I think I really disagree with my response above. This hand has stuck with me, because it does feel like a really awkward spot. Trying to think about why, a few things jump out:
loose passive ... calls super liberally
Everyone checks
2 calls
So, that implies that initial ranges are really wide, the flop gave people draws, air, or monsters, and the Q
gave people something, or a draw to something, or a confirmed monster, although confirmed monster range actually goes down, as wouldn't that be the right point to r/r?
I think the key to the hand is how much of the turn calling range contains A9, K9 and x7s that remain missed draws along with 22-44.
Assuming no r/r, you are calling $40 against a pot of either $150 or $190. You really don't need to be right very often ... meh. I still don't know. The lack of aggression makes it really hard to eliminate much from their ranges, even with the t calls.
That, I think, is the key to the hand: how much of their range do you think the turn call removes?