Rook and Pawn endgame

2 comments

• Reply

  

  Yancey Ward says:

  April 13, 2012 at 11:48 pm

  Almost certainly a draw without a lot of thinking involved. White can definitely win the rook for the pawn with 1.Kc7, but he will then have to give perpetual check or trade his rook for black’s h-pawn. It might well play out this way:

  1. Kc7 Rd2 (Rg7 2.Kc8)
  2. d8Q Rd8
  3. Kd8 Kg5

  And whenever white does not check the black king, black moves either the pawn or the king forward. White’s king is just too far away to play a role.

  Now, white can put his rook behind the pawn on the first move, but this doesn’t change anything major- black still gets the rook back by pushing the pawn:

  1. Rd3 Rg7 (clearest line to me)
  2. Kc8 Rd7
  3. Kd7 Kg5

  The only thing black need really avoid here are backwards/sidewards king moves since it is essential that the king not let itself get stranded on the 6th rank, or allow white to play Rh3 after a move like Ke5. With Kg5, the pawn is supported and can advance to h1 where white will have to sacrifice for it. And, lastly, in the the preceding line, white cannot cut off the king:

  1. Rd3 Rg7
  2. Rd5 Ke6!

  I can’t imagine any other move being playable here for black- he must liquidate at d7 Continuing:

  3. Rd4 Rd7 (h3 ok, too)
  4. Rd7 Kf5!

  Another only move for sure, but now black reconnects with the pawn just in time:

  5. Rd4 Kg5 (h3?? 6.Rh4+-)

  And, again, black moves forwards whenever white does not check, with either the king or the rook. Draw for sure.

• Reply

  

  psyche says:

  April 15, 2012 at 3:56 am

  Rook and Pawn Endgame 13 April

  With respect this is not a “draw for sure”.
  It is a win for white but with best play it is a difficult win.

  As pointed out the more obvious approaches here lead to a draw. Yes, the black rook has to sacrifice itself, but, with the line suggested, so does the white rook because the king supports the black rook pawn in its advance.
  So the solution is to cut off the black king from his pawn but still allow white’s pawn to queen. Effectively:

  1. Rc5! wins e.g. option A is h3 and option B is Rd2!
  (all other moves also lose; either the White rook is going to get in behind the pawn and take it; or when the pawn is sufficiently advanced and separated from the black king, the white rook is going to cover with c1, h1 and R*P._
  Option A;
  1, Rc5! h3
  2. Kc8 Rg8+
  3. d8=Q+ R*d8+
  4. K*d8 Kg6 (or h2; 5. Rc1, Kf5; 6. Rh1 Kg4; 7. R*h2) Now the zugzwang. Either black moves his King away e.g. 4. K f6 so White plays R h5; and R*P next; or black move the pawn so a transposition above: So
  5. Ke7 (or R d5, b5 or a 5); h2 6. Rc1, Kf5; 7 Rh1 Kg4; 8. R*h2.

  Option B is the complex one.
  The only other try for black is to try to win the White pawn. This requires precise play but the White rook should remain on that 5th rank unless taking the Black RP.
  1. Rc5! Rd2!
  2. Kc1 Ke7 {and apparently but wrongly 3. Rc2? looks like it wins but it likely does not; the Rook must not leave the 5th rank. so 3. Rc2? with apparent zugzwang: (If e.g h3, then d8=Q discovered check) 3. … Kf6 then [not 4. d8=8? R*d8
  5. K*d8 (not K-g6 to prevent R-h7 but) 5. … Kg5 7. R-h2 and the black king marches with the pawn)]}
  Instead the white rook must check the black king to chase it away;
  3. R-e5+! Kf6
  4. R*h5 (then 4. … Ke7 loses to 5. Rh7+ Ked6; 6. advances d8=Q R*d8 7. K*d8 Kf4 8. R*h4) and the R*h4) Rc2+
  5. Kd8 Rc4!
  6. Rd5 Rc3 ( ***or Kg3 7. Re4, then 8 Ke8, 9 d8=Q)
  7. Kd8 , Re3+
  8. Kf8 h3
  9. d8=Q+ Kg6 (and mates 10. Qg5+, Kh7; 11 Qg7#)

  Psyche

  PS: I’m also posting the clear win on Hallerod – Monin posted 7 April 2012.