check top pair?

My guess here is we range check this board OOP. This is a very dry board where checking our very strong hands will go far to protect our checking range, as not many cards will come on the turn which really hurt our hand. Having the A spade also helps in this regard ... but my gut tells me the solver will find checks at a good frequency for our range here.

Solver aside, if you think of villain's range here and our perceived range (after checking) it can be really advantageous for us to take this line. Villain will often put us on AK/AQ types of hands after raising UTG followed by checking flop and assume that their pair is best hand and will bet for protection/value. Also a good chance villain bets with non paired hands attempting to bluff us off the A hi they assume we have. We also don't need to worry about equity denial too much either as the only bad turns for us are K/Q (non spade). Either way, it seems our check will often yield a bet here from villain which is obviously a great outcome. Even if they don't bet, once we start betting on later streets they may be more inclined to call down with middle pairs thinking we'd bet a Jack or better on flop. I do think, however, without the As here, the check becomes a bit riskier.

I think there's a few reasons. 1st, the solver likes have a check/raising range as OOP preflop raiser and since we're betting most of our overpairs on the flop, we still want hands that are strong enough to ch/r for value. Secondly, although we have a range advantage, it isn't so strong that we should just range bet against optimal players. Button has more suited cards and most of his offsuit hands are centered around AJo. We have the overpairs but we also have more wiffed high cards (since his AK/AQ should frequently be all-in pre, and many opponents don't call ATo/KJo etc here).

Thank you all

HU I am not checking here basically ever. Because we have a BDFD with the A it means there are just not that many flush draws out there. My flop bet size will be my pre-flop bet size. What I don't like in checking is that a K or Q can come on the turn and we will have no idea what to do OOP and will likely have to check/call two streets vs hands like KQ/KT/QT/etc.

The flop range favors us though BTN will have more 33 than us (I would always raise with 66 UTG but fold 33 a bit).