Catching this interesting thread late.
OP, I'm wondering if your logic would be the same if it were a $200 tourney and not a $2 tourney (and let's assume the same opponents)?
Because it sounds to me like you're saying: "I'm gonna gamble to go big or go home because there's no point in hanging around this thing if I don't have a big stack." I don't really see anything wrong with that logic. In fact, I think a lot of pros play the $1k and $1.5k events at the WSOP that way.
That said, I think from a pure odds standpoint (considering the payout structure as well as the tourney chips), it's still wrong. You just aren't going to hit your perfect flop often enough. And I also disagree that having 120 BBs at this point would make you that much more of a favorite for the FT. It's a long way to go with 30 or 50 or 120 BBs. At this stage, were talking about having 2 pct of the chips vs 4 pct, at best, or something like that.
I think you just need to admit: "I'm playing incorrectly because it's a $2 tourney and I've got better things to do with my time than grind this thing out properly. I'm playing for the fun of a big score, not the highest possible long-term ROI."

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