In the initial position, it is the White king that is stopping the Black a-pawn. But in order to win, the White king has to support the g-pawn in its advance. Also, the White rook has to keep the Black king from advancing toward the g-pawn.
The White rook can cut off the Black king from its 4th rank by playing 1. Re5, and then the rook can play 2. Ra5 to keep an eye on the Black a-pawn as well. Then the White king can be transferred over to support the g-pawn. Rather than do my usual exhaustive analysis (it would have taken about a year on this problem), I decided to play the White pieces against my computer. Here is the scoresheet:
It looks like Re5 followed by Ra5 will allow the White K to support the advance of the g-pawn. That must be the right plan. I doubt that there is a tactical trick involved here, it looks like it’s just going to be a grind.
The first move is easy, and is likely the only winning move: I would cut the black king off from the 5th rank first in order to keep the pawn safe:
1. Re5
Now, in a lot of endgames like this, the player with the rook can sacrifice the rook for the bishop and pawn to reach a winning K+P vs K endgame, but in this position, white’s pawn is too far from the squares a4 and b3 where such a sacrifice would take place, so black’s king will win at g3 before white’s king can get over to defend it. So, the other way to often win this is to bring the king over to support the pawn’s advance while using the rook to keep black’s pawn under observation. Black will keep the king close to the g-file:
1. …..Kf6 2. Ra5
Not the the only winning move, but this move is the most direct- prevents a3 and sets the stage for bringing the white king to the kingside. Continuing:
2. …..Kg6
Black can do nothing to frustrate white’s plan, so his moves are not critical at this moment. Continuing:
3. Kb4 Kf6 4. Kc3
White need only be careful to not play the king to the 5th rank allow black to play Kf5/g5 and Kg4. Continuing:
4. …..Kg6 5. Kd4 Kf6 6. Ke4 Kg6 7. Kf4 Kf6
Now white can use the rook to push the king back:
8. Ra6 Kg7 9. Kg5 Kf7 10.g4 Bd1
There is no hope with king moves here. This move is the most frustrating for white, but he can still win with proper technique:
Mate in 38 moves was written by inserting the position in Nalimov’s tablebase the existence of which I learnt from Yancey. It did not give variation but just the number of moves but I reported wrongly as 38 moves instead of 39.
For such positions it is difficult to give variations but only plan can be made like cutting of K from 5th rank ,keep the R behind black’s P and move K to the right side of the board nearer to the white p etc. Any variation shown is a plausible one to assess the plan.
Re5 and Ra5 should be winning.
In the initial position, it is the White king that is stopping the Black a-pawn. But in order to win, the White king has to support the g-pawn in its advance. Also, the White rook has to keep the Black king from advancing toward the g-pawn.
The White rook can cut off the Black king from its 4th rank by playing 1. Re5, and then the rook can play 2. Ra5 to keep an eye on the Black a-pawn as well. Then the White king can be transferred over to support the g-pawn. Rather than do my usual exhaustive analysis (it would have taken about a year on this problem), I decided to play the White pieces against my computer. Here is the scoresheet:
1. Re5 Kf6 2. Ra5 Kg6 3. Kb2 Kf6 4. Kc3 Kg6 5. Kd2 Kf6 6. Ke3 Kg6 7. Kf4 Kf6 8. g4 Bc2 9. Ra6+ Ke7 10. Ke5 Kf7 11. g5 Kg7 12. Ra7+ Kg6 13. Kf4 Bb3 14. Ra6+ Kg7 15. Ra7+ Kg6 16. Ra6+ Kg7 17. g6 a3
I freaked out when the computer played this move. I realized that I couldn’t take the a-pawn here.
18. Kg5 a2 19. Ra7+ Kf8 20. Kf6 Ke8 21. Kg7 Bc4 22. Kh8 and White is winning.
Lucymarie Ruth
It looks like Re5 followed by Ra5 will allow the White K to support the advance of the g-pawn. That must be the right plan. I doubt that there is a tactical trick involved here, it looks like it’s just going to be a grind.
The first move is easy, and is likely the only winning move: I would cut the black king off from the 5th rank first in order to keep the pawn safe:
1. Re5
Now, in a lot of endgames like this, the player with the rook can sacrifice the rook for the bishop and pawn to reach a winning K+P vs K endgame, but in this position, white’s pawn is too far from the squares a4 and b3 where such a sacrifice would take place, so black’s king will win at g3 before white’s king can get over to defend it. So, the other way to often win this is to bring the king over to support the pawn’s advance while using the rook to keep black’s pawn under observation. Black will keep the king close to the g-file:
1. …..Kf6
2. Ra5
Not the the only winning move, but this move is the most direct- prevents a3 and sets the stage for bringing the white king to the kingside. Continuing:
2. …..Kg6
Black can do nothing to frustrate white’s plan, so his moves are not critical at this moment. Continuing:
3. Kb4 Kf6
4. Kc3
White need only be careful to not play the king to the 5th rank allow black to play Kf5/g5 and Kg4. Continuing:
4. …..Kg6
5. Kd4 Kf6
6. Ke4 Kg6
7. Kf4 Kf6
Now white can use the rook to push the king back:
8. Ra6 Kg7
9. Kg5 Kf7
10.g4 Bd1
There is no hope with king moves here. This move is the most frustrating for white, but he can still win with proper technique:
11.Kh5 Ke7
12.Rc6 Ke8
13.Rd6 Bb3
14.Rd3 Bc2
15.Ra3 Bd1
16.Ra1 Bb3
17.g5 Kf8
18.Kh6 Bc2
19.g6
And now the black king can no longer go to f8/g8 since the back rank mate will be fatal to black’s bishop. Continuing:
19. ….Ke7
20.g7 Bb3 (Kf7 21.Kh7 Bc2 22.Kh8)
21.Ra4 wins easily now.
Too hard.
Mate in 38 moves.
Of course 1.Re5 is the right move.
Mate in 38 moves was written by inserting the position in Nalimov’s tablebase the existence of which I learnt from Yancey. It did not give variation but just the number of moves but I reported wrongly as 38 moves instead of 39.
For such positions it is difficult to give variations but only plan can be made like cutting of K from 5th rank ,keep the R behind black’s P and move K to the right side of the board nearer to the white p etc. Any variation shown is a plausible one to assess the plan.