Interesting spot. I think whatever I plan to do, I would 3bet this hand. For one thing, that way if btn 4bets, you can re-evaluate. But also with this type of hand, you want the bb out and want it HU. And again, you can re-evaluate if the bb also participates.
I think pitching both the 3 and the 6 is a viable option too, and drawing at 258. Because if you ditch the 6, keeping the 3 doesn't help you that much, and obviously hinders for badugi drawing purposes. I think I would probably do that if the bb came along.
I think I would lean towards just patting though - if the btn doesn't 4bet and it's HU - as have you more fold equity that way too. Which is pretty important in this game.
My thoughts, I think its an easier pat once bb calls. Your half the pot equity is pretty high Three ways and worth it.
The more I think about it if bb folds I draw two. I think button is calling down any decent three card whole way. You are going to actually bet whole way hoping to get half. I really don't think you have very much fold equity hu vs button patting
Bert is the ultimate rakeback grinder, he sits down on Sunday and plays until he's sure he's got the leaderboard locked up. Never refuses action, and plays wherever he can get the most krill. I tried to keep up with him one week and lost my ass because unlike Bert I can't play three different games HU with three different villains at once.