Focusing on Captures and Threats (CT)
If you have a close look at CMCT, as I have done lately, then you discover that it is actually quite a mess. The first C stands for Check. Which is actually a Threat of the King. So why do we have two threats, one for the king and one for the other pieces? It is a half-baked solution for pruning. The threat against pieces can be ignored while the threat against the king cannot. It doesn't solve the difference between the threat against a queen in comparison to a threat against a bishop. How differs a check from a mate? It are both threats against the king But in the first case the king has the room to escape the threat (by walking away or interfering with the attacker, while in the case of mate the king can't do both. What about the M? It is in fact a threat (to mate in 1), and it works because two potential extra conditions: the king can't escape, and the attacker can't be interfered with. So CMCT tries to combine 3 elements: type of threat (capture or threat to cap...