This is the fifth and last part on rook vs two connected pawns.
If you missed the previous parts, you can find them under
rook vs two connected pawns
rook vs two connected pawns (part two)
rook vs two connected pawns (part three)
rook vs two connected pawns (part four)
White is able to draw, due to Black's bad king position.
1.Ra2+, Kb8; 2. Rb2+, Kc8;
Returning to the a-file wasn't an option, because of the repetition of checks.
This threatens mate. Black has no other defence than moving forward with his king. If he returns, there's a perpetual check.
3....Kd8; 4.Kd6 (following the black king and keeping the mating threat alive),
Returning with the king still isn't an option, because the king can't escape on that side if the board.
4....Ke8; 5.Ke6, Kf8; 6.Kf6, Kg8;
And now White has to repeat his checking maneuver.
7.Ra8+, Kh7; 8.Ra7+,
Because of the possible perpetual, the black king has to descend along the h-file now.
8....Kh6; 9. Ra8!,
And White threatens mate again. By now, you'll probably recognize the idea.... Returning with the king leads to a perpetual, so the king has to descend even further.
9...Kh5; 10 Kf5, Kh4; 11 Kf4;
And finally, in this position, Black has run out of options. If the king goes to h3, it will be mated, so he has to return up the h-file. This will finally allow a draw by repetition after 11....Kh5; 12.Kf5 etc..
I recommend you to go over this example several times, until you're an expert at it.
Why this is important?
Well, for years I thought this example to be a nice study, without much practical value. Until I recently saw some high-level games end in a draw due to this motif. Wouldn't you like to draw a game this way?
You should be able to solve this position by now.
White to move draws.
Yes! Use the motif found in the previous example!
1.Kf5 (threatening mate), Kh4; 2. Kf4, Kh3; 3.Kf3, Kh2;
And here it looks like the white threats have come to an end. But have they?
With the black king on h2, Black can't play 4...a2 as this loses both pawns (due to 5.Rb2+). Due to this bad king position, Black's threats have been stopped and White has reached a draw. White heads for the pawns now.
4. Ke3, 4...Kg3 (White will reach the pawns after 4....Kg2; 5.Kd3, Kf3; 6.Kc2).
The black king has nothing better than to retreat.
5...Kh4; (5...Kh2 runs into 6.Rb1)
6. Kf4, Kh3; 7.Kf3,
Now 7...Kh2; will even lose to 8.Rb1,
Black has no better than to play
7...Kh4 and a draw by repition will follow.
And this ends the series on rook vs two connected pawns.
I hope you've enjoyed it and learned something as well.