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He opens to 4x bb ($0.16c), and we are contemplating 3betting to 11x ($0.44c) IP with ATs. In order for this to be profitable, we must win 11/16.5, or 66.67% of the time. Do I believe he will fold more often than 66.67% of the time to our 3bet? Sure. I do not dispute that 3betting preflop is likely +EV. As you will find the majority of players fold to 3bets an exploitable amount, as it's just usually better to fold than to call OOP, or 4bet without reads.
Does a 3bet being +EV mean that we should do it? No. If it's not the most +EV decision, then we should refrain from doing it, if we know what the correct most +EV decision is. In this case, I believe that correct decision is to call, and play with a fairly strong hand IP against a wide range.
This is ABCD theorem at it's core. We can 3bet our value hands, ones that he will continue with worse often enough preflop to be +EV (such as QQ+, AK), and place that in our A range. Then we formulate our B range from all of the hands that we feel is profitable to call with (KQ, AJ, AQ, AT, 22-JJ, etc), and we place those hands in our B range, and call. Then from the hands left we determine the next strongest hands that we can't 3bet for value, or call with, and we decide to 3bet bluff those hands with a predetermined frequency. We choose these hands because they aren't profitable to 3bet for value with, and they aren't profitable calls, however, we feel he is folding to 3bets often enough that we can exploit this by 3bet bluffing, and therefore turning these unprofitable hands into +EV decisions.
Here, you are essentially choosing to take a B range hand and place it in your C range, not because it's the most profitable play, but because it's the easiest play. When we could show approximately the same profit (maybe a little less) by 3bet bluffing a hand like T7s, or A5s, that we can't profitably call with.
This is essentially the same way to think about hands postflop. Say we call preflop with 99, and we see this flop and villain cbets. Sure, we are likely ahead of his range at this time, as he has loads of unpaired broadways, and worse pairs in his range. However, does that alone make raising correct? No it does not. If we raise his cbet with 99, and he folds everything but 77+, 44, 87, 56, then clearly raising is incorrect. As we have simply allowed him to fold all hands with worse equity and continue with all better.
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