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No...he does not have JJ. You raised it enough to that he only barely has odds to call, and if he's a rock, he's not normally calling raises with PP's to hit the set. Not to mention, if he does have JJ, he would reraise more, because he doesn't want you to hit a flush draw when he has top set. If he has JJ and you have ANY spade, he's giving you odds to call. Think about it, if you had AA with the As in your hand, you'd still call that hoping for a spade.
Most likely he has KK with the Ks in his hand. YOu are a slight favorite.
Call his raise.
Then, bet 1/2 the pot on the turn, assuming no spade falls. If it does, well damn. check, and then see what he does.
If you bet 1/2 the pot on the turn and then he reraises all in, you can probably safely fold your hand. KK will merely call your bet, hoping you have QQ or an ace high flush draw.
I think I covered all the contingencies?
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