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Possible Lines
I find myself in these spots some of the time too, so I'm going to try to break it down a little deeper. Obviously simply folding AK to a 3-bet from a semi-nit is a good option, as Fnord suggested, but lets assume you call.
Based on the villain's stats, I would guess his 3-betting range is probably somewhere between AK+, QQ+ and AQ+, JJ+. We'll consider both separately as the "worst" and "best" case scenarios.
With you having an A and a K, there are 3 combinations each of AA/KK that are possible, 6 combinations of QQ, and 6 of JJ. There are 9 combinations of AK (considering you have an A and a K) as well as 12 combinations of AQ.
If Villain's 3-betting range is AQ+, JJ+ (best case scenario imo), then he is only likely folding AK/AQ on this flop to a donk-bet, and very possibly floating with them some of the time. Lets assume villain floats 20% for sake of argument. In that case, he is calling/raising with 3 combos of AA, 3 of KK, 6 of QQ, 6 of JJ, and folding 80% of 21 AQ/AK combos.
Thus, in the "best case" scenario, villain is folding 17/39, or ~%43 of the time. A 3/4 pot donk bet is possibly +EV, though by a small amount.
In the "worse case" scenario, villain is only folding 80% of 9 AK combos, and calling with 3AA, 3KK, and 6QQ. So he folds 7/21, or ~%33 of the time. A 3/4 pot donk bet here is very probably not +EV.
I suppose it's also very possible the particular villain has an extremely tight 3-betting range of KK+ as well, and though unlikely, probably should be considered given his stats.
Given these scenarios, I think c/f flop is best as played, and Fnord is right about folding AK to 3-bets from those with similar stats in the future, unless you notice them 3-betting you very frequently.
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