Theorem: If Quackle plays the ensuing positions relatively well, and a sufficiently long simulation is run, then the difference between a 2-ply and a 4-ply represents a trend that approaches each play's true value. Thus, if two plays are simulated first as a 2-ply and then as a 4-ply, and one play does significantly better during the 4-ply relative to the other play, then the "true" value of the play that improves during the 4-ply is greater relative to the other play, since the 4-ply is more representative of the play's worth than the 2-ply. Thus, if play A wins against play B by 3 points during a 2-ply and only 1 point during the 4 ply, then the plays are nearly equal: in fact, play B might be better than play A.
Example: Let's take the opening rack BDIIKSW. Quackle's 2-ply lists KIWI at 31.9 and KIWIS at 31.1. Quackle's 4-ply lists KIWI at 34.3 and KIWIS at 31.2. Therefore, the difference between KIWI and KIWIS is greater than 3.1, and is probably somewhere around 5 or 6 points, since the trend indicates that Quackle's shortcut algorithm of evaluating leave and board position are underappreciating KIWI and will continue to do so for multiple turns. In other words, BDS is undervalued by more than the difference between the 2-ply and the 4-ply in this specific example.
Intuition: Let's say that we start with two cultures of 500 bacteria (or pigs, or any animal you want really) that we release into the wild in two different locations. Bacteria are allowed to move where they want to spawn, but obviously environment is relatively consistent over the space, and bacteria move slow, such that it will take hundreds of generations for the different strains of bacteria to meet. Each bacteria can reproduce up to twice and die. The environment strongly influences both survival rate and reproduction rate. The resources in the environment are finite.
Group 1 after one cycle of reproduction has delivered 550 offspring, while group 2 has delivered 520 offspring. After two cycles of reproduction, group 1 has delivered 580 offspring, while group 2 has delivered 560 offspring. Which group will have more offspring after reproduction cycle 3?
This is more similar to simulation than it first appears, since it appears that survival is easier for group 1, but reproduction is easier for group 2. Likewise, there is more immediate value for play 1 and more long-term value for group 2.
Thoughts? I'm not sure how useful this is long term, but it's another way to understand Quackle as a tool. While the applications for this are limited, I think that this is a good theorem to keep in mind when assessing plays using Quackle. Of course, if your understanding of Quackle is this sophisticated such as you know when the postulates are satisfied, you shouldn't need Quackle anyway...