How does white progress towards getting checkmate in the above position? Use the rook to hem in the black king. Here’s a simple technique: First move the rook: Rb4.
Notice, in the above position, that the rook has created a wall against the black king, a wall from a4 to h4, preventing that king from escaping to the top area of the board. The best that the defender can do is attack the rook. The first move for black is Kd3, getting us to the position below:
From the position above, white moves left with the king and black does also:
The above position is after white and black moves of Ke5 and Kc3. Now the rook is attacked and needs to move. Don’t abandon the wall, however. The best kind of move with this technique is to move the rook to the right, with something like Rh4:
It’s time we consider what white and black are trying to do. The black king needs to get as close to the center of the board as possible. Why? Checkmate can only come, in this particular endgame, when the defending king is on the edge of the board, on one of the squares shown by “X’s” below:
White’s objective is to drive the defending king to one of these squares and then set up the attacking king and rook in a way to force checkmate. Black tries to avoid all of the squares marked “X” in the above position.
Black has just moved Kd3 in the above position. White now makes a waiting move. The reason for it will soon be explained.
Why did the rook move slightly to the left, from the h4 square to the g4 square? It makes possible the king-to-king lineup that now follows:
This is the kind of position the attacker tries to get to, with the attacker’s turn to move. Watch what happens after white moves the rook to g3:
White has just moved the rook down from g4 to g3. In standard modern chess notation, this is Rg3+, meaning the rook moves to the g3 square, checking the king.
Now notice three squares between the two kings: d4, e4, and f4. The white king makes a small wall of its own, blocking the black king from escaping towards the center of the board. In other words, the black king is now forced back towards the lower edge of the board. It will eventually be checkmated there.
Now we can see why the white rook made that waiting move. It needs to be the attacker’s move when the kings are lined up that way, otherwise the defending king moves to one side to escape the little wall made by the attacking king. In the above position, two walls force the black king towards the edge of the board.
The black king, which was in check, just moved to f2, attacking the rook. White will now move that rook to prevent its capture, for its loss will make an immediate draw. White can win this endgame, but it requires patience. Where would you move the rook?
Be aware that the rook’s wall (squares a3 to h3) should not be abandoned. It has taken some work to establish this blockade of the defending king and it needs to be maintained. We might as well move the rook to the left, as far as possible: Ra3.
You may have wondered why the white king should not move Kf4 in the above position, for it defends the rook. There’s nothing really wrong with that move. But with the technique we are now using, it’s best to keep and white king and white rook separated.
Consider now the position after white moves the rook and the black king moves in the same direction.
The black king has just moved to the e2 square. White needs to approach with the king but where should that white king move?
Remember that a direct opposition is ideal for the attacker when it is the attacker’s move. In the above position, it would be black’s turn after white moves Ke4, so that is not the best move. White should move Kd4 instead.
Now if black moves Kd2, white can repeat the moving of the big wall made by the rook.
Does the above position look familiar? It is a key position for moving the rook wall. The rook now moves to the a2 square, for the white king is blocking the defending king, which will be forced back to an edge of the board.
After white moved Ra2+, black moved Ke1. What should white do now? Remember the pattern: Do not move the white king to e3, the blocking position, for it would then be black’s turn. Move the king to d3 instead.
We now see the beginning of the final stage of the mating net. White has just moved Kd3, forcing the defending king to the right. If black moves left with Kd1, white wins with checkmate: Ra1++. Black must move Kf1. If this were an actual game, it would be no surprise for black to resign. There’s nothing wrong with giving up in a hopeless position.
Black has just moved Kf1, above, to avoid immediate mate. What should white do? Chase that black king towards the other edge of the board, the edge on the right.
In the above position, white has moved Ke3 and Black has moved Kg1, to avoid immediate mate. But the defending king is running out of room. It will soon be forced to move to the left and into a position allowing checkmate.
White has just moved Kf3. If the black king move left to the f1 square, the white rook checkmates it with Ra1. Black has only one choice that delays mate, although it’s only a short delay.
Now, in the above position, the worst mistake white could make would be to move the rook to the g2 square: Rg2=, for that would be stalemate. (A draw is halfway between a win and a loss.) The correct move is to continue following with the white king: Kg3.
In the above position, it’s now black’s turn, with only one legal choice: Kg1. If only that black king had a passport to cross the border and escape that chess board altogether!
The we finally have the final setup for checkmate: Ra1++ (mate).
This particular technique is not the only way to force the defending king to the edge of the board, but it works.
Grigoriev chess study (beginning with one pawn on each side)