Check behind, then raise river -- a call for an attempt at an analysis

[sweetjazz]

Hero has xx in the CO and open raises. All fold to the BB who 3-bets. CO calls.

Flop is Q [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/heart.gif[/img] 4 [img]/images/graemlins/heart.gif[/img]. BB bets, Hero calls.

Turn is 3 [img]/images/graemlins/club.gif[/img]. BB checks, Hero checks.

River is 9 [img]/images/graemlins/club.gif[/img]. BB bets, Hero raises.

What range of hands should Hero have? Let's assume the BB is a thinkingTAG who has a photographic memeory and a huge database of hands on Hero, so Hero needs to try to match the ideal game theoretic distribution of value-betting and bluff-raising.

I realize it's not possible to spell things out precisely...we don't know how often hero raises the flop with, say, KT and how often he just smooth calls. But maybe we can get a discussion going as to a rough range of hands one would have to play all streets this way.