Folding AA preflop
"But in a winner-take-all situation, I'd have to push. In this situation, I have to win it all to win anything. So I don't think folding into a short-stacked heads-up matchup is the best possible use of AA."
With chip stacks of 3900-3900-200, I definitely play AA in a winner-take all situation, but I would fold it if the payouts were 50-30-20.
If I fold, I'm basically guaranteed second, for a payout of 30. In practice, it's maybe a bit lower because of the chance the other two players chop.
If I call and win, I get 600. It's still almost worthless in heads-up play if the opponent has any clue what he's doing. My EV in that case is about 31.7, if you assume we're equal heads-up players. But if I lose, I get 20. So you'd need a better than 85% chance of beating two opponents to make that call worthwhile, and AA doesn't have that (no matter what reasonable assumptions you could make about their range of holdings).
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