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1. …Kd1
2. Ka2 Kc1
3. Ka1 a3
4. b3 Kc2
5. Ka2 Kc3
6. Kb1 Kxb3
7. Kc1 Ka2
8. Kd2 b3
9. Kc1 b2+
10. Kd2 b1=Q
(black wins)
The key thing to take away from this position is that the black king can shepherd a b-pawn to the queening square from c1 or c2- he just has to force the white king to the a-file, and white can’t avoid being pushed there after 1. …Kd1. What this means is that white can’t take at a3 without allowing the b-pawn to simply pass by and reach b1 long before the a-pawn reaches a8.
Let’s look at either pawn move as black’s first move:
1. ………….a3?
2. ba3! b3?? (of course, 2. …ba3 is a drawn ending with a rook’s pawn)
3. a4
And, oops, white wins, not black!
Or
1. …………..b3?
2. Ka1= since black can’t ever play Kc2 or Kc1 without allowing a stalemate.
Finally, any other king move at move 1 draws at best:
1. …………..Kd3
2. Kc1! Ke2 (pawn moves are no better than what I showed above)
3. Kc2 and this is clearly drawn now.
I like that, Black can sacrifice the a pawn to avoid a stalemate problem with the b pawn advancing without check in some lines.