|White to move|
There are 3 separate subjects to count:
- Value of obligation
First, you count for domination. I don't know whether "domination" is the best term for it, but it seems appropriate. You count from -/-1 0 +1 (-/- is minus sign). -/-1 = you don't own the square. 0 = balanced, +1 = you own the square (and the piece upon it). Both a6 and f6 are balanced, but since the pieces on it are both defenders, black is weakened elsewhere if you capture them. Counting for domination gives you a sense of which targets play a role.
Second, you count the tempo change caused by a move. You count 0, 1, 2. 0 = no forcing move, 1 = single tempo move (places one obligation on the shoulders of your opponent), 2 = duple tempo move (places two obligations on your opponents shoulders). 21.Bxa6 is a single tempo move. Black is obliged to take back a piece of the same value. Sooner or later. With a postponement move, black can postpone his obligations, but there will come a time that he has to comply with his obligations. In this position there are no postponement moves, so black must take back on a6 immediately. 22.Bxf6 is a single tempo move, and black is forced to take back immediately.
23.Nd5 is a duple tempo move which attacks two undefended pieces. Black needs a duple defense move to save them both. There are two of these duple defensive moves: 23. ... Qd8 and 23. ... Qd6
Both move has as drawback that the black queen is now overworked, it cannot defend both bishops on f6 and d7 at the same time. White finishes with the duple offensive move 24.Nxf6+, and since black hasn't an appropriate duple defensive move, he looses a piece.
Counting the tempo change of a move is a simplification of the tempo counting system. It is based on the assumption, that the obligations for both sides are in balance. If you play a game, you know that for sure, since if it were not, you would have gained or lost a piece already. If for a puzzle the obligations are not in balance, you simply gain the wood you dominate. Only if you have to analyze a position that is not your own game or a puzzle, you need an absolute obligation counting system. Since such system is rather complex, we should avoid it when solving puzzles. The relative tempo counting system I propose here should be sufficient. At least, that is what we have to test.
You must realize that you can have obligations already. This means, that if you attack with a piece that was previously under attack itself, you gain two tempi. One defensive, and one offensive. We must develop a sense for this.
Value of obligation
If you capture a rook, your opponent is obliged to take one or more piece(s) back of equal value. It doesn't suffice for him to take only a minor piece back. I don't like counting with numbers like 3, 5 and 9, since I easily overload my poor short term memory with it. So I'm going to experiment with Minor piece = 1, rook = 2 and queen = 3. I'm interested in the mechanism of the combination. Once I have unearthed the mechanism, it is soon enough to calculate the exact value for the gains and losses on both sides. When I don't have a clear sight on the inner workings of the combination, it suffices to know that if my rook is taken, I need at least a rook or two minor pieces back. It is just a precaution for overloading my STM.
Anyone who can count from minus 1 to plus 3 should be able to use these 3 counting systems.