Endgame Studies 3

This study is an excellent exercise for schematic thinking. White is a queen up, but the king cannot move and a lone queen cannot give checkmate. So it's clear that white has to give up their queen for the bishop and promote the g-pawn.

This raises the question of where the black king needs to be so that white can win the king and pawn endgame. It's important to keep in mind that white needs to spend a tempo to get the queen to the h-file and the black king, therefore, needs to be farther away from the pawn.

With this in mind, one can work out that the black king needs to be on the first rank. The only question that remains is how to get the king there.

1.Qg5 Kh7 2.Qf6 Kg8 3.Qh6

This is the mechanism white uses to get the black king to a1 or b1. Black has only one legal move and has to go to the a file.

3...Kf7 4.Qg5 Kf8

Black tries to keep the king as far away from the first rank as possible.

5.Qg6 Ke7 6.Qf5 Ke8 7.Qf6 Kd7 8.Qe5 Kd8 9.Qe6 Kc7 10.Qd5 Kc8 11.Qd6 Kb7 12.Qc5 Ka8

Now white needs to employ the same mechanism to get the king to a1 or b1.
Playing 12...Kb8 puts up less resistence since white wants to force the king there anyway to set up the same mechanism.

13.Qb5 Ka7 14.Qd5 Kb8 15.Qc6 Ka7 16.Qc8 Kb6 17.Qd7 Ka6 18.Qc7 Kb5 19.Qd6 Ka5 20.Qc6 Kb4 21.Qd5 Ka4 22.Qc5 Kb3 23.Qd4 Ka3 24.Qc4 Kb2 25.Qd3 Ka2 26.Qc3 Kb1 27.Qh8!

Now the black king is far enough away.

27...Kc2 28.Qxh3 gxh3 29.g4 1-0
The white g-pawn will promote and white wins easily.