in BB with 66778 ds. UTG raises 3x, another calls, you are in bb. People are stacking off generally light in this game. Defend? What kinds of flops do we expect value from if we call, and what are trap flops that we should be folding?

No.

Value flops: We're hopping for miracle flops of SF/Full house, and only a low draw that never completes, hoping that you can string A2xxx and the like along for a couple of streets before they brick out on the river. Your hand needs 8 and under cards to make the high side, and your low side is worthless; at best you're playing for the high side [which isn't likely], but in doing so you're always going to be playing on a board that either has a completed low or a draw to a low.

Trap flops: 876, 765, and every other one.

tl;dr Never play this hand.

Do you think the fact that its 40BB makes a difference? The SPR would be roughly 3 on the flop. We have effective position, and on any decent flop (ex. 876 765 et al) where we hit a set, or straight we can likely repot allin.

It is worth noting that against two very tight ranges, you have 40% equity in roughly 40% of flops. Does that not warrant consideration at the very least? You have a disproportionate amount of equity on a disproportionate amount of flops, and 3-1 immediate odds on the preflop call plus the implied odds from the effective position.

Please show your work on the ranges you've constructed for your two opponents. Intuitively I have severe doubts that your equity is 40% on 40% of the boards.

It's Big0. A hand like 77799 has 23-25% 3-ways.

Dunno if you have done your homework, but if this is a 20bb cap game, we can sometimes squeeze this hand for value.

FWIW I'd also fold this hand in this situation for the reasons you listed. I have no idea how to realize my equity.

Intuitively this seems like a fold based on raw equity. This is not even a 50 percentile hand and aside from low boards where we smash the flop we are never really happy putting a lot of money in.

http://propokertools.com/simulations...5%25&s=generic

That's 40% of 37 flops. Or ~15 flops. Not really the entire universe of boards to draw conclusions from.

Even low boards that we smash are most likely splits as we have the nut worst low. We might see equity against opponents who are willing to get it in with broadway cards only (are those even in the 15% range of hands?), but other than that example I believe the chances are too high that we're going to get scooped at worst and split at best - I just don't see any scoop potential for us, regardless of what equity a hot and cold sample says we theoretically have and as such while we might return 40% equity, it's going to be in this pattern:

split pot
split pot
split pot
get scooped
split pot.

Yes, we've got 40% still, but if we're heads up preflop all in (or just take a flop heads up and play poker) and no dead money in the middle, how is 40% equity good for us here? Also, with 40BB only, who are we folding out to get dead money in the middle?