Gain of wood
If we would allow a chess game to have one more move, we would take the king in the last move. That simplifies the game of chess as the art of gaining wood. A mating attack is then equal to a trap. With the only difference that the wood that is gained is of infinite value.
It is possible to see promotion as a way to gain wood too. If a pawn queens, about 8 points are added to the material balance. Which is almost a similar advantage as capturing your opponents queen. The reason for simplifying mate and promotion to a mere gain of wood, is that it helps to find rules that are more broadly applicable. That way, we might find that rules that govern duplo attacks can have a broader application. The complicated rules around the king which isn't allowed to move into a check becomes simpler the moment that you realize that it could be taken the next move. That's why the kings cannot approach each other and why they must escape checks. A lot of rules would become immediately clear when you would allow to capture the king. The set of rules about king and check can be replaced by one simple rule: prevent that your king is taken at any cost.
The hierarchy of checks, captures and threats is based on their degree of forcefulness. Although that line of thought can be quite useful, I like to look at it from a functional point of view. Since that might help me to see "the bigger picture". Functionally, a check and a threat are the same. It is the value of the king versus the value of the threatened piece that makes that we treat them differently. But exactly the same is true for any piece of higher value in comparison to a piece of lower value.
A threat against your queen is handled before a threat against your knight.
A capture is definite, while a threat is temporary. That makes it dangerous to answer a capture with a threat in stead of a recapture. If the threatening piece is taken, both your piece and your threat are gone. The hierarchy of CCT invites you to start at the begin of the tree of analysis. Functionality helps you to start at the end. To enlighten the load of my STM, I like to have a functional chain of events before I start to worry about the administration of the value of the mutual gain of wood. Practicality before the correctness that only a computer can deliver fast.
The length of the mutual chain of attack
In a previous post and its comments, we found the importance of the length of the line of attack. The length is determined by the amount of captures. This reveals something about the chain of tempos that I have totally missed so far. I wrote about it in the past, btw.
When I capture an unprotected piece, my line of attack is 1, while the line of attack of my opponent is 0. Maybe it is better to speak about the chain of captures. This leads to the following rule that is actually still only a hypothesis.
Rule: the longest line of captures gains wood.
We chase the 'tits', saddling the opponent with the 'tats'.
Serial and parallel
If my bishop captures an unprotected knight and my opponent answers this by capturing an unprotected knight of me, the length of both our chain of captures = 1, so nobody gains nett wood.
If my white bishop captures a series of 4 pieces in a row (serial), and my opponent has 4 separate attackers which capture 4 separate targets (parallel), both chain of captures add up to 4, so no one gains nett wood. This implicates that the total amount of possible captures can consist of both serial and parallel attacks, for both sides. If your amount of captures is not at least 1 greater than the amount of captures your opponent can do, than the combination cannot work with equal value of the captured pieces. If both amounts are equal, then you can only gain wood when the captured value of the pieces is higher. This way, we can predict which lines can't possibly gain wood. Thus pruning the tree of analysis.
Captures and threats
Only captures collect wood. Threats don't. Threats postpone captures. Only moves with duplo threats can bring the opponent into trouble, when he isn't able to answer the two threats in one move. All duplo attacks are based on this principle. If the opponent lacks space, it might be possible that he can't find an answer to even a single threat. That is called a trap. Or mate, if the involved wood is the king.