Basic Rook and Pawns-Is this winning?

I just wanted a second opinion, as I didn't know enough about rook and pawn endgames to prove him completely wrong using only words.

Yeah, I believe this position is a draw also.

After 1. Rd7+ Rc7 2. Rd6 Rc6 3. Rd7+ Kb6 4. Rf7 it is impossible for black to win 

I think it may be a draw with black to move, too. 1. ... Rf8 saves the pawn, but white's rook cuts off the black king from helping, then the white king gets in front of the pawn.  ie 1. ... Rf8 2. Kc1 f4 3. Kd2 f3 4. Ke1 f2+ 5. Kf1, then 6. Rd2 and white wins the pawn.

I'm no endgame expert, though. What does everyone else think?

--Fromper 

Black shouldn't give up his f-pawn so easily. 1. Rd7+ Rc7 2. Rd6 Rf7 3.Rxh6 f4. Black can't force a win, but he has winning chances, unlike the other line.

1. ... Rf8 2. Kc1 f4 3. Kd2 f3 4. Ke1 f2+ 5. Kf1, then 6. Rd2 and white wins the pawn. I'm no endgame expert, though. What does everyone else think?  -- Fromper

3...Rd8+! 4.Ke1 Rxd1 5.Kxd1 Kc6 and White is completely losing. I think simple rook endings are trickier than they seem, and even theoretically drawn positions are often won or lost in practice. Heck, I still don't fully understand Lucena.

it's a theoretical draw, but Black has practical winning chances. It's good to keep both aspects of the position in mind, especially when you're comparing this position to others where it's both a theoretical and a practical draw.

"Indeed, as Likesforests put it, simple R endings are trickier than they seem."

An average player knows maybe 6 rook and pawn vs rook positions, but a good tournament player knows 40-50, and Nunn wrote a book on the subject. That provides a clue as to how complicated such positions really are.

Yes, rook and pawn are extremely complicated...

But everyone has to start somewhere.

Absolutely! And about 1 in 9 endings are rook endings, so we're definitely getting good bang for our buck by studying them. Also, the first 3 positions you learn (Lucena, Philidor, Vancura) are much more important than the last 3 positions you learn.  

This is probably a win. After 1. Rd7+ Rc7 2. Rd6 Rf7 3.Rxh6 f4 Black is threatening to queen the f pawn. The pawn can't be stopped by the White king, so White has to immediately move his rook back to the first rank. After 4. Rg6 Rh7 5. Rf6 Rh4  Black wins the h-pawn while protecting the f pawn.

Black's rook is passively placed on h4, all it does there is protect the pawn. It needs to be helping the pawn advance, or attacking White's pawns. To do this Black would like to get the rook in front of the pawn with ... Rh1+ and ...Rf1. To prevent this check, White has to play 6. Kb2 but then he has no more useful moves after 6. ... b4 7. a3 a5  8. ab ab. The only good move is 9.Ka2  

Black then makes progress by shifting his king to e7 to drive the White rook away from its ideal position. If the White rook stays on the f file, Black's king advances to guard the f pawn, freeing his rook for active duty. If the White rook stays on the sixth rank the pawn is free to advance.

What about 1. Kc1  Rf8 (or ..f4) 2. Rg1

This is probably a win. After 1. Rd7+ Rc7 2. Rd6 Rf7 3.Rxh6 f4 4. Rg6 Rh7 5. Rf6 Rh4  Black wins the h-pawn while protecting the f pawn.

Splane, good analysis, but White has a hidden defensive resource.

5.Rg4! and now White's rook threatens the Black pawn and defends his own pawn. If 5...f3 6.Rf4 settles the draw. So 5...Rf7 and White is free to proceed with his original plan of 6.Rg1. Note, 6...Rh7 can again be met by 7.Rg4!.

If White missed this defensive resource or played 4.Rd6? then maybe play would have continued as you explained. An interesting and tricky position.

What about 1. Kc1  Rf8 (or ..f4) 2. Rg1

Well, after 2...Rf6 White cannot win the h-pawn. And 3.Rg6+ doesn't help because it only forces Black's king to move where he should go anyway 3...Kc6. We can stop there and say this position looks better for Black than the mainline.

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