Stack depth matters a lot, of course. At SPR, PIO thinks hands like Jx are mostly playing for stacks. It won't think that at bigger SPR. I looked at 5/10/20/35:
Going to 10 SPR (about 50BB preflop) dramatically decreases OP ability to check raise. Now, one pair is not going to be enough to get it in. When the stacks get even bigger, the amount goes up a little. I think the difference is that now PIO is looking to check raise hands that can run out the nuts: Hands with the BDNFD, and hands that can make the nut straight, either with hands like 43,63,64, and the double back door hands like QTs with a BDFD.
A good example of this is QTs at 20 SPR. PIO is check raising that hand about 85% of the time with the BDFD, and folding 85% of the time without it.
Another interesting one: 92s with BDFD is check raising 99% of the time; 92s without the BDFD is only check raising 7% of the time.
Another interesting note (still 20 SPR): PIO is pure check raising ALL of its 2P plus. This surprises me a little, as it seems to leave our check call fairly weak going to the turn. But, we do have some Jx, and PP that can turn into a set.