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I would definitely call if I knew he had AK. I used to think calling in these spots was bad as you are essentially flipping, but this completely ignores big stack dynamics. You are 56% to win the hand and that big stack will carry a lot of weight around the table, particularly in the early stages. It will be worth more than what ICM predicts since you can really push other players around.
Text results appended to pokerstove.txt
164,381,184 games 0.250 secs 657,524,736 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 56.148% 55.94% 00.20% 91959624 336876.00 { JJ }
Hand 1: 43.852% 43.65% 00.20% 71747808 336876.00 { AKs, AKo }
As for his real range something like 99+ or AQo+ seem more or less right. You don't have enough against this range. The problem here though is ranging your opponent is really difficult. Some opponents will only make this move with QQ+, others will do this with 66 or KQs. Obviously, if he's using the latter range, it's a push.
Text results appended to pokerstove.txt
647,250,912 games 0.781 secs 828,746,366 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 50.184% 49.22% 00.96% 318570540 6243024.00 { JJ }
Hand 1: 49.816% 48.85% 00.96% 316194324 6243024.00 { 99+, AQs+, AQo+ }
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