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a6
If Rxd4 Rb4! Kxb4 Rxd4 Kb5 a7 and the pawn queens. Be4 is not possible because the king guards that square.
If Ra8 Rd6! Kb5 a7 and let’s say Kc4 (d7 square is guarded so no Bd7), Rc6+ Kd5 Rc7 followed by Rb7-Rb8. Black cannot stop the rook from getting to b8.
1. a6! R:d4
2. Rb4+ K:b4
3. K:d4 Bc8
4. a7 Bb7
5. f5 and white will promote a K-side pawn (or the a-pawn)
something along the lines of:
e6 Bxe6
a6 Rxd4
Rb4+ Kxb4
Kxd4 Bc8
a7 Bb7
f5
Well, I would definitely be interested 1.a6 since black cannot successfully take the bishop without allowing 2.Rb5, and white’s pawn will run away from the black king, and while the black bishop can make it back in time to stop the pawn at a8, white will create other passed pawns on the kingside:
1. a6 Rd4 (alternatives later)
2. Rb5 Kb5
3. Kd4 Bc8 (Bd7 not different)
4. a7 Bb7
5. f5 gf5
If black doesn’t capture at f5, white just pushes e6 to force the issue. Black’s best bet now is to try to create his own passer, but white has the necessary time to put the kibosh on this idea:
6. h5 f4 (in for a penny….)
7. h6
Here, 7. gf4 also wins. Continuing:
7. …..fg3
8. Ke3! g2 (again, in for penny..)
9. Kf2 Be4 (g3 10.Kg1 wins)
10.h7 and one of the white pawns queens safely.
So, the question is, does black have a better reply at move 1? Black can try to maneuver the bishop to cover a8, or he can try to block the pawn at a8 with either piece. Blocking with the bishop is going fail on its face since white will put the pawn on a7 and the rook on b8 forcing the exchange of rooks on that square. So I see two plausible tries- 1. …Ra8 and 1. …Be6 (with the plan to come to d5, but these should lose:
1. a6 Ra8
2. Rd6
There may be other winning moves here, I just haven’t looked. This move is totally forcing and most limits black’s king and bishop (takes away d5 from the queen). Continuing:
2. …..Be6 (nothing better now)
3. a7 Bd5
So, now black has established his last line of defense- he has blocked the pawn, has a8 double covered whenever the rook is moved along the 8th rank. However, this defense has fatally weakened the kingside pawns, and white now uses attacks on those to win the game:
4. Rd7 Rc8
What else can black do here? If black moves the bishop off of the g8/a2 diagonal, white just takes at f8. If black moves the bishop to e6, white then plays Rb7 followed by Rb8 then f5 to win similarly to the lines I described earlier where black captures at d4 on move 1: [4. …Be6 5.Rb7 Bd5 6.Rb8 Bf3 7.f5+-]. Of course, any king move drops the bishop, and any pawn move allows white another passed pawn to win the game. The point of 4. …Rc8 is that it prevents Rc7+ from white. Continuing:
5. Bb2
This is done to both threaten to maneuver the bishop eventually to b8 trapping the rook on a8, but also to free white’s king from guarding the bishop sitting d4. Black is totally tied up defending the a8 square and can do nothing:
5. …..Kc5 (what else?)
6. f5 gf5
Black may as well take it now. If he doesn’t, white will just exchange at g6 and then play Kf4 creating, eventually, two new passers. Continuing:
7. h5 Kc6 (again, what better?)
Black can’t threaten the h-pawn with the rook and capture it without allowing Rxd5 followed by a8Q, so black tries to relieve the attack on the bishop first. Continuing:
8. Rd6 Kc5 (or lose the bishop)
9. h6 Rh8 (no choice now)
10.h7 f6 (Rh7 11.Rd5 Kd5 12.a8Q)
11.Rd5! Kd5
12.ef6 Ke6 (what else?)
13.f7 and the discovered attack on the rook is fatal to black.
Lastly, at move 1:
1. a6 Be6
2. a7 Bd5 (Ra8 3.Rb7 etc.)
3. Rb8 Rd7
4. a8Q Ba8
5. Ra8 wins a bishop since
5. …..Rd4?
6. Ra4+ wins a rook.
It’s pretty amazing that White can actually push the a-pawn here with 89. a6 and get away with it.
Black does best to reply 89. .. Ra8 here, but if Black ventures the obvious 89. .. Rxd4 to win the bishop, this is what can happen:
89. a6 Rxd4 90. Rb4+ Kxb4 91. Kxd4 Bc8
(91. .. Bd7 92. f5 (92. a7 Bc6 93. f5 gxf5 94. h5 f4 95. gxf4 g3 96. Ke3 Be4 97. h6 g2 98. Kf2 Kc5 99. h7 Bxh7 100. a8=Q) 92. .. gxf5 93. a7 Bc6 94. h5 f4 95. gxf4 g3 96. Ke3 Be4 97. h6 g2 98. Kf2)
92. a7 Bb7 93. f5 gxf5
(93. .. Kb5 94. e6 fxe6 95. fxg6)
94. Ke3 with this White does not have to worry about Black sac-ing the f-pawn to push the g-pawn Kc5 (94. .. Ka5 95. h5) 95. h5 Bd5 96. h6 Kb6 97. h7