sauce obv nothing wrong with 3-betting AK in 4)

I've never thought out the reasoning behind the perhaps unnecessarily tricky AK flat-call pre, CR flop vs tight ppl's ranges when OOP but I've had pretty good success using it.

Here are some possible justifications for the play, along with assumptions/conditions for it being worthwhile :

-post flop a mediocre/standard nitty player will likely call 1 street with a mid-strength hand in a reraised pot if we have an aggro image, the main exception being A-high boards (one of the only spots where we want him to call)

-3-betting from the blinds and firing the flop reps much less strength to the avg nitty reg than CR the flop after smooth-calling from the blinds (wider range of hands we can have - depending on texture - more likelyhood they fold with less of their stack commited)

-we usually only fold out the very bottom of villain's range preflop (something like AJs, maybe AQo and 77, maybe 88 and lower PP's). We either have these hands crushed or else have a huge amount of fold equity when we CR flops where they don't have a set

-our hand is underrepped

-we can balance with sets and big pairs if we get caught

-vs a hand like QQ JJ or TT on a low flop, we set ourself up to take villain's stack more often when we suck out on the turn. If we CR a low flop, villain calls with QQ-TT (unusual for nit to get it in when we can clearly have a set), it'll be more likely we get paid off on an A/K turn than if we fire flop, villain calls, and we hit our 6-outer as the aggressor with AK clearly in our range

When you 3-bet and are called pre and on the flop by the nit, I think you'll need to 2-barrel shove the turn quite a bit looking for the nit to make a relatively big fold (much of the time with an overpair).

On balance I think the ev of the line is similar to that of the 3-bet pre line. What makes me think it's slightly better in terms of ev and meta game is the extra money we get from the bottom of villain's range (good aces that whiff the flop and small PP's that c-bet) as well as the deceptiveness of hitting our 6-outer vs QQ-TT on the turn.

Finally, I think that most nits have a much tougher time stacking off to an "obvious set line" (flat-call pre, CR flop, fire turn) than they do stacking off with an overpair to an aggro 3 bettor's bullets.

There are other factors I think might be important, like balancing with sets, not spewing with AK (much of this will depend on turn decisions after a CR is called) but this post is already probably too long.