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Strategy:
If at all Black promotes one of his pawns to a queen or even a rook, he checkmates White!
Not only White must queen his pawn first but also with a precondition that it should be done well in advance to go and stop Black from queening
or
White must queen at f8 square to gain a tempo by the check to Black king!
If the pawns after exchange end up in opposing each other without a chance of creating a passed pawn, Black king is in a better position to grab them.
1.h5
[If...I try... 1.e5
fxe5
(If... 1...f5
2.h5
gxh5
3.gxf5
exf5
4.e6
yes, White queens well in advance, but Black will prefer to avoid 1...f5 and win by the main variation) 2.fxe5
Black wins by his King moves; If...I try... 1.f5
exf5
(1...gxf5
2.exf5
exf5
3.gxf5
Black king moves and wins) 2.gxf5
gxf5
(2...g5
will let White win 3.e5
fxe5
4.f6
queening with check to Black king) 3.exf5
Black king moves and wins; If...I try... 1.g5
fxg5
(1...hxg5
2.fxg5
fxg5
3.hxg5
Black king moves and wins 3...Kb3
4.Kb1
Kc3
5.Kc1
Kd4
) 2.fxg5
hxg5
3.hxg5
Black king moves and wins]
1...gxh5
[1...g5
2.e5
fxe5
(2...f5
3.gxf5
gxf4
(3...exf5
4.e6
gxf4
5.e7
f3
6.e8Q
f2
7.Qe2
wins.) ; 2...gxf4
3.exf6
and queens with a check) 3.f5
exf5
4.gxf5
and queens with a check]
2.e5
[2.gxh5
will let Black king move and win]
2...fxe5
[2...hxg4
letsWhite to get f file 3.exf6
queening with check]
3.f5
exf5
4.gxf5
queening on f file with a check and winning a tempo and game! 1-0
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