The weaker the hand is, the more likely I am to check it behind on the flop. So while I’m not often (though I am occasionally) checking AA or KK, I’m somewhat more often checking JT or A9. Even in a 3-bet pot, there aren’t too many second best hands I can expect to get it in with me on the flop.

You’re right that a lot of my flop checking range is weak, but most of that range is folding to the turn bet. When I check flop and call turn, it looks like I have either a moderate hand that doesn’t want to play for stacks but is good enough to bet the river for value, or a 9 that just improved to trips. Even a monster like quads or T’s full is possible.

The bottom line though is that it’s not very often that I’m checking the flop and calling the turn with a hand that needs to bluff on the river. Looking at it now, I can’t imagine he folds a T, but I’m pretty sure he does let go of an underpair.