In the first position, I erred and lost the game. My error is an instructive tactic that might work in other circumstances.
White to move
I played 52.e6+ with the intent of deflecting Black's king from defense of g6. After 52...Kxe6 53.Kxg6, the game would have been drawn. However, my opponent played 52...Kg7! As it turns out, his move wins. It is also the only winning move after my attempted deflection.
Some of my students are learning this deflection tactic for the first time. For them, understanding how it might have worked is more important than comprehending why it failed.
Most of this game is presented with some detailed discussion at "Stronger King".
The second position comes from my first round game. My opponent had a tactical shot that she missed. After her move, I immediately eliminated the vulnerabilities that made this tactical knockout possible.
White to move
My opponent played 25.Bd2 and then I removed my rook from the e-file.
She could have played 25.Bxb6, capturing a pawn with a discovered attack on my rook. If I capture the bishop, I lose quickly. 25...cxb6 26.Rxe8 wins a rook for bishop and pins the queen against the king, winning it for a rook. Hence, I would have been forced to play 25...Rxe1 and after 26.Rxe1 the problem of the pin remains, so 26...Re7 27.Bxa5 when White has gained two pawns on the queenside for no cost and the bishop now guards White's vulnerable rook on e1.
I often say there is no luck in chess, but I was lucky that my opponent missed this tactic.
From the third position, my opponent executed a fork combinations that forced the exchange of his two knights for one of my rooks and a pawn. He failed to anticipate, however, my in-between move. In chess, there are two names for an in-between move. There is a German word, zwischenzug, and an Italian, intermezzo. These words mean the same thing. Chess students will find both words used interchangeably by different writers and speakers.
Black to move
21...Ngxe3 22.fxe3 Nxe3 23.Qe2 Nxf1
I need to capture this knight on f1, but before I do, I have my in-between move. Because my move gives check, the knight does not get time to escape. The importance of my in-between move is not the check, but that it gains a pawn and protects my pawn on d6.
24.Qxe6+ Kh8 25.Rxf1
My d6 pawn was vulnerable and is now secure. Because it is so far advanced, it is also extremely dangerous. After my opponent offered the exchange of queens, I was left with an overwhelming advantage due to the the queening threat of my advanced pawn.
My opponent could have played 21...Qxe6. Then, both players have chances as the game continues.