2. The basics of rook and pawn endings
A common strategy for white is to sacrifice one of his pawns, to aid the other's advance. It is, therefore, essential to first master the resulting rook and single pawn endgames.
In the above position, black to move draws with 1. ... Rb6. White cannot advance his king. If he tries to maneuver his rook to the sixth rank to allow his king to advance, black will trade rooks leaving a drawn pawn and king ending. His only means of making progress is to advance the pawn by 2.f6 this will allow Kg6 next move threatening mate
Black must switch his rook back to where it can attack vertically. 2. ... Rb1 3.Kg6 Rg1+. There is no way for white to escape the checks. There is no room for him to hide behind the pawn and if he tries to escape the checks by retreating toward the rook, the pawn will be left unguarded and at the right time black will switch his rook to attacking and winning the pawn. A draw.
This is even easier. After 1. ... Rb6 there is no way for white's king to advance even after h6. Another draw.
In the above position, white can also draw with Rb8. He then shuttles his rook back and forth Rc8, Rb8 etc. and there is nothing white can do to him.
This time passive defense doesn't work. 1...Rb8 2.Kg6 Rc8 3.f6 Rb8 4.Rh7 threatening mate 4...Kg8 5.f7+ Kf8 6.Rh8+
Passive defense doesn't work because this time white has room to get his rook to the other side of the king, to the side away from black's rook.
This is the Lucena position. It is won for white. Black's only hope is to try and check the white king when it comes out from behind the pawn. White wins by playing 1.Rh2+. The black king is forced to the g file where it provides cover for he white king against checks. 1. ... Kg6 2.Kg8 Now, the only way black can stop the pawn from queening is to capture it, but this loses the rook 2. ... Rxf7 3.Rg2+ Kf6 4.Rf2+ Ke6 5.Rxf7 .
The Lucena position is more interesting with the black king on the other side of the pawn. In our endgame, this seldom happens because the black king is normally on the h file after capturing the h pawn. But in the interest of mastering the Lucena position let us look at it.
Again white begins by checking the black king. 1.Rd2+
Now, if black moves to the e file, white wins the same way as he did in the last section. To avoid this, black moves his king to the c file. 1. ... Kc6 White has forced the black king further from the pawn. Now, he must make the precise move 2.Rd4. This is called "building a bridge". I guess it is a matter of taste whether you think this is an apt description. If black just makes a waiting move, 2. ... Rg2 3.Ke7 and black must start his checks.
3. ... Re2+ 4.Kf6 Rf2+ 5.Ke6 Re2+ Up until now, white has been careful to keep his king touching the pawn in order to protect it, Now, he finally breaks the bond. 6.Kf5 Rf2+ 7.Rf4 This is the bridge. The white rook protects the white king from checks and the black king is too far away to stop the pawn from queening. White wins.
But black doesn't have to let white build the bridge. Black could have played 2. ...Kc5 chasing the rook away. White, however has an alternate way of winning in this case 3.Rd8 Kc6 4.Ke7 Re1+ 5.Kf6 Rf1+ 6.Kg6 Rg1+ 7.Kh5 Rh1+ 8.Kg4 Rg1+ 9.Kh3 Rf1 10.f8(Q)
The Lucena position with a knight's pawn doesn't occur in our ending but in the interest of mastering the Lucena position, let us look at it anyway.
1.Re2+ Kd6 2.Re4 Kd5 now the alternate method of winning based on Re1 doesn't work. In the previous example, white needed 2 files to the right of the pawn to zigzag towards the black rook without stepping in front of the pawn or the white rook. This time the 2 files to the right of the pawn do not exist. Any zigzag maneuver would require stepping in front of the pawn or rook and allowing a skewer. Fortunately, there is another alternate 3.Rg4 Ke6 4.Kf8 Rf1+ 5.Ke8 and white wins.
Black is lost in the above position no matter what he does but he has some resources which allow him to confuse the situation. No problem for a Grand Master who can find the solution over the board but for an ordinary player who has been playing for hours to reach the Lucena position and who only has a few minutes left on his clock, the confusion can cost ½ a point. So let us look at the above position more deeply. Suppose it is black" s move and he plays
1...Ra1 now 2.Re2+? Kf6 and white can't play 3.Kf8? Ra8+ 4.Re8 Rxe8+ 5.Kxe8 Kxg7 draw. In order to win this white must play 2.Rh2 Rg1 3.Kh7 Kf7 4.g8Q+ Rxg8 5.Rf2+ Ke7 6.Kxg8 winning.
Another attempt to confuse white is:
1.Re2+ Kd6 2.Re4 Rh2 3.Kf7 Rf2+ 4.Kg6 Rg2+ 5.Kf6 Rg1 Black is not cooperating with the bridge building plan. What do you do? 6.Re6+! Kd7 7.Re5 Rg2 8.Rg5 and you built the bridge anyway.
The rook pawn endgame is not so easily won.
White cannot get his king out from in front of the pawn. 1.Ra2 Kf7 2.Ra8 Rg3. Even if the black king were on d7, it would be impossible. Only if the king were cut off at c7 could white win.
We have learned that it is very difficult to queen the rook pawn. Therefore, if white is going to sacrifice a pawn, he will sacrifice the rook pawn and keep the bishop's pawn. Thus, we need to look more carefully at bishop pawn endings.