what happens if Ra1 is answered with Rb2? If Bd6, Rc2+, and the Black King escapes for a while (doesn’t it?).
1.Ra1 Rb2
2.Ra7 Rb1
3.Rc7+ Kd8 (3…Kb8 4.Re7)
4.Re7 Rc1
5.Re2 and another zugswang
6…. Rc4 (6…Rc3 7.Rf2 wins)
7.Rd2+ Ke8 (7…Kc8 8.Rf2 wins)
7.Rf2 wins
The other Ra1 lines were given by Tiger Karthik.
1.Rf1 Rd2 2.Ra1 Rb2 and 1.Rg1 Rd2 2.Ra1 Rb2
transpose to the Ra1 line.
You have the elements of the essential pattern, but you underutilize the bishop- it can be used to shorten the path in all the variations. Also, you don’t find the most tenacious defenses for black in the line outlined in your comment- for example, what if black plays 4. …Rd1? It is possible to use the mating threats to drive the black rook off of the 1st and 2nd ranks earlier. This aids by making key squares like a3, e3, b4, and d4 unavailable when the bishop has returned to c5- in other words, the rook is hindered in the attempts at preventing mate by shielding the king when he is checked by the rook on the 8th rank. So, at move 3 in your line, white missed an opportunity to significantly shorten the path by playing Rc7+ too early.
Yes, I thought 4…Rd1 5.Re2 followed by Bb6+ would work but 5…Kc8 removes the initiative of the check.
This arrangement of pieces is always a forced win when white is to move- and it doesn’t matter where on the board it occurs. So, the question is, can the method of bringing it home to victory be effectively described so that one can work it through when needed?
So, the first thing to note is that the bishop on c6 covers the squares a7 and e7, making the black king’s escape much more difficult. So white is going to repeatedly threaten mates from the flanks with the rook. Now white can threaten this immediately with the following moves: Ra1, Re1, Rf1, and Rg1. I have decided to only discuss Re1 first because it is the one move of the four that fails to win, and I think I can show the average player why it fails, and they can then describe the winning method from the remains.
1. Re1? Rh6
This makes perfect sense from a defensive point of view- it the only check available to black, and to keep the black king on the edge of the board, white must block with the bishop:
2. Bd6
Here, black is given two options- play Rh8 preventing Re8#, or move the king. Even a patzer like me can see the problem with Rh8, so black has an easy defense to find:
2. …………..Kd8! (if 2. …Rh8, then 3.Ra1 is mate on the next move)
And now I hope everyone can see the problem white has- the black king is now going to escape via e8 and f7 if white tries another flanking maneuver like 3.Ra1/b1 or Rg1. What is really left is the attempt to mate with 3.Rf1 and Rf8 since the bishop has f8 covered:
3. Rf1 Re6!
Again, this is an easy defense to find since black’s options are constrained anyway, and Rh8 again loses to Ra1 (or Rb1) because, even if black then plays Ke8, he will lose the rook on h8 to a skewer. So, can white find productive move now? There are really only three options here- Kd5 attacking the rook, Ra1/b1, and Rf7. On 4.Kd5, black will just move the rook to a square like g6 since the d7 square is open to the black king to prevent the mate, forcing white to again put the king on c6. So let’s look at the other two options:
4. Ra1 Ke8
Again, circumstances make black’s defense easy to find- now white can prevent Kf7 and the escape of the edge with Ra7, but white’s king is now way out of place to enforce any kind of mate on that edge. Indeed, white will never again be able to force a winning position:
5. Ra7 Rg6
I am not 100% sure, but I think this is drawn on any non-suicide move of the rook or Kd8- i.e. moves like Rf6/h6/e4/e3/e2/e1. I don’t see how any of those moves of the rook allow white to trap the black king again. Continuing:
6. Kd5
What else is there? White must try to get his king in front of the black king again so that mate can be threatened. Continuing:
6. …………Rh6
Again, black has a lot of options here, I am just picking the obvious one to my own eye, but feel free to suggest others. Continuing:
7. Bf4
Of course, white might try Be5 here with the idea of shielding the king when he is on e6, but the question is, how does the king get on e6 with the black rook on the 6th rank? At least Bf4 makes black’s defense a bit more challenging. Continuing:
7. ………….Rg6
I think Rf6 will draw, too. All black need do is to keep the rook safely covering e6 for the moment- if black had played another move like Rb6, for example, white will then play Bd6 opening the e6 square for the white king, or play Ke6 immediately if the rook leaves the 6th rank, even on Rh4. In any case, how does white make progress here? He must try to attack the rook with the king:
8. Ke5 Rc6
With the path of the bishop to d6 blocked by its own king, black is now free to move the rook to the queenside of e6. However, I think black had other options, too, like moving the king either direction.
9. Kf5
If white tries Kd5, black just returns the rook to g6/f6.
9. …………Rb6
The rook can stay on the queenside since the bishop can’t reach d6 without the king’s guard. In short, the king and bishop are constantly in each other’s way, giving the black rook the flexibility to stop the king from safely getting back in front of the black king. I hope this is enough for people to design the actual winning plan out of the other first move options for white I mentioned at the start- 1. Ra1, 1.Rf1, and 1.Rg1. They all should win in less than 15 moves. If by tomorrow morning no one else has shown a conclusive path, I will fill in the details.
Of course, I mean the bishop on c5, not c6 in the first part of the comment. A pity there isn’t edit functionality in the comments.
Hello! I put it in reply to Lenny’s post since he asked first.
Here are the starts for 1. Rf1 and 1.Rg1. I was wrong yesterday when I supposed that they might be shorter lines than 1.Ra1- they are longer and Ra1 eventually has to be played, or white transposes into the same essential positions later on via a transfer of the rook to the seventh rank at f7 or g7 respectively, without going through a1.
1. Rf1/g1
Obviously, this threatens 2.Rf8/g8#. Black can check from h6, but after white blocks with 2.Bd6, the only way to prevent mate on the next move is 2. …Rh8, then white transfers the rook to a1 and will mate on the other side of the black king, and it can’t be stopped. So, the black rook can either go immediately to h8, or prepare to block the check by playing…..
1. …………..Rd2 (if Rh8, then 2.Ra1 Rh6 3.Bd6)
So, black has parried the immediate threat. Note why this line was different than 1.Re1 I discussed yesterday in which black manages to escape the trap. When white has played 1.Re1, black can check from h6 driving the bishop to d6, but then black can meet the immediate threat with 2. …Kd8 preventing 3.Re8#- that is why 1.Rf1 and Rg1 are superior- that king move can’t save black. At this point, white can now transpose to the 1.Ra1 line with 2.Ra1.
As I showed above, white can win with 1.Ra1, 1.Rf1, and 1.Rg1. The latter two moves eventually fold into the former through transpositions to identical positions, or to positions that are essentially the same. So, 1.Ra1 is the keystone to build on:
1. Ra1
Threatens 2.Ra8#. Black cannot prevent this with 1. …Kb8 since white first checks with the bishop from d6, then plays Ra8#. Additionally, as mentioned above by myself and others, the check from h6 is impotent due to the block by the bishop from d6. The only plausible defense is to prepare to block the check with the rook:
1. ……………Rb2
Now, the question at hand is this- how does white stop the black rook from blocking the mate threats- specifically, how does white prevent the black rook from coming to b2 and d2 in this present arrangement? The key insight is the idea of forcing the black rook off the second rank (also to keep him off the 1st rank!!) so that some of those squares are taken away by the bishop at key junctures. James above had the right idea to get this going- the white rook is quite flexible and can make its threats from any of the ranks not occupied by the kings and bishops- 2.Ra7 makes perfect sense here because it continues to threaten Ra8 in addition allowing some scope for the bishop:
2. Ra7!
Other rook moves don’t throw away the win, but this is the one that makes progress. The rook can still transfer back and forth on the flanks as needed. The black king still cannot move in either direction without losing, and the black rook is pinned to the b-file. Continuing:
2. …………..Rb1
It is this or Rb3, or lose the rook outright, or get mated. If black played 2. …Rb3, James’ line above with 3.Rc7, and the line I will show below, leads to the same sort of situation. Rb1 is the most resistant line black has. Continuing:
3. Ba3!
The shortest path. Note, this move covers the c1 square preventing the check, still threatens 4.Bd6 check if black tries 3. …Kb8, it keeps the black rook tied to the b-file, and it prevents the rook from returning to the second rank. Additionally, it still covers the e7 square making later Kd8 moves less effective. The initial goal is accomplished- the black rook is forced onto ranks less amenable to the defensive tactic of blocking the checks on the 8th rank with the rook. Continuing:
3. ……………Rb3 (if Rb8 4. Rf7 wins easily since e7 is covered by the bishop)
Black attacks the bishop. It might appear that white has gained nothing- he will return the bishop to c5 allowing black to repeat moves, but that is not the case……
4. Bd6!
White attacks the weak point of the black defense- the b8 square the rook will block on. Black has no choice but to check from c3:
4. …………..Rc3
5. Bc5!
Now black must either give up the exchange at c5, return the rook to b3 to block at b8 if white plays Ra8, or now play Kb8 preventing Ra8. We will discuss the latter two options since the former is just a K+R vs K ending which is beneath the scope of this discussion.
5. ………….Kb8
6. Re7
Or Rf7, Rg7, Rh7 wins the same. White is now threatening mate again from the other side of the black king. In addition, there is no way to block this mate with the rook because the c-file is plugged up by white pieces. Black’s only longer defense is to give up the rook at c5 for the bishop. So, lets back up to move 5 and discuss Rb3:
5. ………….Rb3
Now, note- if white tries to flank with Re7, Rf7 etc, the d3 square is still open to the black rook for a block. What white wants to do is to make the black king move off the c-file, then threaten the mate with a flanking maneuver…….
6. Rc7! Kb8
If black tries Kd8, it won’t matter- white would play 7.Rf7 and the e3 square is unavailable to the black rook- this is the reason one wanted to drive the rook up the board from the 1st and 2nd ranks. The rest is quite simple:
7. Re7 Ka8 (opening the b8 square for the rook)
8. Re4
Why this move is shortest will become obvious in just a moment- it is a stalemate issue. All white is doing here is threatening Rafile+ to force Kb8 followed by Bd6+. Black is in zugzwang (has been from the start, but you know what I mean). The black king cannot move off a8, and the black rook can’t leave the b-file. The black rook has two safe squares to move to:
8. ………….Rb2 (if Rb1 9.Ra4 anyway; also if Rb4 9.Bxb4!)
9. Ra4 Kb8
10.Bd6 Kc8
11.Ra8 Rb8
12.Rb8#
If, at move 8 white had put the rook on e1 or e2 black could have forced the rook to play to e4 by blocking with Rb1 or Rb2 respectively- white can’t take the rook without stalemating black. With Re4, white forecloses this option for black since the bishop can be used to take the rook at b4.
The other variations of this problem can be used for practice where the black rook is on h2 at the start, and the other men are moved to the various other files. Some are longer and a bit more challenging, but should be solvable using the principles discussed above.
Thanks very much 🙂
Thanks!
3. … Kb8 4. Bd6+ leaves the rook on a7 hanging, doesn’t it?
Thanks!
3. … Kb8 4. Bd6+ leaves the rook on a7 hanging, doesn’t it?
Karthik,
It is an interesting line, but it didn’t make the final edit because it was a shorter loss for black. However, that was probably an error of judgment on my part- it is interesting in itself and should have at least been included up to a certain point. Here is the analysis of it in full:
1. Ra1 Rb2
2. Ra7 Rb1
3. Ba3
You then suggest Kb8 attacking the rook, however, white just transfers the rook to the kingside. The threats of mate on the edge will come in two dimensions now- 8th rank threats, and a-file threats. They are all but identical to the main line in the earlier comment:
3. ………..Kb8
4. Re7
The threat is now Bc5 followed by Re8#. There are no plausible defenses other than Ka8 opening the b8 square for the rook, and Rf1/g1/h1 to harrass the white king from the flank:
4. ………..Rh1 (intending Rh6+)
5. Re8 Ka7
6. Bc5 with mate coming on the next move.
And, at move 4 for black, he can open b8 for the rook. This is more tenacious than 4. …Rh1, but only just:
4. …………Ka8 (allowing Rb8 to block)
5. Re4!
Also good is Re5. This threatens Ra4, Bd6+, Ra8, and Rxb8# when necessary as in the earlier comment; and it threatens Bc5 and Ra8# as above. The only other defense not already described is Rb7 to shield in both dimensions from b8 and a7 respectively, however this fails either way since all white need do is simply wait for black to move again- either the rook or the king:
5. …………Rb7
6. Re5 Kb8 (if Rb3, then 7.Ra5 starts the mate; if Ka7 then 7.Ra5 Kb8 8.Bd6 as earlier comment showed)
7. Re8 Ka7
8. Bc5 Ka6
9. Ra8 Ra7
10.Ra7#
And I now see why you asked. I forgot to remove that part when pasting into the comment box. I keep several docs opened when I do these analyses. Some of them get advanced to the end before I close up the sidelines. I then combine and edit down so that my comments don’t stretch out to 10000 characters or more. In the first run through, I had initially thought Bd6 was possible after Kb8, but it was an afterthought left for they tying up of loose ends (why I didn’t paste in an actual line), and I had completely forgotten it by the time I was done, and didn’t notice it was still there when I started constructing the final comment document. That error is what happens to me when I don’t do the analyses over an actual board, and why I am a terrible player in all but correspondence chess.
One last loose end to clear up, I had erroneously stated this was a win for white regardless of where the arrangement of the black king, white king, bishop and white rook occurred with the black rook on h2 (or a2 when the others are on the h-file). This was a miss in my memory- when they are on the b or g files, it is a draw with best play. All of them, however are instructive, and the ones with the line-up on the d/e files and a/h files contain little nuggets that were missed in the one in this puzzle, which is the easiest of them to win for white.
k7/8/K7/B7/8/8/7r/R7 b – – 0 1 white to move and win.
3k4/8/3K4/3B4/8/8/7r/3R4 w – – 0 1 white to move and win.
Oh to have edit functionality! That first position should have read k7/8/K7/B7/8/8/7r/R7 w – – 0 1. I hate FEN!
And finally, it sometimes matters where the black rook is in some of these positions, and for reasons I described earlier. For example, see below. I suspect this is the source of my faulty memory- sometimes winning became always winning. I hadn’t given this ending a lot of thought in the last couple of decades or so. Indeed, I only remember having this kind of ending in a game only once in 1000s of online games.
1k6/8/1K6/1B6/8/8/7r/1R6 w – – 0 1 is a draw, while, if you place the black rook on some non-attacked fourth rank squares, it is winnable again.