[highlight]Part 3 Dvoretzky's variation[/highlight]
5.Rc7, Rb3 6.b7



Black now has several possibilities
B1) 6....Kf5       (Dvoretzky)
B2) 6...,Rb1
B3) 6...,g5
B4) 6...,Ke6

Variation B1
6....,      Kf5                Dvoretzky
7.Kc2,      Rb6
8.Rxf7,
I will show later that 8.Kc3,f6! Is a draw.
8........, Kg4

And here we have a further split
(x)9.Rd7  (Dvoretzky)
(y)9.Rg7  (My intended improvement) 

variation B1.x

diagram 6

9.Rd7,      Kh3!!
Here Dvoretzky stops and says draw!
But for us mere mortals a little clarification is helpful.
He further cites Kantorovich that
9...,Kxg3 10.Rd3+,Kg4 11.Rb3,Rxb7 12.Rxb7,g5 wins
10.Rg7,
10.Kc3,Kxg3! 11.Rd3+,Kxh4 12.Rd4+,Kg3
13.Rb4,Rxb7 14.Rxb7,h4!=
10......,   Rb5!
Black has to evacuate his rook from the 6th rank in order to take on g3.
10....,Kxg3? 11.Rxg6+ wins
11.Kc3, 
11......,   Kxg3!
If black hesitates just for one moment his position is lost. 11...., Rb1? 12.Kc4,Kxg3 13.Rd7 wins. (see variation 1y)
12.Rxg6+,Kxh4
13.Rg7  ,Kh3=
diagram 7

A sample line:
14.Kc4,Rb1 15.Kc5,h4 16.Kc6,Rxb7=
with a theoretical draw.

variation B1.y
diagram 6 (repeated)

9.Rg7!, Kh3
9....Kxg3? 10.Rxg6+-
9....Kf5 10.Kc3,Kf6 11.Rc7 wins.
10.Kc3,
Here it is, we have a gained a single tempo over Dvoretzky's line.
10......,   Rb1
10...Kxg3 11.Rxg6+
10...Kg4   11.Rxg6+
10...Kg2 11.Kc4,Kh3 12.Kc5 and the white king reaches the c-pawn 
10...Rb5 11.Kc4, Rb1  and white is a tempo up on the main line.
11.Kc4,  Kxg3
12.Rd7!      
diagram 8

White threatens Rd3+ followed by Rb3 
Bad was 12.Rxg6+?,Kxh4 13.Rg7,Kh3=

12....., Kg2
12....Kxh4 13.Rd4+,Kg5 14.Rd5+,Kg4 15.Rb5+-
and white gets his rook behind the passed pawn.
and perhaps even more important between the enemy rook and his pawn.
13.Kc3!
Renews the threat to put the rook behind the pawn, now a rank lower.
13......., Kg1
14.Kc2! 
And again the same threat. 
Now white wins simple after 14....,Rb4 15.Rd1+,Kg2 16.Rb1

Going to look at this tonight, but I wonder if Nunn treats this position in volume 2 of Nunn's Chess Endings.  Does anyone have the book yet to check?

Thx guys.
(@TN I really hope you can point out a few mistakes )

Okay let's start off. But the analysis will come in a few parts.

Part1. BackGround.
Diagram 1. Hollis-Florian.

The white rook is in front of the passed pawn. And this is easily the worst position. Better is the defence of the pawn from the side and superior is the position behind the pawn.
Just imagine the position above with the white rook on b8 and the pawn on b7. This would be a dead draw: the white king has no shelter near the b-pawn and can't take help promote it. As soon as it approaches the pawn, black will drive it away with a series of checks.
So white is looking to improve the position of his rook.
1.....,      Rb2
Black cuts of the white king on the first rank
2.Ke1,            
The king plans a journey Ke1-d1-c1 when he can move up the board towards the b-pawn.
2......,      Kf6
3.f3!?, 
Preparing the kings journey by removing the pawns from the second rank. White can afford to put two pawns on the third rank, because as it turns out Black has only time to take one of them.
3.....,   Rb3
4.Kd2
A critical moment. Most analysts now continue with the logical 4...Rxf3. But Kantorovich offers another idea 4...Ke6!!. This was further worked out in an excellent analysis by Dvoretzky (2003). 
I believe this to be blacks only way to draw.
4.....,      Rxf3?
5.Kc2?,

Diagram 2

This was eventually shown to a be a draw.
But I think White can win with 5.Rc7! +-.instead 
The drawing lines given after 5.Rc7 by Dvoretzky seem insufficient to me.(we will get into this later)
5......,  Rxg3?
Not the best move, but I've got a very good reason to take this as the main line.
Black's saving line is 5...., Re3! 6.Rc7,Re8
7.b7,Rb8 8.Kd3,Kf5 9.Rxf7+,Kg4 10.Rf4+,Kxg3 11.Rb4
And now the Averbakh/van Wijgerden discovery is 11...g5!!=  (Hollis gave the winning line 11...Kh3 12.Ke2,Kg3 13.Ke3, Kh3? 14.Kf3+-. This was cited by van Wijgerden/Averbakh overlooking that 13...g5 would still have secured the draw ) 12.hxg5,h4 13.g6,h3 14.g7, h2=
6.Rc7!      ,      
White goes for a position where his b-pawn is covered from the side. The spectacular 6.Rxf7+?,Kxf7  7.b7 was shown to be a draw, by both Averbakh/van Wijgerden (correcting Hollis who thought it would win as well).
Sure, black cant prevent the promotion of the b-pawn, but in the meantime he erects a fortress on the kingside.
6.....,      Rg2+       
Now Black is a tempo short for the Averbakh/van Wijgerden saving line: 6...Re3 7.b7,Re8 8.Rc8+- and black is too late to put his rook in front of the b-pawn.
7.Kb3,      Rg1

Diagram 3


8.Kb2!
With the text move Black again faces the problem how to stop b7-b8Q. 
On the other hand
8.Kc4?,Rb1 9.b7,Rc1+=
offers Black good drawing chances. 
10.Kd5,Rb1 11.Kc6,
(If the white king does not go to the 6th rank, black keeps giving checks and eventually returns his rook to b1 when the position basically remains unchanged)
11...g5!
(note that this is not possible if the king had been on c5 because  White would have the answer Rc6+ followed by Rb6) 
12.hxg5,Kxg5= (van Wijgerden) 
13.Rxf7,Rxb7! 14.Kxb7,h4 15.Rg7+,Kf4= 
(Black can still lose with 15....Kh4? 16.Rh2+-)
8.....,      Rg4
8.....,   Rg2+ 9.Rc2, Rg4 10.Ka3, Rg3+ 11.Ka2+-
And white's king manoeuvre allows him to answer 
11....Rg4 with 12.b7,Rb4 13.Rb2 +-
(finally the rook is behind the passed pawn).
9.Rc3!
Diagram 4


Again white threatens to put his rook behind the b-pawn.
9.......,  Rxh4
There is nothing else since 9....,Rg2+ is answered by 10.Ka3 +- similar to the line given on move 8.

After 9...Rxh4 white  has three ways to win:
10.Rb3,Re4 11.b7,Re8 12.b8Q +- (van Wijgerden)
10.b7,Rb4+ 11.Rb3,Rxb7 12.Rxb7 +- (van Wijgerden).
10.Ka3,Rb4 11.b7,Re8 12.Rc8 +- (Averbakh)
You have to take my word for it that both rook vs. 3p endgames are won for white (or that of the 6-men-table base for that matter). 
Blacks pawns and king are simply too far back.

---------------------------------------------------------
---------------------------------------------------------
So far hardly anything new has been presented.
The underlined analyses represents what was allready known. I left out quite a bit of analysis/explanation if it was not relevant for what I want to present.
I only elaborated a bit to explain what is going on after 5....Rxg3, since I need this variation in the analysis to presented.

I have only one last notion to add. 
One has to admire analysts like van Wijgerden and Averbakh. Remember that in their days table bases where not available, and most reference books dated from the fifties or early sixties (Smyslov/Levenfish, Cheron and Averbakh's own endgame series in 3 volumes). So they had to check even basic positions for themselves.

Yes, please elaborate.

Micawber, you've done all the research I could do from a remote location. 

I'm really curious to see how white could win this against best play. I had studied it once and believed the analysis proving the draw. Please, show us where Averbakh and others got it wrong! If you can prove the win here, it may actually change some of the theory regarding Rooks in front of pawns in such situations.

The rook-endgame from Hollis-Florian is probably one of top 10 most quoted Rook-endgames.
I have two questions regarding this endgame:
1.What was the exact date?
2.When did Averbakh publish his refutation of the analysis of Hollis?
 
Regarding 1:
The dates given vary between 1972 and 1984.
Of these only 1972 (Harding, Dvoretzky) and 1974 (van Wijgerden)
seem probable to me. The difference between 1972 and 1974 may perhaps be explained
(my conjecture, but without any solid evidence) 
as the difference between starting date and finishing date. This being a postal
game, it may have actually taken several years to complete.
 
Mega-correspondence database Tim Harding: 1972
 
Van Wijgerden/(Euwe), Het Eindspel III
Dutch edition (Spectrum, 1981):  1974
note: this edition is less obscure than you might think.
It is cited as a source both by Korchnoi, Rookendgames 1995
and by Marin, Learn From the Legends.
 
Averbakh, Comprehensive Chess Endgames, volume V
Russian edition 1984: no date
English edition (Pergamon 1987): no date
 
Speelman/Wade/Tisdall, Batchford Chess Encyclopedia
(Batchford, 1993): 1979
 
Howell, Essential Chess Endings
(Batchford, 1997): No date
 
Emms, The Rook Endgame Survival Guide
First edition (Everymann Chess, 1999): 1979


Mueller/Lamprecht, Fundamental Chess Endings
(Gambit Publications, 2001): 1979
Note: Mueller/Lamprecht admit that they based their
notes on BCE, so this does not count as an indepent source.
 
Dvoretzky, Endgame Manual
(Russell Enterprises, 1st edition,2003): 1972
note Dvoretzky indicates that his sources were
checked by Harold van der Heyden.
'
Pinter, 1000 Rook endgames
(Magyar Sakkvillag, 2007): 1984 !!!!
Note: I dont speak Hungarian, so I may be wrong on
this, but the quotation -- example 631 is:
Levelezes, 1984 implying it was not a postal game!!
 
Regarding 2
Hollis thought the endgame was won for white, but his analysis was
refuted.
All sources published after 1984, attribute this refutation to Averbakh.
However, van Wijgerden also has this refutation, and as far as I can tell,
his analysis predates Averbakh by 3 years.
Also he does mention Hollis analysis, but does not mention Averbakh, and Averbakh does not mention van Wijgerden or any prior publication of his own findings.
There are three possibilities in my opinion:
1.Van Wijgerden and Averbakh found the refutations independently
2.Averbakh published his analysis in a magazine between 1974 and 1980,
and van Wijgerden copied this without mentioning Averbakh.
3.Averbakh knew about van Wijgerden's analysis and copied it without mentioning the source. This is less farfetched than you might think,
because Averbakh knew Euwe quite well, and may have obtained a copy from him.
(as indicated above more than one GM owned a copy of van Wijgerden's manual)