[King Yao]

I don't think this is a hand where it is important pinpoint any probabilities. There are too many variables. In order to isolate one variable, it means you know exactly what all the other variables should be. In this hand, you would have to figure out many probabilitiies, including:

1. prob he doesn't check-raise with an Ace on the Flop
2. prob he consistently calls with absolutely nothing on the Flop only to call on the Turn.
3. prob he never gives up on any pair and always calls to see a showdown
4. prob he doesn't give up on a inside draw until the River...and even then, does he continue to call if he picked up a small pair?

just too many moving parts IMO to isolate anything useful. Isolating probabilities is a useful tool, but not always applicable.

Here's the way I look at this sample hand:

You played it exactly as I would. I like the bet on the Turn - give him a chance to fold a 2 or 3 (low pair) or 4 or 5 (straight draw). But if you are check-raised, then you can safely dump and give up your 4 outs. Against trickier players, I would check on the Turn, because trickier players are more apt to check-raise semi-bluff on the Turn and/or bluff on the River - but given no read as you said, I'd bet it. With that said, I think it is a small difference between betting and checking (and calling on River).

P.S. What do you need me for anyway? You kicked my ass in HULA!