correct to draw?
 

Am I correct to draw here? I'm reading Yao's book, and am learning to calculate the EV of my plays. If this is an incorrect draw, can someone show me why? Thanks!

The SB has been playing 60%+ of the last 100 hands. The BB has lost 30 BBs in the last 30-40 hands, showing down unsuited single gappers, and small aces (in bad places..I think) ... very aggressive, but not showing down enough for me to label loose. The CO poster is an unknown.

PokerStars 1/2 Hold'em (10 handed) converter

Preflop: Hero is Button with Q[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/spade.gif[/img]. CO posts a blind of $1.50.
<font color="#666666">6 folds</font>, CO (poster) checks, Hero calls, SB completes, BB checks.

Flop: (4.50 SB) 9[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/heart.gif[/img], T[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, <font color="#CC3333">BB bets</font>, CO calls, Hero calls, SB calls.

Turn: (4.25 BB) 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, <font color="#CC3333">BB bets</font>, CO folds, Hero calls, SB calls.

River: (7.25 BB) J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
SB checks, <font color="#CC3333">BB bets</font>, <font color="#CC3333">Hero raises</font>, SB calls, <font color="#CC3333">BB 3-bets</font>, <font color="#CC3333">Hero caps</font>, SB calls, BB calls.

Final Pot: 17 BB

Re: correct to draw?
 

You have a clean 8-out straight draw on a rainbow board. You're definitely correct to draw on the flop and turn.

You also might want to consider raising preflop and/or raising the flop.

Re: correct to draw?
 

Postflop is solid.

Preflop can go a few ways. If the blinds can actually fold it's an easy, easy raise. But if you're pretty sure they'll come along anyway (and won't raise preflop), I don't think a limp is too bad.

That said I'd really like to raise it up preflop.