Don't like your call, unless this guy has a Hx of doing crap like this. YOu made it quite clear you have a good hand, and then he made it even more clear that he likes his better. You are only looking at AK, AA, KK, or QQ here IMHO vs a decent player. And as you found out, you are basically break even vs AK.
Lets look at a EV breakdown given this hand range:
There are 16 ways for him to have AK, and 6 ways each for him to have AA-QQ each (53% of the 34 possible combinations). Vs AK, JJ is a 56/44 favorite, and vs AA-QQ its a 81.5/18.5 dog.
So vs with the 16 ways to have AK we win 1570 56% of the time:
1570 x .56 = 879.2 x .47= +413.2
Vs the 18 AA-QQ, we lose 1100 (and our tournament) 81.5% of the time:
-1100 x .815 = -896.5 x .53 = -475.1
Adding those two numbers together, we get -61.9, whihc means, every time you make this call, you are losing 62TC, making this a -EV move.
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