So, I took today's Daily (26 Nov, dwarf bloodmage on halls of steel) to test the algorithm. I have no intention to hack dailies or anything, it's just since today is probably not very difficult, any spoilers about shop pool will likely not hurt anyone's enjoyment.
I took preps in a way that they do not impact shop spawn (I took first preps; preps in red impact shop spawn):
Slot #1:
Extra Mana Boosters / Flame Magnet / Apothecary
Slot #2:
Jehora Jeheyu /
Wicked Guitar /
Elite ItemsSlot #3:
Bear Mace / Compression Seal / Mystera Annur
Slot #4:
Smuggler's Den /
Agnostic's Collar / Fewer Glyphs
The items I got are:
So, there were three preparations that could potentially impact shop pool. Slot # 2 had option for Elite Items and for Wicked Guitar; slot # 4 had an option for Agnostic's Collar.
I think that preparing Elite Items in Slot #2 and not preparing the Collar in Slot #4 would swap items as follows:
Now, the more tricky part is the item preparations. Because depending on the RNG rounds, it may alter other items. So my assumption of preparing the Wicked Guitar in Slot #2 and not preparing the Collar in slot #4:
If the Collar is prepared in slot #4 and neither the Guitar nor Elite items in Slot #2, change is pretty much as above, except all last 3 changes become "should" instead of "may".
If both item preps are taken, then:
If Elite Items are taken with Agnostic's Collar, then list should slide up:
Now. If anyone cares to confirm / deny some of these, it would be much appreciated!

"Thinker", just without the "ache".