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1.Rh1 Ka4 2.Kc3
1. Rh1 Kb4 2. Ra1 Kb3 3. Rxa2 Kxa2 4. b4 h4 5. Ke3
1Rh3and Ra3 wins
there are two important concepts to remember in this position: first is that pawns can move 2 squares on their first turn and second that the white king is still in the "box" for black's h-pawn.1. Rh1 Kb4 (now you can not keep the black King out!)2. Ra1 Kb3 (the K is going to take our pawn and it will be a draw, unless...)3. Rxa2! Kxa24. b4!! (remember the pawn can jump TWO squares! Now the black king can not catch our pawn)4. ... h45. Ke3 (and the White King will catch black's h-pawn!)
1.Rh1 Kb4 2.Ra1! Kb3 3. Rxa2!! Kxa2 4.b4 h4 5.Ke3 h3 6.Kf2 h2 7.Kg2 and white wins
Rh1 Kb4 Ra1 Kb3 Rxa2! Kxa2 b4!The white king is in the box and can stop the pawn. For example:h4 Ke3 h3 Kf2 h2 Kg2 h1=Q+ Kxh1However the black king is outside the box and cannot stop white's passed b pawn: Kb3 b5 Kb4 b6So ya, 1-0
Let's dispense with the "obvious" move first to see the problem more fully:1. Rh5? Kb4!And, now, white must deal with the a-pawn. He can play to h1, but then black will play Kb3 and then capture at b2 to support the advance to a1 to force white to give up the rook for a draw. In addition, white could play to h7 or h8 and threaten Rb7/b8+ followed by Ra7/a8+ to skewer but Kb3...2. Rh8 Kb3!3. Rb8 Kc2!4. Ra8 Kb2 with an easy draw.
Sacrifice the rook for blacks a pawn. The black king won't be able to catch the b pawn
There is only one way to win this- white must play Rh1 immediately:1. Rh1 Kb4If black plays Ka4, white will cut the king off with Kc3, and then white will play Ra1 followed by Rxa2, and then will go back to win the h-pawn and the game. If black pushes h4, white plays Ra1 followed by Ra2+. Finally, if black doesn't play the king to the 4th rank, white again wins with a simple Ra1 and Rxa2. Continuing:2. Ra1Any other move, and black plays Kb3 followed by Kxb2 for the draw. Continuing:2. ......Kb3 (h4 3.Ra2+-)3. Ra2!This move looks difficult to find, but here is the thing- you know the problem is white to win, so, with the threat of Kxb2 being unstoppable, what else is there here but Rxa2 that even has a prayer of winning (it is the only chance of preserving the pawn)? Now, the key to this move winning is not easy to see (unless you have spent time on similar chess endings like I have). It is this idea that is actually the reason Susan calls this a "must know ending" I believe. Continuing from 3.Ra2 above:3. ......Ka24. b4 h4If black plays Kb3 or Ka3, white just pushes b5 and nothing fundamental changes from what follows below. Now comes the part that is "must know". White's pawn is safe- if the black king attacks it, white just pushes forward towards his queen, but there is something about black's pawn that costs him the game.....5. Ke3!Also 5.Ke4 wins- white has time to stop black's pawn- with Ke3/e4, white has entered the square formed by e4-h4-h1-e1- a visual aid that is very useful in quickly determining that a king can capture a passed pawn before or immediately after it promotes. Now, if black pushes the h-pawn to h3-h2-h1, white will reply with Kf3/f2-Kg2-Kxh1 while black can do nothing about white's pawn since every king move gives white the time to push the pawn. White wins.
1.Rh1! Kb42.Ra1 Kb33.Rxa2!! Kxa24.b4! +- wins because the black king can't capture the b pawn and the white king can capture the black h pawn.Marcelo
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