White to move. Is this a win or draw for White? How should White proceed?
k7/p7/1r6/Q1K5/8/8/8/8 w – – 0 2
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White wins … Moving the queen to either a4, a2, a1, c3, d2, e1
One might guess this is drawn as the white king cannot advance beyond the fifth rank, and the queen cannot mate the black king, or even drive him from a8/b8/b7 by herself. The truth is, though, I happen to know this is a winning position, though I doubt I could win it over the board in a time control. Susan actually posted a couple of puzzles several months back that ultimately reduced, if memory serves, to King+Rook+g or f-pawn vs Queen + King. Those were draws theoretically. The difference in this position, of course, is the lack space on one side of the rook’s pawn, and this is a decisive disadvantage for black as it allows zugzwang to be enforced at key positions to require black to move the pawn away from the king, at which point it can be won, thus reducing the position to King+Rook vs Queen+King, a theoretical win.
I really don’t have a clue what the shortest way to win this is, but a plausible winning strategy to me would be to bring the queen to c6 with check and pinning the rook at b7. One way to accomplish this might be to check on the back rank from d8 or d7 if black moves the king to b7, so, I might play Qd2 as a start. Below, I will give what I can only consider to be the most favorable line of moves for white that don’t involve outright blunders by black.
1. Qd2 Kb7
2. Qd7 Ka8 (Ka6 loses quicker?)
3. Qc8 Rb8
4. Qc6 Rb7
And, now, the white king can advance to d6:
5. Kd6
And, now, black is in zugzwang- Kb8 loses to Qe8#, so black must play a pawn move:
5. …..a5 (a6 is same)
6. Qa6 Kb8 (Ra7?? 7.Qc8#)
7. Qa5
And, now, we have reached a queen vs rook ending which is a win with proper technique. So, now, did black have any way to hold the draw with any of the moves above? In the line above, everything was forced after 2. ….Ka8. There were two options- Ka6 and Kb8. I will take each in order:
2. …..Ka6
3. Qc8 Ka5 (Rb7 4.Kc6+-)
4. Qc7 Ka6 (else, lose R or P)
And, now, white need only keep black from checking with the rook at b5. White accomplishes this by covering b5 with the queen:
5. Qd7
And, now, a king move loses the a-pawn, and black has only rook moves that separate him from his protective king and pawn:
5. …..Rb2 (Rb7 6.Qa4#)
And, now, it is just a matter of technique to get a double attack on the king and the unprotected rook:
6. Qd3 Kb7 (Ka5 7.Qc3+-)
7. Qf3 Kc7 (Ka6 8.Qa3+-)
8. Qg3
Why this square? I want to take the seventh rank away from black with the threat of Qg7+. Continuing:
8. …..Kc8 (other moves same)
9. Qg8 Kb7/c7/d7
10.Qg7 wins the rook. For this variation, one might ask does it make any difference if black moves the king differently at move 7? It doesn’t. The technique for white is identical- get the white queen to g-file with check- for example:
7. …..Kc8
8. Qg4 and white will check from g7 on one of his next two moves. Or
7. …..Kb8
8. Qg3 with check from g7 coming soon. Also, there were no better rook moves at move 5 in this line. Any move of the rook off the b-file allows Qb5#, so we need only consider Rb8, Rb3, and Rb1:
5. …..Rb8 (Rb7 6.Qa4#)
6. Qa4 Kb7
7. Qc6# Or
5. …..Rb3
6. Qa4 wins the rook immediately. Or
5. …..Rb1
6. Qd3 wins the rook immediately. So, clearly, the line below is losing for black:
1. Qd2 Kb7
2. Qd7 Ka6.
We now need to consider black’s second move alternative of Kb8. Continued in my next comment.
In my previous comment, I had shown the following line was a forced win for white:
1. Qd2 Kb7
2. Qd7 Ka8 or Ka6.
We need to consider black playing Kb8 with his second move.
2. …..Kb8
Here, the clearest way I see to win is to wait for black to move again:
3. Qe7
And, now, black must play the king to a8 (or lose the pawn), move the pawn, or move the rook. Of course, moving the pawn just drops the rook, so we can ignore that option. I will consider the other two in order:
3. …..Ka8
4. Qc7
And black must move the rook away from protection or to b8 or b7:
4. …..Rb7 (we saw this earlier)
5. Qc8 Rb8
6. Qc6 Rb7
7. Kd6 a5
8. Qa6 Kb8 (Ra7 9.Qc8#)
9. Qa5 with a won ending of Q vs R. Or
4. …..Rb8
5. Qc6 Rb7 and we are in the line above which is a loss for black. So, at move 4 the black rook must put himself on a square on which he is unprotected.
4. …..Rb3
5. Qc6 Kb8 (Rb7 loses as above)
6. Qe8 Kb7 or Kc7
7. Qf7+ with a fatal double attack. Or
4. …..Rb2
5. Qc6 Kb8 (again, Rb7 loses)
6. Qe8 Kb7 (Kc7 7.Qe5 wins)
7. Qe4 Ka6 (Kc8 8.Qg4 prev. comm)
8. Qd3 and we saw this line in my previous comment- black either gives up the a-file, or loses eventually to a check from g7. Or
4. …..Rb1
5. Qc6 Kb8
6. Qe8 Kc7 (Kb7 7.Qe4+ wins)
7. Qe5 Kd8 (Kb7 8.Qe4; Kd7 8.Qf5)
8. Qf6 Kc7 (Ke8 9.Qg6; Kc8 9.Qf5)
9. Qf4 Kd8 (only move)
10.Qh4 Ke8/c8 (K 7th rank 11.Qh7)
11.Qh8 K to 7th rank
12.Qh7 wins the rook. Of course, it does no good to move the rook along the sixth rank due to Qc8#.
At move 3 in this variation, the only other option black had was to move the rook. But this will clearly lose:
3. …..Rb7
4. Qd8# Or
3. …..Rb3
4. Qd8 Kb7
5. Qd5 wins the rook. Or
3. …..Rb2
4. Qe5 wins the rook. Or
3. …..Rb1
4. Qd8 Kb7
5. Qd5 Kc7 (Ka6 6.Qa2; Kc8 6.Qf5)
6. Qf7 Kb8/c8/d8
7. Qg8 K to 7th rank
8. Qh7 wins the rook. Or
3. …..Ra6 (definitely the best)
4. Qd8 Kb7
5. Qd7 Kb8 (Ka8?? 6.Qc8#)
And, here, I have to admit, it took me a bit of time to find the winning method- I basically had to run through the possible white moves, but it became obvious that only one method really changes the position is an effective way:
6. Kb5 Rb6
Here, any move by the rook anywhere else is going to lead to an eventual fatal double attack by the queen. Continuing:
7. Ka5
Taking a6 away from the rook. This is basically a zugzwang for black. He has the moves Ka8, a6, or rook moves along the b-file and the 6th rank. I consider each in order:
7. …..Ka8
8. Qc8 Rb8
9. Qc6 Rb7
10.Ka6 Kb8 (only move obviously)
11.Qb7#
Or,
7. …..a6?
8. Kb6 trivially. Or
7. …..Rb3
8. Qe8 Kb7/c7
9. Qf7 wins the rook. Or
7. …..Rb2
8. Qe8 Kb7 (Kc7 9.Qe5)
9. Qf7 Ka8 (Kc6 10.Qf6; Kb810.Qg8)
10.Qd5 Kb8 (Rb7 11.Ka6)
11.Qe5 wins. Or
7. …..Rb1
8. Qe8 Kc7 (Kb7 9.Qe4)
9. Qf7 Kd8 (Kc6 10.Qg6)
10.Qg8 and the check from h7 is unavoidable. Or
7. …..Rf6
8. Qd8 wins the rook. Or
7. …..Rg6
8. Qe8 wins the rook. Or
7. …..Rh6
8. Qe8 Kc7 (Kb7 same)
9. Qf7 Kc6 (K 8th rank 10.Qf8)
10.Qa7 with theoretically won ending.
So, the line
1. Qd2 Kb7
2. Qd7 Kb8 is losing for black. Now, we need to only consider the first move alternatives. Continued in my next comment.
Kxb6, no?
No, fernglaser. You can’t put your king in check.
In my first two comments, I had shown that the following line was losing for black:
1. Qd2 Kb7
2. Qd7
We need to consider black’s first move alternatives. I think, by now, we can dispense with rook moves along the b-file at b3 and b1, and along the sixth rank at f6 and g6 since all of them should reduce to wins with minor variations in the methods I have outlined previously. First, lets look at Kb8 since it is the easiest to deal with:
1. …..Kb8
2. Qd7 and we have already seen this position earlier with the queen at e7- black must either move the rook (Ra6 best), or move the king to a8 (which we have shown loses to Qc8+). So, Kb8 is no way for black to draw.
So, of the rook moves that black can play at move 1, we really only need to consider Rb7, Rb8, and Ra6 since anything else is sure going to fail to a fatal double attack
1. …..Rb7
2. Qd6 Rb6 (or lose the pawn)
3. Qc7 and we have already proven this position is a win for white. Or
1. …..Rb8
2. Qd5 Rb7
3. Qc6 Kb8
4. Qe8 Kc7
5. Qa8 and the black pawn is lost. Finally
1. …..Ra6
2. Qd7
With the threat of Qc8#:
2. …..Kb8 (Rb6 3.Qc8 as before)
3. Kb5 Rb6
4. Ka5 and we saw this position earlier was a loss for black.
In my next comment, I will pick this line immediately above as a reference for how to win the queen vs rook endgame.
From my previous comment, I am going to pick up with the last line and reduce it to a simple queen vs rook endgame to give those curious a look at how to win this type of endgame.
Continuing:
4. …..Rh6 (most resistant)
5. Qe8 Kc7
6. Qf7 Kc6
7. Qa7 Rh5
8. Ka6
And, now, without any immediate checks, black must be careful with where he puts his rook. To speed this up a bit, lets just bring the rook into contact with his king:
8. …..Rd5
9. Qb6 Kd7
10.Kb7
You want to push black onto the edge of the board while giving him a minimum of annoying checks. Continuing:
10. ….Rd6
Now, in this position, with no immediate check for black coming on the next move, white need only play a waiting move leaving an attack on the rook:
11. Qb4
Here, a careless move like Ke7 loses the rook immediately to Kc7 (I have won quite a few blitz endings of this type in this way), so black must play Ke6, or move the rook. With either, black must give ground:
11. ….Ke6
12. Kc7 Rd7
13. Kc6
And, now, the black rook must move again:
13. ….Rf7
14. Qd6 Kf5
15. Kd5
Again, pushing black back with a move taking the king out of checking range:
15. ….Rf6
Here, I want to once again get the king and the rook connected diagonally, with the rook behind, or get him to separate the rook from the king by even one square:
16. Qg3 Rf7
17. Qf3 Kg6
18. Qg4
Keep pushing black back:
18. ….Kf6
19. Kd6
That corner and edge just keep getting closer and closer:
19. ….Rg7
20. Qf4 Kg6
21. Ke6
Here, I will cover a one continuation, though there are others like Kh7, Rg8, and Rh7, but they are largely the same, but with slightly different sequences of moves:
21. ….Kh5
22. Qe3
The point of this move is to cover g4 and threaten mate if black checks with Rg6:
22. ….Kg6 (Rg6 23.Kf5+-)
23. Qc3
A motif we saw earlier- keep an attack on the rook forcing the king back, or forcing the rook to move back or away from his protector:
23. ….Rg8 (Rh7 24.Qg3 Kh5 25.Kf6)
24. Qf6 Kh7(Kh5 25.Qf7 Rg6 26.Kf5)
And, again, a waiting move seems to be best here, but I could be missing something quicker:
25. Qd4
Here, trying to check the king is going to lose for black-Re8 and Rg6 both lose to Kf7 with twin mating threats. The longest resistance seems to be
25. ….Kg6
26. Qe4 Kg7
27. Ke7
And black is in near paralysis.
27. ….Kh8 (alternatives below)
28. Qe5 Kh7 (Rg7 29.Kf8)
29. Kf7
And the twin mating threats cannot both be stopped without giving up the rook, and that will only buy a couple of extra moves anyway. The trickiest attempt is
29. ….Rg6
and if white pins with Qf5 and carelessly plays Qg6 after the king retreats to h8, it is stalemate, so white must take with the king:
30. Qf5 Kh8
31. Kg6 with mate to follow. Back at move 27, black is still mated with
27. ….Kh6
28. Kf7 Rg7 (or give it up)
29. Kf6 with a position similar to one I just described immediately above. At move 27, rook moves away from the king are equally futile:
27. ….Rc8 (Rb8 28.Qe5)
28. Qe5, and no matter where the king goes, a double attack from e6 or f5 will follow. Or
27. ….Rh8
28. Qg4 Kh6 (Kh7 is same)
29. Kf7 Rh7 (Or mate)
30. Kf6 and the mate can only delayed, not stopped.
This ending is tough, even if you have time on your clock, and I have occasionally mucked up in moderate time trouble, but I get better each time I play it by following a couple of simple rules and motifs I have shown above. The hard part is pushing the king to the edge of the board, once I have him there, the mate is actually pretty simple.
Get the queen to e4, and something’s got to give.
Anonymous commenter at 2:29 wrote:
You can’t put your king in check.
You should always let your opponents put their king in check. Then take it.
There are quite a few positions similar to this that are drawn, depending on the location of the pawn. This is not one of them, according to the tablebase.
lost endgame with a-pawn or h-pawn
1. Kxb6 Kb8
2. Qxa7+ Kc8
3. Qc7++ Mate