I think this one is pretty hard, so I have a question. Because hero has a lot of outs, he really wants to see both the turn and the river.

If he checks this high-card flop, somebody will probably bet. So he'll probably have to call one SB to see the turn. After hero's flop call, the flop bettor will probably bet the turn, and hero will have to call 1 BB, for a total of 1.5 BB to see the river.

So why not check the flop with the intent of raising if it's 1 bet back? It is likely that the bettor will call one bet back. Then check the turn, gambling that the flop bettor will also check for fear of being checkraised. If it works, you get to see the river for 1 BB. If the turn is a blank and the flop bettor bets again, you can be much more sure you're beat and fold.