[elindauer]

good analysis, but I think a range of {66-44,AJ-A3,K7,Q7,J7,87,97s,T7s} is more reasonable. Quads, 3s full and overpairs would have probably spoken up, even from a passive player.

Removing these, the range calculator has us as very slight dogs:

There are 171 combinations in this range on this board.

* full house: 87 combos (50.9%)
A7(9) A3(9) K7(9) Q7(12) J7(12) T7(3) 97(3) 87(12) 66(6) 55(6)
44(6)

* trips: 84 combos (49.1%)
AJ(12) AT(12) A9(12) A8(12) A6(12) A5(12) A4(12)


Which would make it seem that checking is best. It's really close though, because with these very mediocre hands, a bad player is almost certainly not going to play the hands the same every time. He'll fold ace high sometimes to your bet. He'll call KQ sometimes. He'll fold 55 once in a while.

Further complicating the situation, even a passive player is going to come alive sometimes and bet the hands in this range. Surely even a passive player will bet his turned 7 on occasion... so you have to discount him having a pair while the ace high hands look solidly in his range.

Figuring out how to discount this stuff is hard, but my experience is that you'll find yourself up against ace high often enough to get value out of a bet. I play in pretty aggressive online games though, where even passive players don't just check call 44-66 on a 332 flop, and where check-calling a turned top pair is also rare. With a read that your opponent really will just check and call all these hands, checking is best.

-Eric