How to win this endgame?

Rp vs. R is not always drawn. Check out the Lucena position.

No, definitely not. Anyone who thinks the endgame must be easy because there aren't a lot of pieces left on the board should look at this position and find out how deep the rabbit hole really goes...

Thanks to everyone who posted, it is very helpful to hear the opinions of players who are stronger than me.

I was intrigued by Am64360_2's idea of exchanging rooks via 6. Rea5 f6 7. Ra8 Rxa8 8. Rxa8+ Kf7 but instead of 9. a5 (moving the pawn away from the white king) trying 9. Kf3, moving the king closer to the pawn since it's obvious that that pawn won't queen without help from the king. With 9. ... Ke6 10. Ke4 White's king takes opposition but then there is the possibility of black breaking thru on the King's side and the threat of a queen there.

For what it's worth, there are pawnless endgames that are even more complicated than ones with pawns. For example, there is a KQNvKRBN endgame with a DTC of 517 moves (white can convert to a winning endgame, despite nearly material equality):

[EDITED - initially I found winning moves against all sidelines without playing Rb8+ - lol]

The position under discussion is an interesting problem. My blitz instinct was to slam the second rook on the seventh rank with 1. Rdd7, but I believe this is an error (maybe even enough to give the win away). Why? Simply because it allows black to capture a pawn with a threat of mate, which is a gift to black.  1. Rd5 is a possible alternative that creates problems for black. Now white threatens to take a pawn with check, so 1. ... Rxc4 2. Rxe5+ is not so good for black. But black has only two ways to protect the e-pawn, both of which leave a skewer for white. Prospects look good.

Sometimes general ideas such as a pair of rooks on the seventh is very valuable can be deceptive (I recall winning one online game where my opponent had two rooks on the seventh for most of the game. I played badly to get to this position, but the rooks were never a winning advantage, due to lack of a way to cash in. In this game it is a different matter of rather a lot of black counterplay).

 I don't understand your comment.  The move Rb8+ is made to take away black's castling privilege.  As I stated, the line is an idea that might work as black is left with three isolated pawns while white has three connected pawns.

The above is another possible line.  Black cannot use his king to help promote the a pawn because he needs to defend against white's connected pawns.

LOL. Nice thread from the OP and interesting analysis that followed. I learned a lot here.

Elroch, in your line, 32... Ra1 wins.

Yes. I'll leave that in the diagram for a laugh. What matters is that the position is definitely winning for white.

I still don't see a win though.

With all due respect to the players better than me who have contributed, this endgame is beyond our ability to give any high quality analysis on... and even if we managed to it could easily be refuted later... GMs can't even give set in stone answers for endgames simpler than this is what I mean.

Here's me as black vs Rybka (take backs allowed lol) in the line you gave.  Sure it ends up giving white an eval of +2.00 but it can't make any progress... I know this engine isn't the best at endgames, just pointing out it's not such a clear win.

So it seems like Rybka was way too eager to advance the c pawn, not only is it too far away from the white king, but it blocks possible rook activity on black's 2nd rank so maybe 33.Rc7 is a try? kind of an ugly move though.  And of course I'd rather be white in a tourney game, white has pressure, but I really don't see a win here.

Wonton, your line is interesting, I was wondering why not 2...Ke6 instead of 2...Kf6 (so that when the pawn is taken there's no check) you showed a similar line this time with Ke8 (which I don't like because in my mind the king has to go forward) so here's a line with Ke6.

Wouldn't Rb8+ win the rook and the game??? Heeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllooooooooooooooooooooooooooooooooo!!!!!

It would win the rook on h8, but white's rook on d4 is hanging so material would stay even.

@orangehonda   30. ... Ke6 and 31. ... Rf8 put a damper on my idea.  I've analyzed it with Fritz 9, and after 20+ moves, it's a win for white.  However, I'd never find the moves on my own.

Dude, the two NMs posting here are right.  Rook and pawn endings bring out the worst in the best of players.  They are just hard to win even if you have an "advantage".  Most of the time, material being equal, they are dead drawn.  Trying to push a win in one is a good way to wish you'd settled for a draw.

So true.  However, they're fun to play around with when there's nothing at stake.

But the side with an edge has a much better chance of winning than the defender, so I don't see why you wouldn't go for it. It is unlikely it would result in anything worse than a draw anyways.

I dunno, sometimes fritz and the like don't find the best defensive moves for the weaker side either... just as long as you don't find any of black's moves unnecessarily helpful to white or somehow questionable... but since I'm not going to analyse it all out I'll just have to take your word for it

I like it much better too now that you've mentioned it.

I'm pleased to have got the first two moves right! Didn't think it would be that difficult after with that powerful c-pawn, but Rybka definitely knows better than me. But then again, maybe it doesn't.

The evaluation numbers given shed light on how surprisingly crude this appears to be. Of course 1 point is for the material, the other is probably mainly for the pawn being advanced (plus any for a questionable claim that the rooks are more active). But we humans know that rook endings with equal pawns on one side of the board, and one side having a passed isolated pawn on the other side, are more commonly drawn than not.

Also, woton was right. 1. Rb8+ Ke7 2. Rb7+ Re8 does of course achieve something of value.