Monday, October 13, 2014

Rook-Pawn endgames: Three vs Two (Part 2)

In the second part of our discussion I will stray off slightly from the main focus (pawns on one side of the board) and take a look at what may possibly go awry in a situation where there are outside pawns.

NN - Staunton
London 1842
White to move

Over here White is a pawn down, and there are pawns on both sides of the board. Now White faces a tough choice: Should he trade rooks?

I'll let y'all think about it for a while; assess the position and determine whether White should trade rooks, before scrolling down for the rest of the analysis.

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And the answer is yes: White should trade rooks. While this might sound counterintuitive compared to what i have been harping on for the past couple of articles (that the weaker side should strive to keep the rooks on the board!), this is an exception. The presence of the kingside pawns means that a rook trade enables White to obtain an outside passed pawn, which he can use to distract the enemy king and force a draw:


1. Rxf6 gxf6
2. Kg4

As with all endgames, it is always important to centralize the king.

2... Kg7
3. Kf5 c5
4. h5 c4
5. h6+

White's outside passed pawn distracts Black and pulls his king to the side of the board.

5... Kxh6
6. Kxf6 b5
7. Ke5 (D)
1/2-1/2


Black's king is at the sidelines

White's king is more centralized; by the time Black's king crosses over the the Queenside, White would have been able to win at least one pawn and hold the draw.


...


That was simple enough, but as math and science peeps we'd prefer making life more difficult for everyone. So rather than just saying "Hooray, draw!" and ending here, many of us would ask the question: What if White were to reject the rook trade? Can he still defend his position successfully? To satisfy our curiosities, we shall take a look at what happens should White play something else; let's say 1. Rd2:

Position after 1. Rd2: Can White draw?

Once again, you can spend some time analyzing the position before scrolling down.


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 My answer to the earlier question is: Yes, White should be able to draw, because I have not yet found a line where Black can win convincingly. In any case, with rooks on the board, things suddenly get complicated... and so much more fun to analyze.


1...a5

After 1... Rf7 2. Rd8+ Kh7 3. Rd6 c5 4. Kg4 Rf2 5. Rd7 we have a position similar to the main line analysis.

2. Kg4 a4
3. Rd7!

Following the same principle of keeping the rook active by tying down the enemy king to the pawns. And now I will diverge into two lines: The main line  3... Rf7 and the variation 3... Rf2. Let us go through the Rf2 variation first:

3... Rf2

Black also keeps his rook active by attacking White's pawns, and this soon leads to a massive trade of pawns:

4. Rd6 Rxb2 5. Rxc6 Rb3 6. Rc8+ Kh7 7. Rb8 7... Rxa3 8. Rxb6 Rc3

After 8... Ra1 9. Ra6 a3 10. Kg3! a2 11. Kg2! g6 12. Ra5 (D) we arrive at the following position:

A familiar position

Does this position ring a bell? Yes, once again we see the power of Tarrasch's rule: White's rook is behind the enemy passed pawn, while Black's rook is tied down to defending the pawn and at the same time obstructs its promotion. So long as White's king stays on h2 and g2 (which is why 10. Kg3 and 11. Kg2 were played; to ensure Black doesn't try something nasty like ... Rg3+ which clears the way for his pawn!) and shuffles his rook on the a-file, the game is a dead draw. This means that even if Black wins the pawn on h4, he still cannot win since the g-pawn cannot chase White's king away from g2 or h2.

To refresh your memories with more details, here are the links to the relevant positions:

http://nushsblackknights.blogspot.sg/2014/03/challenge-yourselves-difference-with.html

http://nushsblackknights.blogspot.sg/2014/03/a-difference-wth-extra-pawn-part-1.html

Returning to the position after 8... Rc3:

8... Rc3 9. Ra6

Same as always: Put your rook behind the pawn!

9... a3 10. Kf5 Rh3 11. Kg4 Rd3 (D)
1/2-1/2

Position after 11... Rd3

It should not be too hard to tell that Black cannot make progress in this position. Both White's king and rook work together to prevent Black's king from touching the h-pawn, while Black's rook is once again tied down to defending the a-pawn. After something like 12. Kf5 Rd4 13. Rxa3 Rxh4 14. Rg3 the a and h-pawns have been exchanged, and White's king will be in front of Black's remaining pawn... which means an impending Philidor Position.

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So that was one variation cleared. Now let's return to the position after 3. Rd7 and proceed with our main line: 3... Rf7

3... Rf7 (D)

Position after 3... Rf7

4. Rd8+

This is the time when White should not trade rooks, since he can no longer get an outside passed pawn: 4. Rxf7? Kxf7 5. Kg5 b5 6. h5 c5 7. Kf5 b4 and the series of pawn trades on the kingside will give Black the outside passed pawn instead.

4... Kh7
5. Rd6!

Once again we see the power of keeping your rook active.

5... Rc7

This is a passive move, but we have already seen that the more active variation 5... Rf2 leads to a draw.

6. Kf5

Preparing to march over to the kingside to assist the White rook. 

7... b5

6... Rc8 7. Ke5 g6 8. Ke6 Kh6 9. Kd7 and White still wins the pawn

7. Ke5 Kg8 (D)

Position after 7... Kg8

White might be a pawn down, but can hold out thanks to his active rook and more centralized king.

8. Kd4 c5+
9. Kd5 c4
10. Rb6 c3
11. bxc3 Rxc3
12. Rxb5 Rxa3
13. Rb4

Or 13. Ra5 Rd3+ 14. Kc5 (not 14. Kc4?! Rh3! with some problems for White) preparing to win the a-pawn.

13... Rd3+
14. Ke4 Rh3
15. Kf5 a3
16. Ra4 Kh7
17. Ra6 Rc3
18. Kg4 (D)
1/2-1/2

Position after 18. Kg4

And we have reached a similar position as the one in our first variation. Since Black cannot make any progress, the game can be agreed drawn.

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Thus, we have seen that despite the complications of having extra pawns at the side, a Three vs Two situation in rook endgames can still be a draw as long as the defender remembers the correct drawing technique. As always, active play is key!

P.S. In the actual game, White refused the rook trade, and then proceeded to lose the game after making a couple of mistakes.

Links:
Two vs One: http://nushsblackknights.blogspot.com/2014/09/rook-pawn-endgames-two-vs-one.html
Three vs Two (Part 1): http://nushsblackknights.blogspot.com/2014/10/rook-pawn-endgames-three-vs-two-part-1.html

Sources:
"Silman's Complete Endgame Course" by Jeremy Silman

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