Facing a Minimum Check-Raise With Pocket Aces
DECISION POINT: In a $1/$2 no-limit hold'em cash game, you raise from under the gun with A♠A♦. It folds around to the small blind who calls, and the big blind folds. The flop comes K♣2♥6♠. The small blind checks, you bet, and the small blind raises. You call. The turn is the 9♥ and the small blind checks again. Action is on you...
PRO ANSWER: If you call a standard size check-raise on a very dry heads-up flop, a good default line with better one-pair hands would be to check behind on the turn and then call a river bet or bet if check to on the river. This allows you to get more value against Villain's range on the river as compared to the turn as well as giving your opponent the opportunity to bluff one more time on the river.
You are generally less concerned with giving free cards in these scenarios, since the flop is dry and it's less likely that Villain can turn many outs against you. That said, betting the turn may have more merit than usual here given that Villain specifically "min" check-raised. Some specific opponents will have lots of one-pair hands in their minimum check-raising range as compared to their range if they had 3x-ed your continuation bet.
In other words, their range is often more linear and capped, rather than polarized. This means they likely have fewer very strong hands in their range and more one-pair hands when they use this specific sizing. That also means you may get value from many of these one-pair hands with a turn bet and that you are simultaneously less worried about being up against a strong hand.
Note that this does not apply to all opponents. Some opponents simply have a very strong flop minimum check-raising range of two-pair or better. Against these opponents betting the turn (or often even calling the flop) is a big mistake. Other opponents will have a polarized range of strong hands and bluffs, which also makes betting the turn a mistake.
Overall, you should check the turn most of the time here against a completely unknown player. You would need a specific opponent read that they likely have many one-pair hands in their flop min check-raising range in order to bet this turn for value.
Checking is the best play.
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