I would bet 99. I would probably x/c 8 with a medium kicker.

why checking the river with 99 ? vilain only call preflop so he is unlikely to have TT+, I doubt he can have a str8 or 2 pairs un this spot either. So, basically, we are loosing vs a set. At higher stakes, I agree with checking the river, but even reg at 10nl might call 3 streets here with A8 or worse.

This is a pretty nutted hand on most rivers isn't it? And on the 3h turn villain's "floating" sort of turn calls are mostly going to be A-high which will just check behind. Seems like an easy bet-bet-bet.

As far as what hands to check flop, against villain's perceived range 99 is beating just as many hands as AA on the flop, but has far less equity against villain's range because stuff like JT has 25% equity. So we want to bet with something like 99 because we benefit from getting folds from those hands and check with something like AA because it benefits much less from that portion of what the bet does.

99 ca get theee streets from an 8, and you don't block the strong 8x that call down.
the 4 dpesn't change the board tpo much, so there aren't that many mediocre hands to protect now, sonce they were moslt mediocre flop hands that are good check-calls on that street.

Agreed. Just play bet bet bet on the most rivers.