Mix game badui round. 4-5 people to first draw and I draw 1 to 1-2-3. I bet, button raises ( took 2) 1 other call, I 3 bet, butonn caps, call call. 1:1at.

Now fun part. Check/check button tables 10-7-6-3, and I tell him there's a draw left..... Draw or pat?

You still have guy behind you to worry about who might already be pat or make it on final draw. With super strong 3 card you have potential for winning multiple bets on river if both of you draw good.

You can always try the ghetto version of what you are considering by drawing and betting river anyways.

If you draw there is a chance guy behind might attempt what you are considering, if successful to make card exposer break or fold you can call river with 123.

Draw. You don't just need him to draw, you also have to dodge ~10 outs per villain. The best candidate for a semibluff pat would be a J badugi with button holding one of your outs (preferably the 3).

The third guy called between button's raise and Hero's 3-bet so he must be OOP.

OK, with V in the middle, patting is slightly more attractive but I still prefer drawing. Villain might be able to sniff out what you are up to and just pat behind anyways.

In the case of hero pat, villain pat, bluff the river?

In the case of hero pat, v break, check river, right?

I think its an easy draw too, I would prefer pat if his hand was 234T or if your hand was like 358x (hard for you to have this but maybe you made J8 and broke or something after first draw)

Yeah your draw is too good. I can't imagine the card exposer ever breaking (T763 is basically unbreakable) and I'd expect him to be super suspicious of anyone representing a big hand.

I draw for all the reasons others state, but also because I don't think I'd ever be able to sell a pat hand at game speed here. My guess is that you need to fade too many outs from both players to justify trying to pull off what would be a pretty epic snow.