I feel like this is the most efficient layout. it is tileable. you'd just add the 4 by 4s in a cross pattern. you want to have the most 4 dice around a dise roller where each dice completes a 3 row of sixes for the least amount of unrolled dice. In this design it's 6 dice per dice roller. I don't know how you could make it more efficient but I'd like to see other people try to improve on my design
for those amount of dice and dice rollers I think yes it is the most efficient but after some time you'll notice that you will have too many dice rollers and not enough dice because of how the price scales. you want to use as few dice per dice roller and still use the three of a kind ability because it gives the most points. if you had infinite of both this would indeed be the most efficient but you don't.
1. Maybe this was changed in an update, but there isn't a 3-of-a-kind bonus. There's a 2-of-a-kind bonus, though I don't think boosting the odds of that are worth that many unused dice.
2. I don't think you actually boost the odds at all. I think they're actually lower. With your setup, the dice being rolled only have two dice next to them. Contrast mine (I took a screenshot time).
As you can see, with the exception of the outer edge, every die has three neighboring dice, for roughly 50% greater odds of Two of a Kind triggering. You could have that for all your autorolling dice by adding another 24 dice to your setup, but at that point you have 72 dice to twelve cups, whereas I have half that many dice for nine cups.
I just don't see any way that a setup could be better than this one, mathematically speaking. Every die is being actively used, and has as many neighboring dice as can be crammed next to it while using them all. None of the buffs give bonuses for anything except being next to dice or...rolling more dice, I guess. Aside from rotating the setup 90 degrees, no other setup can match it.