Horseshoe Hammond, effective stacks $400, I raise on the CO with JJ and BTN, SB, BB, and aggrospew UTG call $12 each.

Flop is J76ddd.

Checks around, I bet $40, loose passiveish BTN calls, fold, fold, UTG x/r to $140. He's showed up with plenty of wild holdings in the last couple hours.

Action? UTG covers all, BTN has slightly less than myself at about $300.

Raise more pre
Gii utg can have worse 2p, trips, lp player could be chasing, on weaker ect

What does "wild holdings" mean? Does it mean he can have 82dd here? Or does it mean he can have J6o here? Or both?

I'm getting it in most of the time with top set.

Ship it- UTG can have a naked FD if he's as spewy as you suggest (and will probably reason he's "priced in"). Not sure if BTN is flatting with made flushes all that often here, cos he should expect UTG to come along if he raises. He's very likely to call with nut and possibly second nut FDs as well as sets and 2 pairs, so you're doing really well against his current range.

You are 60-70% favorite if ahead (flush, OESD, combo) and no worse than 35% if behind (made flush).

You would be putting $350 into $880 (40%) if B folds out and UTG calls your shove, so you are -EV when behind here but 'most' will suggest that you are ahead more than behind so it's a call.

You are actually $350 into $980 (36%) if UTG folds when B calls your shove .. so that would be =EV against a flush. AND I would suggest that if B calls a shove, its going to be with a flush, so that is your variable here.

If you can handle the swing, then call it is. GL

If I'm behind, is it more profitable to call for a BTN overcall?

Wild holdings as in yes, 2P+ is plausible here, and maybe even a pair with the Ad.

Also, why open more than $12? I'd assume because of the propensity for multiway play. LHE and tighter 1/2 home games are my main games.

Game dependent imo. Most of the time 12 is pretty standard in the games I play. Raises outside of the norm are often seen as telegraphing and dont by players afraid of a flop. Pretty much every time I see a $17-$20 raise pre, it's JJ or QQ, very rarely TT.

More profitable? Does that mean win more? Or 'better' call/use of your chips?

It's certainly better math anytime there's more chips going in the pot. But the ranges don't change, do they? How much larger is B range when 'only' calling $100 v calling a shove? Probably not by much, but you give B a better price to call at 'only' $100 when you flat.

I'll let others plug the computer, but if you call you get no folds. And there is a % of the time when you shove that you will just take it down. Some might consider that lost value, but when you can increase your stack by almost 50% ($230ish) without a showdown you should be happy.

To get back to your original question. Yes, it's better 'odds' to just call and let B also call to draw to your boat going to the Turn. $100/$480 is 21%. Rember that win % is based on getting to the River, so if you think you might fold to 'any' Turn bet, then this is actually 'the same' or worse use of your chips since you are only using them to get to one street, not two.

You really cant determine the answer to your question without putting some ranges for both players into the mix. If you want to solely look at this when you are behind, then you need both players in there at showdown to break even at 35% to justify putting any chips into the pot. The less chips you put in, the better you will look since the dead money in the pot ($180) will have a bigger factor on any pot math.

So I guess I have concluded that it's better to just call ... if ...
... you want to assume that you are behind ...
... and you 'know' that B is calling as well ...

Otherwise any chips put into this pot 'knowing' you are behind would not be a correct move ... that's why we have ranges, because sometimes the math just aint too good. GL