Yep, I know, I'm no Chernev! But here is my two cents on a game I recently completed on RHP . Game 4064642
I start by posting the comments of the opeining stage of the game, I'll follow up with the middlegame and with the endgame in this same thread. Let me know your ideas and correct my many mistakes (I mean chess mistakes, my English is bad and we'll have to live with it).

Here we go:
1.d4 {The queen's pawn game. I chose this first move when I want a
more positional game as compared to the e4 openings, that are often
more tactical.} 1...Nf6 {This is a very popular reply to d4. It is
probably more flexible for black than d5. Black keeps white in the
dark about how he plans to continue, and can keep challenging the
center with pieces via an Indian defense or can attack with pawns via
e6 and d5.}
2.c4 {I go on with my plan, I have a good control of d5 and e5 thanks to my pawns.} 2...c5 {Immediately challenging the center. This is called the Benoni. In d4 opening black often strives for a freeing c5, undermining white's strong center, and in this case black chose immediately a very aggressive continuation.}
3.d5 {I don't know much of the Benoni, but at this point I was pondering between d5 and e3. I ruled against e3 because I didn't want to exchange a central pawn for a side one, and I was uncertain about my chances of effectively using an eventual couple of hanging pawns in c4 and d4.} 3...b5 {Black doesn't waste his time in this game, and goes for the Benko gambit. After my advance d4-d5, it seems quite logical to undermine my central pawn via a pawn break, but I didn't really expected it so soon. }
4.cxb5 {I don't see any serious alternative than accepting the pawn for the moment.} 4...a6 {Black sacrifices a pawn for a lot of activity on the queenside.}
5.b6 {and I refuse! Sure, he gets anyway to develop his queen with the recapture, but at least he doesn't get total freedom for his rook and bishop.} 5...Qxb6 {Quite logical, and although in general it is not a good idea to develop the queen too early, in this case the queen
doesn't seem in danger. Black has achieved his goal of speeding up his development. He has two pieces out against white's zero. White has a pawn in d5 which can be an asset to cramp black, but also a liability beacuse it needs protection. White has also a possible outpost in c4, which seems juicy for a knight, especially since the black's queen is in b6. }
6. Nc3 {time to develop.} 6...g6 {Again, quite logical, since trying to
develop the dark square bishop via e6 would have left black with an
unfortunate pawn structure. }

7.Nf3 {The plan is simple, to bring this knight to c4.} 7...Bg7 {Black correctly finshes his finachettoing.}
8.e4 {To avoid possible tactics connected to Nxd5 and a possible weakness of the knight in c3 or of b2, and also to free the light square bishop that will support the knight in c4..} 8...d6 {freeing his bishop.}
9.Nd2 {The knight continue his trip to c4.} 9...O-O {The king goes to safety.}
10.Nc4 {White completes his plan with tempo.} 10...Qc7 {By move 10 it seems that white has a bit more space. In exchange for his position that is a bit cramped on the queenside, black has a nice lead in development and a king that sits safe and sound on the kingside. If white can develop his pieces rapidly, he should stand slightly better in the middlegame. If black can pose enough threats to force white into an unnatural development, he can use his lead in development for an attack against white's king (who is still quite vulnerable in the center)}

11.Be2 {This seems unabitious but white really wants to castle by now, and in d3 the bishop has less scope. Also, g4 could have been used by black to bring an attack on the kingside.} 11...Nbd7 {Black goes on with his own development. Probably he will try to chase the knight away from c4 via b6.}
12.O-O {White put his king to safety, a natural follow up to the previous move. Bg5, trying to exploit the undefended nature of e7 to pin the knight, or Bf4, getting a nice diagonal and putting some pressure on the queen in c7 could have been more enterprising.} 12...Nb6 {And white has to depart from his beautiful knight. At this
point, it costed me three tempi to put the knight there, and I got in
exchange a tempo of the queen, and two tempi of the knight. My plan is to sit tight and let him spend another tempo to capture, and
replace the knight with my bishop. Well, in c4 I rather have a knight than a bishop, but you cannot get anything for free. }
13.a4 ?!{Ok, this maybe was too ambitious, and Bf4 or Bg5 are probably better. But I was under the impression that black's queenside was not very strong. I was wrong, I didn't consider the fact that black has a semi-open b column for his rook, and that b2 is now backward.} 13...Nxc4 {Naturally.}
14.Bxc4 {The only move.} 14...a5 ?! {Surprising, mainly because it gives white an outpost in b5, and there was no need for it. Rb8 looked natural and strong.

Ok, let's wrap it up for the opening stage.

Material is even.

White has more space. His bishops are both quite unhappy, the dark
square one because of the weakness of the backward pawn in b2 (and
the presence of the black indian bishop), the light square one
because of lack of mobility in his current position. The king is safe
but the lack of a piece in f3 doesn't make him so invulnerable to
attack (for the moment no attack is in the air though). White has a
possible outpost in b5 that looks nice, although care should be put
in the defense of that point against the mounting pressure of black
rooks, bishop and queen.

Black has a slight lead in development, his king is rock solid and he
has a gigantic pawn island that can become troublesome in the
endgame. His bishop in c8 is a bit unhappy for lack of exploitable
lines. His rook in a8 has a nice and natural developing square in b8.

Overall, black stands better. He can grab the b file and put
pressure on b2. He should probably seek simplification to relieve his
crampiness.
White has to solve a few problems with his bishops, and the b2 pawn
can be a pain. His seems to have most of his play on the queenside,
but should probably strive to seek counterplay in the center via Re1
and Bg5 (although risky).

There is a problem in the first fen I posted, the edit button went on vacation so I can't fix it. The fen showed in the post is after move 5, not move 6.

I think 57...Rd4+ is a mistake.

Doesn't 57...Rc3+ force the win?

Originally posted by Red Night
I think 57...Rd4+ is a mistake.

Doesn't 57...Rc3+ force the win?

This looks like a win for black with proper play, but it's not so easy to suggest a winning continuation. For the line Red Night proposed: 57. ... Rc3+ 58. Kd2 if 58. ... Kc4 58. Rg1 and it's not totally clear to me how black can make progress. e.g.
a) 59. ... Kb3 60. Rb1+ Kc4 [ or Ka2 61. Kxc3 Kxb1 with obvious draw]
b) 59. ... Rh3 60. Rg8 and if black tries to get his king out of the way with 60. ... Kd4 61. Rg4+ pushes the king back, while 60. ... Kb3 61. Rb8+ and black's king has to go back to c4 or 62. Rc8 draw.
c) 59. ... Kb4 60. Rg8 and we fall in previous cases except for the move 60. ... c4?? 61. Rb8+! and now it's white who wins easily.

I don't see alternatives to 58. ... Kc4, beacuse if white is allowed to play Rg4, cutting the black king off, this position should be a draw from there.

Please let me know if there are holes in this analysis. I'll finsh the comments on the middlegame and on the endgame later this week. Please also comment on the opening stage, especially if you have experience with Benoni / Benko gambit.
Thanks!
J34

Originally posted by Joan34
[fen]8/8/6R1/2pk4/2r5/4K3/8/8 w KQkq - 0 1[/fen]

This looks like a win for black with proper play, but it's not so easy to suggest a winning continuation. For the line Red Night proposed: 57. ... Rc3+ 58. Kd2 if 58. ... Kc4 58. Rg1 and it's not totally clear to me how black can make progress. e.g.
a) 59. ... Kb3 60. Rb1+ Kc4 [ or Ka2 61. Kxc3 Kxb1 with o ...[text shortened]... opening stage, especially if you have experience with Benoni / Benko gambit.
Thanks!
J34

My Sigma engine ( at 30secs per move) gave this line as +2.43 for blacks move 58:

+2.43 58... Kc4 59. Rg6 Kc3

Marching the black king down ahead of the pawn....possibly a winning line for black. In the game (according to this analysis) blacks lead ebbs away over the next few moves. Interesting endgame worthy of more study.

This is the position, white to make move number 58. Here I played 58. Ra6?. From there, Mahout seems right to me in pointing out that after 58. ... Kc4!, I'm very well lost. To no avail I would check with 59. Ra4+ 60. Kc3 with the same idea pointed out by Mahout. The black king is in front and can safely stay in front of his pawn.

Did I miss a draw (well, I got it eventually, through a number of mistakes on both parts) with 58. Rg1 Kc4 59. Rc1+ ? It seems so.
I'm working through the middlegame now, although it seems that there is much more interest on the endgame - no surprise, the endgame is the reason I chose this game to analyze in the first place. Feel free to comment on any part of this games.
J34

I agree with your computer, the only way to get a winning position out of these single pawn rook endgames relies on restricting the movement of the enemy king, the rook being where it was would have done that and allowed black to slowly wander his king and pawn down to the first rank.