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Betting or checking flop is fine here imo. Your obviously not worried about your hand, and enough worse hands will call that you should likely cbet for value, especially if he has a low fold to cbet % and you expect him to peel light/float often. I'd be more apt to check like A8/AT/AJ/KK/etc type hands here.
If we are betting flop, I likely check/call most turns here if he floats often, or is prone to betting worse hands without a reason (like if he bets 77 if we check turn). If he is still likely to peel all of his Ax type hands, and some lower pps, then EV of a check and the EV of a bet is probably pretty close.
If we are checking flop I might play the hand the same as you, unless he's the type of player to raise stuff like weaker Ax hands on the turn. I don't think check/calling the river is atrocious, as he isn't likely to have a better Ace, and 9x, 88, is such a small part of his range. If he is bluffing any % of the time then a call could very well be +EV.
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