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I was thinking with an AF of 11 I just ship this PF. The obvious problem is you may well be folding hands like TT or JJ that you may stack on an under-card flop.
This may boil down to the maths and I don't have time now to do it, but shoving or calling would likely depend on his calling range to your shove. When he calls your shove it seems likely you will have <50% of the equity. So I suspect the best course of action is actually to call PF and hope for a flop without a A or K.
Text results appended to pokerstove.txt
359,583,840 games 0.391 secs 919,651,764 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 52.634% 51.06% 01.58% 183588540 5675268.00 { JJ+, AKs, AKo }
Hand 1: 47.366% 45.79% 01.58% 164644764 5675268.00 { QQ }
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