The following tactic is fairly easy to calculate, yet it gave me some trouble. I'm finding that, when calculating forced variations, I have more difficulty when I have a choice of moves than when my opponent has a choice of moves.
White to play:
4r1k1/ppn1bppp/q7/7Q/1nN1P3/1B1P4/PP5P/KN4R1 w - - 0 1
Black to play has a straightforward mate in 2 starting with
1...Qxa2+, so White's play either has to interfere with this mechanism, or be with check. Moves like
1.Nca3 or
1.Na5 don't lead to anything. That leaves two checks:
1.Rxg7+ or
1.Qxf7+. The former check doesn't seem to lead anywhere either (e.g.
1...Kxg7 2.Qg4+ Qg6).
1.Qxf7+ looks like an "obvious" queen sac, because after
1...Kxf6 the knight can move to e5 or d6 with a discovered, double, check. But which knight move?
Correct is
2.Ne5+, because on either 2...Kf6 or 2...Kf8, 3.Nd7#.
However, when I tried to calculate this as I would in an over-the-board game, I would stall at this point. I was seeing the king slipping out of the mating net with
2.Nd7, and didn't immediately see the mate after
2.Ne5 Kf6. That was enough for me to second-guess the entire line and try to find ways to get other first moves to work. In a real game I probably would have bailed out by playing a knight to a3.
This demonstrates both quiescence errors (not calculating out until all checks, captures and threats are spent) and not "thinking like a tree" a la Kotov (calculate each branch of each line only once). And yes, Kotov's technique has been criticized by others, but in general (especially for simple problems like this one) it's an ideal worth striving for.