“Every missed opportunity to play better - even in a drawn game, or a difficult game to win - is your loss.
That is why it is necessary for you to return again and again to study your oversights, regardless of how the game turned out.” - Garry Kasparov

A subtle checkmate in 3 moves problem by Sam Loyd. White to move

The Answer is: 1.Qh1! hxg5 (1...Kxg5 2.Ng2! hxg2 3.h4#) 2.Qg2! hxg2 3.Nxg2#

BISHOP AGAINST PASSED PAWNS

The bishop is a skilful defender when there are connected passed pawns. It can stop a whole row of passed pawns. But stopping two passed pawns which are far apart is a different kettle of fish.

Imagine the position without the kings. Then the only square from which the bishop can successfully stop the pawns is d3. If it is on any other square, White will catch the bishop out by a pawn sacrifice! With the kings on the board, there is an exciting struggle which leaves White in the end with the upper hand.

1.a6!

It would be wrong to start with the other pawn: 1. g6? Kh6 2. Kf6 Bd5 3. a6 Bc4 4. a7 Bd5, and White does not have a good move.

A waiting move such as 1. ... Bg2 is followed by 2. g6 Kh6 3. Kf6 Ba8 4. g7! Bd5 5. Ke5 Bg8 6. a7, wmnmg.

Now it is the turn of the g-pawn. 2. a7? would now be bad: 2 .... Bb7 3. Kf6 Bd5 4. g6 Kh6 S. g7 Kh7, and White can no longer win.

Things can still go wrong: 3. Kf6? Bc4 4. a7 Bd5.

3...Bg2 4.Kf6 Bd5 5.a7
White wins

To be continued...

Sometimes a piece is sacrificed for far-advanced passed pawn. The idea is to get it back with compound interest. This works beautiflllly in the following game fragment:

The first day of blitz games at the 2022 Saint Louis Rapid & Blitz saw quick chess superstars GM Hikaru Nakamura, Alireza Firouzja, and Levon Aronian pick up the most points in a day of decisive results, tactical brawls, and a loss by an illegal move! 
Nakamura was the clear standout, scoring 7.5/9, a result that has allowed him to catapult himself from the bottom of the standings into the top three heading into the final day. 
Firouzja continued his run of great form with a +3 score over nine rounds and extended his lead to three points over second-placed GM Maxime Vachier-Lagrave who had a modest performance by his standards.
The event will conclude with rounds 10-18 of the blitz portion on August 30 at 11 a.m. PT/20:00