[Liberalis]

I'd be checking behind on principal, even if I might be ahead and able to wring a bit more... for two reasons:

1 -- playing smaller pots with weaker cards
2 -- avoiding a bet that will only be called if I'm beaten

You've already seen him min-raise when he check-raised the flop and then check-called an 80% of pot bet on 4th. That FLAT CALL of 520 is very funny.. he's badly misplayed SOMETHING... what kind of cards does a donkey tend to misplay during the early game in such an odd fashion..? more likely something big than something small.. (unless it's AK, which he's not going to call with anyways)

I think our villain falls into one of these three groups:

1 - he made his draw and is laying a very poor trap
2 - he had us beat from the get-go with trip 9s and has misplayed them. Now fears the str and fl draws (but I believe he'd still consider a call of an all-in with his stronger hand)
3 - he has given up on the hand and will fold to a river bet

TPTK or big ppair is possible, and these are the only hands that will potentially call you and pay off a value bet on the river... But WHAT was that check/call of 520 (almost a fourth of his stack) on the turn? do you think that shows weakness? Or maybe a Q9?

all together I don't see a bet here as +ev.

And as Mr. Sklansky says in TOP.. If you shouldn't bet, and you shouldn't fold... well then you just check in the vacuum.