Count The Weaknesses

HERE is an instructive rook-and-pawn ending from Tartakower and du Mont's 500 Master Games Of Chess.

White has just played 49.Kg1-g2 in José Capablanca - Boris Kostić, game one, Havana match 1919  

How many weaknesses does each side have?
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[Notes in italics are algebraicised from 500 Master Games Of Chess.]
Now that the battlefield is cleared, manoeuvring will be superseded by active advances.
Black's disadvantage consists in the fact that he has two weaknesses at c5 and g7, whereas White is vulnerable only at b3.
I guess congratulations are in order if you reached the same conclusion as Tartakower/du Mont regarding the number of weaknesses. I am fairly certain my count, if I had not read their notes first, would have been rather different.
For what it is worth, Stockfish10 reckons the position is dead-equal, while Komodo10 gives White an advantage of 0.14 pawns, which is as good as equal.
49...Ra6 50.Kf3 Ra2 51.Bg3 Ke8
A more-stubborn resistance is offered by 51...Ra7, guarding his second rank, and ...Kf7, to be followed by ...g6, relieving the blockade.
The engines are happy with Kostić's choice.
52.Bf4 Ra6 53.Be3 Ra1 54.Kg4 Ra7?!
In chess, as in life, the right perception often comes too late.
The engines strongly dislike the text, preferring 54...Kf7 or 54...Rg1+.
55.Kh5 Kf7 56.Rd5 Ra3
Seeking salvation in counterplay, for if  56...Rc7 [then] 7.h4 (relying on zugzwang) Bf8 58.Rd8 Be7 59.Ra8, and Black must, one way or another, let go.
After the above variation, a sample line given by the engines runs 59...Bd6 60.Ra6 Be7 61.Rb6 Bf8 62.Bf4 Rd7 63.Rc6 Rd3 64.Rc7+ Ke8 65.Kg6 Be7 (if 65...Rxb3?, then 66.Rc8+ Ke7 67.Be3 etc) 66.Be3 Kd8 67.Rb7 Rxb3 68.Kxg7 Ke8 69.Rb5 Rc3 70.Bxc5 Rxc4 71.Bxe7 Kxe7 72.h5, when the game will be decided on the kingside. This is a long line, but the engines have White winning, or at least massively better, throughout.
57.Rd7?!
Clearer, according to the engines, is 57.Bxc5 Bxc5 58.Rxc5 Rxb3 59.Rc7+.
57...Ke8 58.Rd3 Kf7 59.h4 Ra7 60.Rd5 Ra5?
This seems the decisive mistake. The engines give 60...Rc7, protecting c5 and Black's second rank.
61.Rd7 Ke8 62.Rd3
The engines' 62.Rc7!? may be even stronger.
62...Kf7?!
The engines give 62...Ra3 63.Kg6 Kf8 64.Rd5 Rxb3 65.Bxc5 Bxc5 66.Rxc5 Rh3 67.h5 with a large advantage to White.
63.Rd5
Señor Capablanca has composed a Zugzwang Symphony! If 63...Ke8, [then] 64.Kg6, and if 63...Bf8, [then] 64.Rd7+ Be7 65.Rc7, and still the black king has to give up the control of  g6!
63...Ra3 64.Bxc5 Bxc5 65.Rxc5 Rxb3
Numerically even, but the active position of White's king and rook decides the day.
66.Rc7+ Kf8 67.Kg6 Rf3 68.Rf7+ Ke8 69.Rxg7 Rf4
Or 69...Rxf2 70.Rb7 Rf4 71.c5 Rxh4 72.Kxf6 with a huge advantage.
70.h5 Rxc4 71.Kxh6 Kf8
If 71...b3, then 72.Rb7, eg 72...Rc3 73.Kg6 etc.
72.Rb7 Rg4 73.f3
Challenging a decision.
73...Rg5 74.Rxb4 Kf7
Clearly not 74...Rxf5 75.Kg6 Rg5+ 76.Kxf6, winning at once.
75.Rg4
In a subtle manner White frees his king.
75...Rxf5 76.f4 Ra5 77.Rg7+ Kf8 78.Rb7 f5 79.Kg6 Ra6+
If 79...Rc6, then 80.Rb8+ Ke7 81.h6 etc.
80.Kxf5
Many positions with rook, bishop's pawn and rook's pawn versus rook are drawn, but this is not one of them.
80...Ra5+ 81.Kg4 Ra6 82.Kg5 Rc6 83.f5 Kg8 84.f6 Rc8 85.Rg7+ Kf8 86.h6 1-0
A victory of logic and nerves.

Did Black Miss A Draw?

HAD a 64-move rook-and-pawn ending in round three of the Bad Wiessee Senioren-Cup today … and it seems my opponent missed instructive draws on consecutive moves.

The rook-and-pawn ending began with White to make his 28th move in Spanton (1880) - Elof Cordts (1701)

White is about to go a pawn up, leaving Black with four isolated pawns, including two that are doubled.
I certainly thought I was winning, and the analysis engine Stockfish10 agrees. But another very strong engine, Komodo9, 'merely' gives White plus-over-equals - after all, it is a rook-and-pawn ending!
The critical position came 50 moves later:

White has just played 78.Kf4-f5

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78...Ra6
I thought Black had to play 78...Kg7. After 79.Rd7+ Kh6, the first point is that White cannot play 80.Kxf6 as Black draws with 80...Ra4 81.Kf5 Rf4+! (81...Rxg4! also draws). If instead of 81.Kf5, White tries 81.g5+, then 81...Kxh5 is a tablebase draw.
Since 80.Kxf6 does not work, White is more-or-less obliged to try 80.Rf7. Then comes 80...Ra5+ 81.Kf4 (81.Kxf6 is met by 81...Ra4 with a draw as before) Ra4+ 82.Kg3 Ra3+ 83.Kh4 Rf3 84.Rb7 (84.Rxf6+? Rxf6 85.g5+ Kg7 is a trivial draw) Rf1, and there does not seem to be any way for White to make progress.
One line given by the engines after 84...Rf1 goes 85.Rb4 Rh1+ 86.Kg3 f5! 87.Kg2 (87.gxf5 is the notorious drawn ending of f+h pawns) Ra1, and the best White can get is again the drawn f+h pawn-ending.
Where possible I have confirmed the engines' conclusions with the Nalimov endgame tablebase, so it does seem Black missed a draw. It is perhaps needless to say that neither player was aware of virtually any of this during the game.
Going back to the second diagram and the game continuation of 78...Ra6, there followed …
79.Re4 Kg7?
It seems Black still had a draw with 79...Ra1! (or 79...Ra2! or 79...Ra3!). Here the point is that, after 79...Ra1!, White has nothing better than 80.Kxf6, but then Black has a tablebase draw with 80...Rf1+ as the White king has to let its counterpart into g5, after which the draw is relatively simple. No wonder Tartakower (or was it Tarrasch?) quipped that all rook endings are drawn.
After Black's second missed drawing chance, the game finished:
80.Re7 Kf8 81.Re6 Ra4 82.Rxf6+ Kg7 83.h6+ Kh7 84.Rf7+ Kh8
Black meets a swifter end after 84...Kxh6? 85.g5+ Kh5 86.Rh7#
85.g5 Ra8 86.Re7 Kg8 87.g6 Ra5+ 88.Kf6 Ra6+ 89.Re6 Ra8 90.Rd6 Rb8 91.Ke7 1-0

Did I Miss A Draw?

ROOK endings are notoriously drawish, both in theory and in practice, but what do you think of the following position?

Black to make his 36th move in Thomas Brown (2068) - Spanton (1954), Hastings Masters Round Four

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Firstly, we can dismiss 36...Rxc6?? 37.Rh5+ as completely hopeless for Black.
In the game I played 36...Rd1+? 37.Kc2 Rd6 38.c7 Rc6+ 38.Kd3 1-0
But, as TB suggested afterwards, I should have tried 36...f3! The point is that 37.gxf3 Rxc6 brings about an example of the infamously drawn f&h-pawn ending.*
TB was not sure if the actual position on the board would be drawn, but the Nalimov endgame tablebase confirms the position is indeed drawn.
White could try 37.Rh5+ Kf4 38.Rh4+ Kg5 39.Rg4+ Kh5 40.gxf3, but again the f&h-pawn ending is drawn after 40...Rxc6.
So, yes, I did miss a draw (assuming I would have played it accurately).
*If you do not know about this, consult almost any general endgame book.