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42... Re7+ 43. Kg8 
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If Kh8, then White has forced mate with Kg6  Kg8 Re8#
If Kh6, then Kf5 reaches the key position I'll explain later. | 
   
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43... Rg7+ 
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If 44.Kf8 in this position, then 44...Bd6  45.Ke8 Ke6 (threatening mate) 46.Re2  Be5 reaches the key position.
The text move holds on the longest since it takes Black more moves to force White into the key position. | 
   
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44. Kh8 
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This position is a demonstration of where the attacker's pieces are the strongest in this endgame. The bishop is strongest on a central rank or file, while the king is strongest 2 ranks or files away from the edge, and the rook is strongest one rank or file from the edge, since it restricts the king to the back rank. | 
   
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44... Rg1 
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This patient move is necessary because it unstalemates White's king. If it had been White to move in the previous position, then White could draw with perpetual check since taking the rook is stalemate. | 
   
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45. Rf2+ 
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Once again, checks by the defender make it a little harder for the attacker to acheive the key position and win.
Ra6  doesn't have the same effect because Kf5  already reaches the key position. | 
   
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45... Kg6+ 46. Kg8 Bd6 
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This is a very important position of this endgame, and remembering the concepts is complicated like in the key position, but the key position is more likely to occur. This position is rare, but if you remember it, then you can automatically know you're winning if you reach this position on your opponent's turn. The special thing about this position is that the player to move decides the game. This position (and mirror images of it) aren't hard positions to memorize, but you don't even need to memorize it if you can logically see how both sides would be in zugswang if it was their turn to move. If it was Black's move here, then the position is drawn because Black cannot make a move without disrupting his formation. No matter where Black moves, he'll be allowing the White rook access to a square that was guarded before. In this case, White is the one in zugswang since it is White to move here. No matter where White moves, he will unguard a critical square or set of squares.
47.Rf3 would take away the Rg2  potential checking idea, so Black can play Rc1 with unstoppable mate since the rook no longer has a check.
47.Rf7 would take away the Kf7 potential escape path, so play could continue Kh6  Kh8 Be5 
47.Kh8 would also take away the Kf7 potential escaping route, so play could continue Re1 (threatening mate) Rg2  Kh6 Kg8 Rf1 (threatening unstoppable mate)
To avoid these quick mates, the rook must move along the 2nd rank, allowing the Black king access to the f-file. | 
   
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47. Rd2 Kf6+ 48. Kh7 Rh1+ 49. Kg8 Be5 
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It doesn't seem as though Black has made much progress, but Black is closer to forcing White to play into the key position. Every move counts, and one slight error could change a winning position into a drawn position. Since the key corner of this variant of the RB vs. R endgame is h8, the bishop's key square of the key position is e5, you'll understand later. | 
   
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50. Ra2 
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Rf2  would lose quickly to Ke6, with the deadly threat of Rh8#.
This move holds on the longest, since other moves allow ideas like Ke6 or Ke7, getting closer to the key position. With this move, White prevents Ke6 and Ke7 by threatening to check. | 
   
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50... Rg1+ 51. Kh7 
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51.Kh8 would give Black forced mate with Kf7  Kh7 Rh1 
51.Kf8 allows Black to set up the key position with tempo, because after 51...Ke6, Black is threatening to play the crushing 52...Bd6  forced mate with tempo. Play could continue after 51.Kf8, 51...Ke6 52.Re2(to stop Bd6 ) but Black has 52...Rh1 with the deadly threat of Rh8#. | 
   
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51... Bd4 
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This critical bishop move is to stop Rf2  which would disrupt Black's attack and draw the game. I may create another endgame study on how to draw this endgame from a drawn position, but studying how to win it should be enough for you to understand how to draw it. | 
   
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52. Ra6+ Kf5 
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In this position, Black threatens to reach a form of the key position with Rg7  Kh6 Rg8. I'll explain the simpler winning process once Black forces the key position, but for now, the method of forcing is complicated. | 
   
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53. Rg6 
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This stalemate cheapo stops 53...Rg7 
Other moves lose quicker.
53.Rh6 Rg7  54.Kh8 Rg3  55.Kh7 Be5 reaches the key position
53.Rd6 Bf6 54.Rd5  Be5 reaches the key position, and so does 53.Ra5  Be5 | 
   
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53... Ra1 
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Rb1 and Rc1 are the same as the text move, because they both have similar threats to Ra7  Kh6 Be3  Kh5 Rh7  | 
   
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54. Rh6 
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This move stalls the key position the longest. Other moves allow Black to reach the key position quicker. Once I show you what the key position is, then it shouldn't be too hard for you to see quicker ways of forcing the key position against inaccurate defense. | 
   
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54... Ra8 55. Rh5+ 
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Checking is the only way to stop Rh8# | 
   
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55... Kf6 
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Black's idea is to get his king to f7 and bishop to f6 to seal in White and force the key position. | 
   
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56. Rb5 
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This stalls the key position longest, simply because the rook is most active here. Other moves allow White to force the key position faster | 
   
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56... Ra7+ 57. Kh6 
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57.Kh8 is met by Kg6  with mate to follow.
57.Kg8 is met by Ra(1, 2, or 3) and Black can force the key position quicker.
I recommend that you review this annotation once you're familiar with the key position, so that you can understand "how" when I say "force the key position quicker" | 
   
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57... Be5 
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In the Kg8 variation where the king is trapped on the 8th rank, the key position is reached with the Black king on e6, but in this variation with the king restricted to the h-file, the Black king should be on f5 in the key position. | 
   
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58. Rb6+ Kf5 
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Finally a form of the key position has been reached after all that time and effort spent by Black. The key corner is the corner the defending king has been trapped on for the entire ending. In the key position, the bishop should be on the square three diagonal spaces from the key corner, and the attacking king should be next to the bishop as shown in this position, based on which side of the board the defending king decides to get trapped on. | 
   
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