White to move. Is this a win or draw for White? How should White proceed?

8/5K2/1PR5/8/Bk6/3p4/1r6/8 w – – 0 1

Prokes, 1943

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1. b7 Kxa4

2. Ra6+ Kb3

3. Rb6+ wins

win

Susan, I really like these endgame positions you are posting. As the themes in them repeat it is feeling a bit like programmed learning. Thx.

This is another Q vs R+P. (Third I can remember from the last few weeks).

1. b7 Ka5

2. Bb5 Rxb5

3. Rc5 Rxc5

4. b8=Q

and the mirror

1. b7 Ka3

2. Bb3 Rxb3

3. Rc3 Rxc3

4. b8=q

I formed my own quick view about whether these are won or drawn, without even attempting to analyse them.

I would say is that if I was black I would be confident of holding at least one of them (the Ka3 one) in practice. Even Q vs R can be hard to win in 50 moves.

Then I checked with tablesbases to find the pure result but I am not allowed to post the answer ðŸ™‚

1.b7 Ka3 (or 1…Ka5 2.Bb5!, 1…Kxa4 2.Ra6+)

2.Bb3! Rxb3 3.Rc3 Rxc3 4.b8=Q

Black has here some drawing chances, but the final position is won for white

Promote that pawn! 1. b7 Kxa4 2. Ra6+ Kb5 3. Rb6+ Kxb6 4. b8(Q)+ and it’s all over.

I do not see that clear, without the help of a board or computer assistance.

White can promote his pawn to become a queen, but it is not too easy to win the resulting position. I give the following line:

1. b7 Ka3! (Kxa4 looses after Ra6+)

2. Bb3! Rxb3

3. Rc3 Rxc3

4. b8Q d2

and now Black pieces are ready to support the d-pawn, I suppose White to be obligued to force a draw by a repetition.

I don’t have time to calculate the lines right now but I’m going to go with win for white after playing Bd8. The time black will need to spend getting rid of the bishop will allow white to get a winning position with the passed pawn.

I add one line to my posting before. Beside

1. b7 Ka3 White’s attempt

2. Bb3! Rxb3

3. Rc3 Rxc3

4. b8Q d2, which is not an easy win for White (I assume, it is a draw), …

1. … Ka5

is not an improvement. In this case

2. Bb5! Rxb5

3. Rc5 is winning as White’s pieces are not well co-ordinated.

1. Bb3! K:b3

2. b7 Ka2

3. Rc2!

1. Bb3! R:b3

2. b7 Ka3

3. Rc3!

By Stulzer

it’s win for white

1 b7! (1 … Kxa4 doesn’t work: 2. Ta6+ and 3.b8=D+)

1 … Ka3

2 Bb3 Txb3

3 Tc3 Txc3

4 b8=D

and the resulting end is theorycally win for white, however a dificult win for a human (tablebases say black loses in 36 moves)

1. b7 Ka6 ( Kxa5? 2. Ra7+ Kb6 b8Q+ Kxa7 Qxb2 ) 2. Bb6! should be won ( Rxb6 3. Rc6 )

My first instinct (in about 2 seconds) is to push the pawn, but I suspect I am going to find the same problem we had the other day with a queen vs rook+pawn endgame:

1. b7 Ka4?

2. Ra6 Kb5 (Kb3 3.b8(Q))

3. b8(Q)Ka6

4. Qb2

So, black cannot take the bishop with his first move, but must use it as a shield:

1. b7 Ka3! (Ka5 is below)

And, now, all I see for white is

2. Bb3 Rb3

3. Rc3 Rc3

4. b8(Q)Ka2 (d2? 5.Qd6+-;Rb3 below)

And white must find a way to bring both the queen and the king forward while keeping the the black king from joining up with his colleagues, or allowing black to advance the pawn- not an easy task. Of the moves here, I favor keeping the queen on the b-file to keep the king on the edge, and keeping the threat of check with double attack on the d-pawn should black play d2. This argues for

5. Qb7

Now, if the rook moves off of the third rank, Qd5+ wins d3, and if black plays d2, Qd5+ wins the pawn at d2. As far as I can tell, black has only Ra3, Rb3, Ka3, and Ka1 as moves. Let’s take them in order:

Variation A. with 5. …Ra3:

5. …..Ra3

6. Qb4 Rb3 (what else?)

7. Qd2

And I see no way to keep white from bringing the king forward, attacking the pawn and/or the rook. Continuing with a plausible line:

7. …..Kb1 (Rb2 8.Qd3; Ka3 8.Ke6)

8. Ke6 Ka1 (rook checks pointless)

9. Kd5 Kb1

10.Kc4 Ra3 (pawn lost otherwise)

11.Kb4 and black loses the pawn and the game.

Variation B with 5. …Rb3:

5. …..Rb3

6. Qg2! Rb2 (Ka3/a1/b1 7.Qd2+-)

7. Qd5 Rb3 (pawn lost otherwise)

8. Qa5 Kb1 (Anything else 9.Qd2)

9. Qd2 wins as before.

Variation C with 5. …Ka3:

5. …..Ka3

6. Qb1 d2 (Rc2 7.Ke6, 8.Kd5 etc.)

7. Ke6 Rh3 (Rb3 8.Qa1 Kb4 9.Qd4)

8. Kd5 Rh5

9. Kc4 Rh4

10.Kc3 and the pawn and the game are lost.

Variation D with 5. …Ka1:

5. …..Ka1

6. Qb4 Rc2 (what else?)

7. Qd4 Kb1

8. Qd3 wins.

I will cover the 4th and 1st move alternatives for black in my next comment.

If I were just solving this as a problem, or got this position in a correspondence game, I could just spend an hour doing a “brute force” analysis, like a computer. But in OTB play you typically get a position like this when there’s only a few minutes left on your clock (or, with increments, you have to make a move every 30 seconds or so). Obviously another approach is needed. So how would a strong player tackle this (I’m thinking in general terms, not the specifics of this particular position)?

1. b7 Ka3 (1… Ka5 2. Bb5 Rxb5 3. Rc5) (1… Kxa4 2. Ra6+)

2. Bb3 Rxb3 3. Rc3 and wins. Nice study.

1. b7 Ka3 (1… Ka5 2. Bb5 Rxb5 3. Rc5) (1… Kxa4 2. Ra6+)

2. Bb3 Rxb3 3. Rc3 and wins. Nice study.

The key idea is 1. b7+!, seemingly hanging the Bishop, which actually cannot be taken because then Ra6+ will force the black K to the b file and the pawn will queen.

Better defences lie in 1. … Ka3 and 1. … Ka5, but both fail to the same idea:

1. b7 Ka3 2. Bb3!

Rxb3 3. Rc3!! and the pin ensures that the pawn queens.

On 1. … Ka5 the same theme works, only on the sixth rank rather than the third:

1… Ka5 2. Bb5! Rxb5 3. Rc5!!

A nice endgame which illustrates the maxim “Passed pawns must be pushed”. Such maxims are, of course, always true except when the aren’t.

I confess that, though I saw the key move and the win after 1. … Kxa4, I needed Rybka to help me see the rook pin idea.

Of course, white will need to know how to win with Q vs. R, but the extra black pawn on d3 will not save black.

In my previous comment, I outlined the following plan for white that wins the traditionally difficult queen vs rook + pawn endgame, but there were two loose threads I need to either remove, or discover they unravel the plan altogether:

1. b7 Ka3! (Ka5 is below)

2. Bb3 Rb3

3. Rc3 Rc3

4. b8(Q)Ka2 (Rb3 below)

5. Qb7

And, I had shown that white wins all variations I could think of with this plan. The two unaddressed threads were 4. …Rb3 and 1. …Ka5 in the line above: Taking them in order:

4. …..Rb3

The idea is to provide a shield for the black king to make contact with the d-pawn. As I had shown in my previous comment, the inability to do this led to a forced win for white. Here, I would hope a similar plan to what we had seen before can win, but I can see the king makes contact with his pawn:

5. Qh2 Kb4 (Rb2 6.Qd6 wins pawn)

6. Qd2 Kc4

7. Ke6

Now, here, the lines multiply, but there are only three basic ideas for black- harrass the white king with the rook with moves like Rb6 or Rb8 followed by checks from the back rank; or, Rb5 to keep the white king away; or Rc3 threatening to push the d-pawn. I will take these in reverse order:

Variation 1 with 7. …Rc3:

7. …..Rc3

8. Qf4

Covering d2 and pushing the black king away from the pawn. Continuing:

8. …..Kb3

9. Kd5 Rc2 (alternatives below)

10.Qe3 Kc3

11.Qd4 Kd2

12.Ke4 Rc3

13.Qb4 Kc2

14.Kd4 Rb3 (Rc8 below)

15.Qc5 Kd1 (alternatives below)

16.Qc4 Ra3

17.Qb4 and the pawn is lost. At move 15, black does no better with

15. ….Kd2

16.Qc4 Ra3 (pawn lost otherwise)

17.Qb4 wins rook. Or

15. ….Kb2

16.Qa5 Kc2 (Ra3 17.Qd2;Kc1 below)

17.Qa2 Rb2

18.Qc4 Kd1 (Kd2 19.Qd3)

19.Kd3!

At move 16 in this line immediately above,

16. ….Kc1

17.Qa1 Kc2(Kd2 18.Qa2; Rb2 19.Qc3)

18.Qa2 Rb2

19.Qc4 as above. Or at move 15,

15. ….Kb1

16.Qa5 and Kc1, Kc2, or Kb2 all lose just like the line that starts with 15. …Kb2.

At move 9, in this line, black does no better with the following alternatives:

9. …..Kc2

10.Qa4 Kd2

11.Qa5 Kc2

12.Kd4 Rc8 (Rb3 was seen above)

13.Qa4 Kd2

14.Qa2 Rc2

15.Qe6 and the pawn will fall. Or

9. …..Rc8

10.Qd2 Rd8

11.Ke4 Re8

12.Kf3 Rf8

13.Kg2 Rg8 (Rd8 14.Kf2)

14.Kf2 Rf8

15.Ke1 Re8

16.Kd1 Kc4 (Rd8 below)

17.Qa2 Kd4 (alternatives below)

18.Qa7 Kc3 (lose rook otherwise)

19.Qc5 Kb2 or Kb3

20.Qb5 wins the rook. At move 17 in this line, black does no better with

17. ….Kb4

18.Qd5 Re3 (Kc3 19.Qc6 wins rook)

19.Qd4 wins the rook. So, at the very least, the pawn will be lost. Or

17. ….Kc5

18.Qa5 Kd6 (only move)

19.Qa6 Ke7

20.Qa3 Kf7 (Kd7/d8/e6 21.Qd3)

21.Qd3 and white has a decisive advantage.

Now, back to the 7th move alternatives.

Variation 2 with 7. …Rb5:

7. …..Rb5

And, I have admit, I am finding it difficult to find a winning line here after about 15 minutes of trial and error. The queen, of course, can check from c1, f4, and a2, but without her king in on the action, the black king can just move to keep in contact with his rook at b5 and the pawn at d3. I don’t see a way to separate the three. If the king has to approach, the white queen will need to control the squares c5, d5, and/or b5 since the rook can check from there when the black king holds c4. Let’s try the move that drives the black king from the fourth rank to see the problems:

8. Qf4 Kc3 (Kc5 and Kb3 below)

9. Kd6 d2

10.Qe3 Kd2

11.Qe4 Kd1!

12.Qd3

Here, 12.Qa4 is no good since white doesn’t have time to take the rook and stop the pawn. Cont.:

12. ….Rb2

13.Kd5 Kc1

14.Qc3 Kb1 and white can make no progress.

I am out of ideas, at the moment for this critical line. It is possible the the idea of 5.Qh2 is in error, or the following 6.Qd2, but at moves 5 and 6, I don’t see anything immediately winning for white without doing a truly exhaustive analysis. At this point, I think I am going to give in and go check out a table base.

This just might do. It’s not a complete analysis (that would take at least all day), but I think it is correct as far as it goes.

1. b7 Kxa4 2. Ra6+ Kb5 3. Rb6+ Kxb6 4. b8=Q+

1. b7 Ka5 2. Bb5 Rxb5 3. Rc5 Rxc5 4. b8=Q d2 5. Qd6 Rc2 6.Qa3+ Kb6 [Kb5 Qd3+] Qb3+

1. b7 Ka3 2. Bb3 Rxb3 3. Rc3 Rxc3 4. b8=Q [ d2 5. Qb1 Rc1 6. Qd3+ ] Rb3 5. Qe5 [ 5… d2 Qa5+ ] [ 5… Ka2 6. Qa5+ Kb1 7. Qd2 Ka1 8. Ke6 ] 5… Rb7+ 6. Ke6 Rb4 7. Qc3+ Rb3 8. Qa1+ Kb4 9. Kd5 Rc3 10. Qb2+

Lucy