The critical position arose after White's 67th move (see the diagram), the situation being bishop
and two pawns versus rooks and pawn, with the stronger side's pawn not passed. The tablebase server Probe says that Black should mate in 39 moves.
According to Dvoretsky's Endgame Manual, with pawns on the same or adjacent files it is better to have the pawn on the opposite colour to the bishop to set up a barrier against the enemy king but here White has no choice.
However the win is difficult because Black must first deal with the h-pawn. The critical moment began at move 79 when both players
missed the correct play and Black overlooked a clear winning path. The main line of the analysis diverges
from the actual course of the game (which was in fact drawn) at Black's 80th move.
Gordon W. Scott - Peter J. Batchelor [E04]
British Championship 2015
Best; the only other winning move is 67...Rg1 (one move slower). 68.Bb3
As good as anything. 68...Kf6
Again best, the alternative being ...Rg1. 69.Bc4
It looks natural to defend a2 and attack the R although the tablebase says Ba4 or Bc2 last one move longer. 69...Rf5
Many moves win but Rd1 is best. 70.Bg8
Relatively best (equal with Bb3). 70...Ra5
One of several moves that mate in 37. 71.Bc4
(threatening mate on h8) is the right idea although it is in fact only one move quicker says Probe. The point is that White must then play Kh7 as eventually happens in the game.] 72.Bd5
White can only wait and hope Black cannot find the winning plan. 72...Rc7
(again threatening mate) is one move quicker.] 73.Bb3
At last finding the right idea to move on to the next phase of the solution. 74.Kh7
Before playing ...Kg5 (which wins more slowly) Black wants his rook on a dark square. [74...Kg5?
and White can draw, e.g., 75...Kxh5
The black king has been dragged too far from the queenside, it seems. 76.Be6
It was to avoid this tempo-gaining move that Black first played ...Rd8 before ...Kg5. On e6 the bishop creates a temporary barrier that lengthens the Black king's path to the queenside: a subtle but crucial difference from the main line. 76...Rc5
Several moves draw in fact, now the White king is near enough to the pawns. (A simpler way is 82.Kc6
By no means the only safe move 85...Kb2
White draws as long as only one file separates his king from the Black pawn. 87...Rh2
or Ka5 88...Rh3
should also be met by a B move such as Be6 but not 89.Kc4??
or Be6 or Bf7 or Bg8. ) 82...Ke3
It might look as if the self-pin has got White into trouble. 84.Kc6!
The unpin saves White. 84...Kc3
Black's plan is to win the king and pawn ending, but... 86.Kb6!
The B runs away and Black cannot make progress. Note however that Be6?? loses to Rh6 and also Bd5 loses: (87.Bd5??
forcing the king to the seventh rank, and after 88.Kb7
etc.) ) 81.Kd5
Also Ba4 holds. 82...Kd2
and Black cannot win because his own pawn is vulnerable.] 75.Bc4
This does not spoil the win but Black could have played ...Kg5 at once. [75...Kg5
as in the game is slightly better but still loses.) 76...Kxh5
is the start of the tablebase's longest variation.) 78...Kf3?!
and the White king cannot get near the Black pawn in time.] 76.Bb3
76...Rd8 is one move quicker says the tablebase. Black's idea with the text was presumably to deny Bf7 in reply to ...Kg5. 77.Bg8!?
Ingenious though it makes no difference to the result according to the tablebase. 77...Kg5??
Without this Black cannot make progress but he should have the R on d8 first. Now the game should be drawn because White plays Kg7 with tempo. [77...Rd8!
returns to the winning path: 78.Bc4
Trying to get over to the queenside. (81.Kg8
loses one move faster.) 81...Kf6
The h-pawn cannot be saved, e.g. (84.Be8
and compared with the drawing lines earlier, the White king cannot get close enough to the b-pawn.] 78.Kg7!
This should have been the losing move and the first move on the winning path is not difficult to see. Black had about 7-8 minutes left (plus increments) and thought for most of his time before deciding he could not win and played Rxa2. However... [80.Bc4
White establishes a fortress defending his pawns and may even advance h5-h6 if Black is careless. 80...Ra7+
Black mates in 36. [Instead of 80...Rxa2?
with a draw, as actually occurred.] 81.Bb3
81 Bg8 loses in the same number of moves and others are worse. [81.Bg8
winning as in the 77...Rd8 variation] 81...Rd6
This L-shaped rook manoeuvre is again the key to winning the position. The double attack
on the a-pawn and h-pawn force the White K to abandon its g7 square after which zugzwangs and double
threats eventually force the h-pawn to advance to h6 where it is inevitably lost. Then the white king on the edge cannot get to the drawing zone a6-b6-c6 where it needs to be when Black tries to win by an exchange sacrifice on a2 or b3. 0-1
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