How to play with your rook vs two connected pawns...
Let's first look at a position where the kings are far away.
This isn't a critical position, but it is an instructive one.
White wins by attacking the most advanced pawn with his rook.
Now the pawns can't move without being captured. (1...h4; 2.Rxg4 or 1...g3; 2. Rxg3). So the king moves. 1...Kb6;
This allows the rook to intensify the attack with 2.Rg5,
Now the backward pawn is under attack.
If it moves forward the rook will take the g-pawn, after which the h-pawn will fall as well.
If the g-pawn moves, the rook will take the g-pawn (and the h-pawn next). And if the pawns don't move, the rook will take the h-pawn (and the g-pawn will be lost too).
As it turns out, Black has no useful moves and loses.
The same position, only Black has the move. Would this make a difference?
Well, in this position the pawns haven't advanced far enough. The rook is just able to stop them both.
attacking the g-pawn, therefore forcing h4,
2...h4 (protecting the g-pawn but allowing Rg4);
This wins both pawns again. This time it's a close call, because the pawns have further advanced 3...Kb6; 4.Rxh4, g2; 5. Rg4, g1Q; 6. Rxg1 (just in time).
Starting to run with the other pawn (from the initial position) doesn't help either. 1....h4; 2.Rg8, g3; 3.Rg4, winning again.
Now we've reached a critical position. If the pawns can make it to the third rank, the lone rook isn't able to stop them.
If you're playing White and you have to move, you know what to do right?
Right! Play 1.Rg8 (followed by Rg4) stopping the pawns just in time.
If it's Blacks turn to move first, the pawns will reach the third rank and he'll be winning.
1....h3! (g2 wins as well);
and one of the pawns will promote.
Rule: connected pawns on the sixth (third) rank win against a rook if the kings aren't involved.
If this is clear to you, let's look at some positions where the kings are involved.
Here the black King is in front of the pawns. Black is able to draw.
1....Kf2; and White can't allow the pawn to promote, so his rook needs to stay on the e-file and his king has to cover the queening square. 2. Kd2,
2...Kf1, 3.Re3, f2; 4.Rxe2,Kg1
White has nothing better than to exchange his rook for the last pawn.
Getting the king in front of the pawns is almost always good.
Are you following so far?There's more to discover about this endgame.