HU. BTN opens, we 3bet (lets say we 3bet the top 20%). Flop comes down XXY. Say both players are equally likely to end up with trips here and that's 20% of the time.

I'm trying to come up with something that could remotely try to resemble a GTO line for both sides. Since our range will contain a lot more high overpairs, assuming a non-wet board our opponent will for the most part have a {trips+,air} range and we have {trips+,overpair,air}. I guess our sizing should be pot, because we would like to include as many bluffs as possible while maintaining optimal bluffing frequency (so 1/3 of bluffs preferably those with some backdoors, 2/3 overpairs+trips). As we are up against a {trips+,air} range we don't need a check-raise range. Check-call some trips and stronger overpairs, check-fold the bluffs (which I assume should be less than 50% of our checking range).

I realize this is simplifying things to the extreme as it is not taking into account stack sizes, flop raises and future streets. I also imagine you can create a fairly balanced checking strategy. Or one where you bet a smaller sizing, but include a check raising range. However I'm wondering if you see any glaring flaws in what I come up with. Obviously I won't create a GTO strategy, but I'm more interested in improving my ability to create strategies that are fairly difficult to exploit regardless of how our opponent is playing. And wondering how you approach these sort of boards (hit rarely, but when you do hit hard) in general.

Also an easier scenario - this time the flop comes down 722r. The 3bettor has WAY less trips+ in his range than the caller. Does that mean he should be checking his entire range here?