Thanks for the solutions, Igor. I came to the same conclusions as you, and I'll give you a 10 out of 10 for finding *both* reasons why b2 pawn is necessary. The pawn ending precise play you mention is just 8...Rxe5+ 9.Kxe5 Kb6 10.Kd5 Ka5 11.Kc4 Kb6 12.Kxb4 a5+ 13.Kc4 Kc6 and without a pawn on b2, this is in fact a draw, while with b2-pawn 14.b4 axb4 15.Kxb4 is a trivial win with 2 connected pawns.

I saw a third reason, but it wasn't valid in the end: 10...a5 11.Kd6 Kb7 12.Kc5 Kc7 13.Kb5 Kd6 14.Kxa5 Kc5 15.Ka6 Kd4 16.a5 Kc3 17.Kb5 Kxb3 18.a6 Kc3 (necessary, if 18...Ka3? follows 20.a8=Q+, and if 18...Kc2? follows 19.Kxb4) 19.a7 b3 20.a8=Q b2 and since this is a b-pawn and not an a-pawn or a c-pawn it is always a trivial win (even with the white king far away) and here even easier because 21.Qe4! stops all resistance.

Jadoubovic' advice in blitz is to grab Kc3 and b3 in one hand and place them down with king on b2 and pawn on c2 - now it is a theoretical draw! You should utter a polite j'adoube of course. If he makes a move, the illegal "move" is now valid. I would never do this myself, of course.

Psssstt! Just don't tell Kaitlin in normal text, I don't think she will see us when we are talking in "white text"