$22: Push or wait with an uber short stack

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With a range of 22+, A2+, KT+, QT+, JT+ (which is actually probably overly generous) for the SB, and any 2 for the BB, pushing is, as noted, EV neutral. Even if the SB is slightly tigther (22+, A2+, KT+, QJ+) it remains more or less neutral.

Even if BB folds 20% of his hands, it is only marginally +EV. In a 20, I'd push, because the 20 players I've encountered often do not correctly understand pot odds. I've seen BBs fold for a 1/2BB bet when they were getting 5:1.