Collectable gathering rotations?

[PirateCat]

I've found the four-hit method to be more reliable (in fact, it's pretty easy to prove mathematically to be the better strategy over time, but I'm too lazy to do the math right now)

Math for the record:

The four hit method yields an additional collectable item if at least one of the three Impulsive Appraisals gets you the Discerning Eye buff. The chance of this not happening (which is easier to calculate) is 0.7^3 = 0.343, which means that there's a 65.7% chance of a proc that gets you the extra collect. In other words, the average EV is 2.657 items per node. (This doesn't account for the fact that multiple DE procs will raise the collectability to higher tiers and get you slightly more scrips on occasion.)

The three hit method gets four collectables 9% of the time (two 30% chances succeeding) and two collectables 49% of the time (two 30% chances failing). The remaining 42% is the chance that one proc happens and you get three. The expected yield is therefore (2*0.49)+(3*0.42)+(4*0.09) = 2.6 items per node.

So there's only a tiny marginal advantage to using the four hit method if you just look at average number of items collected, but I still like the four hit method better for a few reasons:
- Potential for higher collectability. While you're not going to ever get enough to collect four items, if more than one DE proc happens you'll get higher tier collectables. This is arguably the best way to go for counterfoils as well since you'll naturally get some items that could be traded in for these as you gather primarily for scrips.
- Less streaky RNG. You get the better result almost 2/3 of the time with the four hit method compared to it being a coin flip for the three hit method, which in turn means you're less likely to hit a bad streak.

Now for blue scrips, there's a clear winner for the rotation. Use Methodical Appraisal three times, fitting in two Discerning Eyes and a Single Mind in there somewhere. This works for blue scrips and not red because of the lower collectability threshold, but it guarantees you three collects, RNG-free (unless you don't have enough GP to hit a gathering chance buff, then you still need to deal with the occasional gather failure.)