[Rush17]

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caveat: raising flop or turn will not get me HU with either player.

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Are you saying that because you read the utg for a nut low/wheel draw, or, do you just feel that he wouldn't fold because he's still steaming, or just doesn't understand the value(or lackthereof) of hands?

I think, if you are ahead of the button, it's probably not by much, and if he has 3 A's, then you're obviously way behind and your 62 might not be the best low draw either.

Given the "caveat", I would either check/call the whole way (hope your hand holds up/improves), or, check/fold.

If you can't knock the middle player out by checkraising the button or betting straight out, then why do either? To me, this hand is either WA or WB to the button, and your low draw is a little too iffy for backup in a 3-way pot, and especially if the utg steamer woudn't throw away a low draw that wasn't the lock draw yet still better than your 62.

So, if continuing, I would keep the pot small and check/call opposed to putting in 2-3 bets on the flop. Keep in mind, that, if the button didn't flop a set(or a hand like A24/A23, then like you pointed out, he'll check behind on the turn anyway. And, because your hand really isn't that strong (but it is, imo, good enough to continue with)and because you can't knock out either of them with aggression, then keeping the pot as small as possible is what I'd be looking to/willing to accomplish against 2 opponents.

By the way, when you lead the turn, did you pick up the nut flush draw? If so, fine, if not, then I don't care for your bet, again, given the caveat.