[Guruman]

On first glance, I thought leading out had the greater upside, but I think I was wrong there. Checking definately has greater variance here, but it seems like the few times that bb has a straight or a worse flush we net a few more bb on the river. It's crazy risky though, because either weaktighty could check the river through with her pair, or 80 vpip guy could have better diamonds than us.

some assumptions here:

1)if bb is going to call, he'll not care where the bet came from, as he's not trying to read any hands. He's also willing to call one bet at a time, but not as willing to call two bets at once.

2)if bb has a flush or straight, he'll be on a checkraise here.

3)if bb missed his draw, he's check/folding here regardless

4)when button bet the turn, she signified that she liked her hand and wanted to show down. (we'll put her on a paired ace for now)

5)button will call a bet, but may ocasinally check through the river with a pair out of fear of being raised.

6)for now, lets assume you'll not push it to three bets on the river. I don't know if you would or not, but I'll make that assumption for now.

since bb is the deciding factor here, lets first look at a hand he's check/folding.

a)sb check, bb check, button bet, sb raise, bb fold, button call(+2bb)
c)sb check, bb check, button bet, sb call, bb fold (+1bb)
b)sb check, bb check, button check (ugh)

now we'll put him on a check/call with a pair.

a)sb check, bb check, button bets, sb raise, bb fold, button call (+2bb)
b)sb check, bb check, button bets, sb calls, bb calls (+2 bb)
c)sb check, bb check, button check. (ouch)

now lets have him checkraising a straight or a flush that we may or may not beat.

a)sb check, bb check, button bets, sb raises, bb reraises, button folds, sb calls (+4bb or -3bb)
b)sb check, bb check, button bets, sb calls, bb raises, button calls, sb calls (+4bb or -2bb)
c)sb check, bb check, button bets, sb raises, bb calls, button calls (+4bb or -2bb)
d)sb check, bb check, button check (yup, zero)

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so instead of checking, lets go through these and bet out instead.

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bb is checkfolding a whiffed draw here.

a)sb bet, bb fold, button call (+1bb)

now bb is calling a pair

a)sb bet, bb call, button call (+2bb)

now he's got a flush or a straight

a)sb bet, bb raise, button fold, sb call (+2bb or -2bb)
b)sb bet, bb raise, button call, sb call (+4bb or -2bb)

In all of these I assumed that the button wasnt going to raise, and that she'd occasionally check through. betting will surely win you money here, but checking is fun if you like to take risks.