Is the passive player playing back at the LAG?

[Moneyline]

Online 8/16 4 handed

SB in this hand is slightly loose and passive to very passive. BB is very loose and his postflop plays don't make sense. By circumstance my image is extrememly LAG and my opponents are aware of it.

I open raise 6 [img]/images/graemlins/diamond.gif[/img] 6 [img]/images/graemlins/club.gif[/img] UTG, button folds SB 3bets, BB calls, I call.

Flop: 9 [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] 2 [img]/images/graemlins/spade.gif[/img] (3 players, 9SBs)

SB bets, BB folds, I call.

Turn: 7 [img]/images/graemlins/spade.gif[/img] (5.5 BBs)

SB bets, I raise, SB calls.

River: A [img]/images/graemlins/club.gif[/img] (9.5 BBs)

SB checks, I check.

[MoDOH]

I like it...

Are you betting this river if a Q,K or an A doesn´t fall?

[jt1]

Come the flop, there are 100 possible combinations that a passive to very passive player would 3 bet with. On the flop 51 of them have you dominated , 32 of them have a 25% chance of drawing out on you, 21 of them you dominate, and 1 of them has you drawing dead. So by the showdown, you will be ahead 6+24+18=48, 48/100 or 1-1

On this flop, I raise and bet turn, check every river.
On most flops, I'd do what you did.

Take out small pp 88 and less and you'll be ahead by the SD, 27/80 or 2-1. You still have odds play to the SD. *pretty cool

Take out AQ and you win by the SD 16/64 or 3-1. you're now about break even to call down and better if you play smartly. *very cool

[Moneyline]

[ QUOTE ]
Are you betting this river if a Q,K or an A doesn´t fall?

[/ QUOTE ]

I probably would not bet the river if another blank fell, but I'm not sure what move is correct. If I somehow knew that he was changing his playing habits because of my image, then I would definitely bet, but I didn't have that information at the time.