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I think with the call, you have to give the reg some credit here for a high probability of holding KK+, so I'd fold.
Without that call I'd call myself. AA or KK forms such a small part of the initial raisers range, that you can almost discount it. The AI shove is usually not AA or KK, since most people don't shove these hands over a 80 chip bet. It's more likely a hand like TT, JJ or AK (I believe the range should be weighted here). If I called and he flipped over AA or KK, I'd make a note on how he plays this for next time.
As for ICM, I reckon it says call with KK+ and fold QQ+, but having a big stack this early is probably worth a few %. I'm prepared to take a slightly -EV gamble here. Plus WIZ isn't weighting the hand range, which I think is necessary is this hand. Below I've thrown out AA in the analysis to weight it less in favour of AA or KK, and you are well ahead.
Text results appended to pokerstove.txt
359,583,840 games 0.437 secs 822,846,315 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 41.814% 40.24% 01.58% 144690252 5667888.00 { KK-TT, AKs, AKo }
Hand 1: 58.186% 56.61% 01.58% 203557812 5667888.00 { QQ }
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