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Nice endgame. You're just in time to save it.
One question: does 5. g5 save white? If 5... Kxg5 then 6. Kg2 with 7. Kf3 should draw, if 5... Kf3? then 6. g6 wins, and if 5... Bd4 then maybe 6. b4 Ke3 7. a4 Kd2 8. Bb3 c2 9. Bxc2 Kxc2 10. b5 Kb3 11. a5 Kb4 12. b6 and white draws (12... a6? 13. b7 Be5+ 14. Kg2 Kxa5 15. g6 Kb6 16. g7 and white wins.
Maybe I'm missing a defense, but that seems fine too.
It seems 5.g5 draws as well. Although in the line given above, 12.b6 actually wins for white as 12...axb6 13.a6! is winning! So blacks best instead would be 10...Kd3 11.a5 Ke4 12.b6 Kf5! with a draw.
3...a5 is an interesting try with the following in mind. 4.Kh2 Bxf2 5.a4 Ke3 6.b4 Kd2 7.Bb3 axb4 8.g5 c2 9.Bxc2 Kxc2 10.g6 Bd4 11.a5 b3 12.a6 b2 13.a7 (or 13.g7 b1=Q 14.g8=Q Be5+ 15.Kxh3 Qh1+ 16.Kg2 Qg2+ 17.Kf5 Qxg8) Bxa7 14.g7 b1=Q 15.g8=Q Bb8+ 16.Kxh3 Qh1+ 17.Kg4 Qg2+ 18.Kf5 Qxg8 - a beautiful line I'm sure you will agree!
Well white cannot play a3 whilst blacks bishop is on c5 as black simply takes it. However, 4.Kh2 Bxf2 5.a3 seems to draw, eg, 5...Bc5 6.b4 Bxb4? 7.axb4 axb4 8.Kxh3 Ke3 9.g5 Kd2 10.Ba4 c2 11.Bxc2 Kxc2 12.g6 b3 13.g7 b2 14.g8=Q b1=Q 15.Qg6+ Kc1 16.Qxb1+ Kxb1 17.f4 actually wins! Obviously then 6...Bxb4 is a mistake, but otherwise all blacks pawns will disappear and it will be a draw.
4.a4 also draws. It is similar to the line I gave a couple of posts previously but a couple of tempi better for white.
On your new board above, you left out two moves. So 5. a3 becomes 3. a3 there :)
Yes, I meant 4. Kh2 Bxf2 5. a3 followed by 6. b4 which obviously draws. So 3... a5 is no good either for black.
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