I enjoy solving endgame studies, but many of them are very difficult and that's why many players under 1800 don't find suitable studies for them. In this post, I present some simpler rook endgame studies and also a couple of theoretical positions to give you an introduction to studies. At the end, I have also written explanations to the solutions which should give an insight into how I approached these positions.
All studies with the name of the composer and the date of the composition are taken from Laszlo Polgar's book 'Chess Endgames'. Some studies are not given from their original position. In such cases I have added an asterisk to the name of the composer.
White to play and draw
2. Lucena position
White to play and win
3. Vencura position
Black to play and draw
4. Theoretical position
White to play and win
5. Duras, 1902
White to play and win
6. Troitzky, 1910
White to play and win
7. Cook*, 1927
White to play and win
8. Cook, 1864
White to pkay and draw
9. Stamma, 1737
White to play and win
10. Kruchkov*, 1926
White to play and win
11. V. Platov and M. Platov, 1923
White to play and win
12. Chekhover*, 1949
White to play and draw
Solutions
1. Philidor position
1.Ra3
Now black's king cannot come to e3 and threaten mate. If black is waiting by moving their king or rook, white will keep their rook on the third rank.
1...e3
This is the only way for black to try and make progress.
2.Ra8
White will start giving checks from behind and prevent the black king from entering the position.
2...Kf3 3.Rf8+ Ke4 4.Re8+
And black cannot make progress.
2. Lucena position
1.Rg2+!
White starts with this check to get the black king far enough away from the pawn.
1...Kh7
It makes no difference where the black king goes on the h-file and white wins immediately after 1...Kf6 2.Kf8 and the pawn will promote on the next move.
2.Rg4!
The rook comes to the fourth rank to build the so-called Lucena bridge.
2...Re1
Black prevents 3.Re4, but white can bring their rook to the e-file with assistance from the king.
3.Kf7 Rf1+ 4.Ke6 Re1+ 5.Kf6 Rf1+ 6.Ke5 Re1+ 7.Re4!
That's why the white rook needs to be on the fourth rank and this also shows why the black rook needs to be 2 files away from the pawn (that was the point of white's first move). Black cannot stop the promotion.
3. Vencura position
1...Rf1+ 2.Ke4 Rf6
Black has cut off the white king and tied the white rook to the defense of the pawn.
3.Kd5 Kh7
Black waits for now, but it is important that the king stays on g7 or h7 since white would win otherwise: 3...Kf7?? 4.a7 Ra6 5.Rh8 Rxa7 6.Rh7+ or 3...Kg6?? 4.a7 Ra6 5.Rg8+ Kh7 6.a8=Q
4.Kc5
White tries to bring their king in to support the pawn. Pushing the pawn to a7 also leads to a draw: 4.a7 Ra6 5.Kc5 Kg7 6.Kb5 Ra1 7.Kb6 Rb1+ and black checks the king away.
4...Kg7 5.Kb5 Rf5+!
It is important that black checks the white king away as soon as it reaches b5 since the white rook would be free to move otherwise. Now white cannot make any progress: if the king steps onto the seventh rank, we will continue with the checks and if the king goes back to the fourth rank, the black rook will return to f6.
4. Theoretical position
1.Rc8!
White brings their rook to the b-file without allowing any back rank mate threats.
1...Kd7 2.Rb8 Ra1 3.Kb7 Rb1+ 4.Ka6 Ra1+ 5.Kb6 Rb1+ 6.Kc5
White managed to get their king out of the way and the pawn will promote on the next move.
5. Duras, 1902
1.Rc7+ Kd8 (Not letting white's king out) 2.Rc6 Kd7 3.Rd6!
This is the point of the rook checks. The black king has to take the rook, since the white king can go to c7 and the b7-pawn will promote otherwise. But white can use the black king as a shield after it takes on d6.
3...Kxd6 4.Kc8 Rc3+ 5.Kd8
And the b7-pawn will promote because the rook cannot attack it along the b-file.
6. Troitzky, 1910
1.d6! Rg7 2.Rh3+ Kg8 3.Rg3!
This is the point. Black has to take the rook, but cannot stop the pawn afterwards.
3...Rxg3 4.d7
And white wins
7. Cook*, 1927
1.Rd4+!
White forces the black king onto the third or fifth rank and can force the exchange of rooks afterwards.
1...Kc5 (1...Kc3 2.Rd3+ Kc4 3.Rf3! and white will promote the pawn) 2.Rd5+! exd5+ (2...Rxd5 3.f8=Q+) 3.Kxf5
And the f7-pawn will promote.
8. Cook, 1864
So you need to look for a different solution. If you have solved many endgame positions, you are probably trying to construct a stalemate after black promoted their pawn and will find that the check is correct, but with a different idea.
1.Rb7+ Kc8 2.Rb5!!
Now white's stalemate idea becomes clear.
2...c1=Q 3.Rc5+! Qxc5 stalemate
9. Stamma, 1737
1.Kc4! a2 2.Kb3 a1=N+
White has mate in one after 3...a1=Q. Black can win in many ways after the promotion to the knight. One example line is:
3.Kc3 Nc2 4.Re2 Na1 (4...Na3 5.Kb3 and white loses the knight because of 5...Nb5 6.Re1#) 5.Re1+ Ka2 6.Re7 Kb7 7.Re2
And white loses the knight.
10. Kruchkov*, 1926
1.Re8+!
White deflects the black king so that they can play 2.g7 next.
1...Kxe8 (1...Kg7 2.f6+) 2.g7 Rg8 3.f6!
Black is in Zugzwang and will lose the rook.
3...Rf8 4.gxf8=Q+ Kxf8 5.Kd7 Kg8 6.Ke7 Kh8 7.Kxf7 Kh7 8.Ke7
And white will promote the pawn.
11. V. Platov and M. Platov, 1923
1.Ra3!
This is the right way to distract black's rook. 1.Rg1? does not work because of 1...Rf3 and black will stop the pawn.
1...Rg7 (1...Rxa3 2.d7 and the pawn will promote) 2.Rh3+! Kg8 3.Rg3!!
Now black has to take the rook.
3...Rxg7 4.d7
And the pawn will promote.
12. Chekhover*, 1949
1.d6! a1=Q 2.d7!
As mentioned above, black cannot take the pawn because of 2...Rxd7 3.Ra8+.
Black is currently a queen up, but the position is a complete draw! This might seem strange at first sight, but the queen can only give a check on a2 and if black plays something else, white will promote their pawn.
2...Ra2+ 3.Kg1!
Again, the queen has only one check (on a1) and this leads to a repetition, so this position is drawn.