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I'd probably just call his 4bet.
Yup this is what I'd do readless, which I forgot to mention.
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But depending on the answers to the questions Bob148 asked above, a 5bet could be good.
(a) my preflop 3 betting frequency, = If high, I'll shove more. If low, I'll call more.
(b) my preflop 3 betting range, = The more suited connectors and Axs I have in my perceived 3 bet range, the more I shove JJ here.
(c) his preflop 4 betting range, = If he's 4 betting TT+, AK, then shoving JJ doesn't make much sense. If he's 4 betting 55+, AJs+, AQo+, KQs and 87s, 76s, A2s-A5s, then shoving JJ should be wildly profitable.
(d) his stack off range vs a 5 bet, = this will be very dependent on the above stuffs. Vs very wide 4 bet ranges, JJ wins the money by shoving no matter if he calls a lot or folds a lot; it puts him in a lose lose situation. Vs very tight 4 bet ranges, call JJ getting a great price.
(e) how solid all of the above reads are.
Very important; idk why I left this for last. If the only hands you've seen him 4 bet are KQs and AA, then calling is probably best. If you've seen em 4 bet 55+, AJs+, AQo+, KQs and 87s, 76s, A2s-A5s, over a large sample of hands, shove and win lots of money.