I'll take a shot at this. First, my apologies; it's my birthday and I've been drinking, so don't take this advice to the Bellagio with your life savings...okay?
You have 45K and you'll be paying 15K to play every 4 hands from now on, so you are incredibly short-stacked. Your M is 3! That means you have 2 options: push or fold. Options A and B are off the table.
Against a tight opponent (one who would call with TT+, AQs+, AKo) it's an insta-push. He doesn't have enough to call most of the time. According to SnG Power Tools (which works fine even though this may not be a sit-and-go) your EV is +4.3% by pushing.
Against an average player (who calls with 66+, ATs+, AJo+) it still is a strong push; +3.7% EV.
Against a loose player (who calls with 44+, A7s+, A9o+, KJs) you still push, EV +3.0%.
Against a maniac (who calls with 22+, A2s+, A3o+, KTs) again you'd push, +1.6% EV.
Those are simply math answers. The decision should be based on more than that, especially when it comes to the last question, what my minimum push hand would be. If the BB is a solid player I'd push any two and take my chances on him folding. If he's an idiot who is sick and tired of my stealing him blind every time he's in the BB, or if he recently took a beating from someone and is on tilt, I'd have to take that into account. Normally...but not this time. I am out of time.
I have almost no fold equity left because my stack is only 4.5 big blinds. The big stacks are to my right. I may never get another chance to be heads-up again. In this case I push any two. Fourth place isn't so bad...
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