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You have too little information about his hand to make a World Class Laydown here.
You informed him that you might have missed overs, low pair, or jack shit by your flop check. Easy flop call imho.
Some alternative lines:
(1) 3-bet preflop
For the most part this defines your hand as AA/KK...certain players with AA will smooth call the 3-bet and stack you postflop, others will push mostly AA/KK preflop and you might be able to make a good laydown then depending on the player, stakes, etc.
(2) Lead out flop
Indicates that you like your hand...you may still be able to get away if he reraises/pushes the flop depending on stakes, reads, etc.
(3) Check-raise the flop, possibly even check-push the flop
If you feel like you aren't getting away from the hand, and/or would prefer to end the hand on the flop...possibility of folding out AA/QQ/TT/AJ here - obviously sets call but if you weren't getting away anyhow so be it, but this is probably the only chance you can get AA to fold if the player is nitty enough (doubt this works often anyway so it's more a matter of making your best attempt to end the hand on the flop). Not necessarily the optimal line.
(4) Check-call flop and reevaluate on the turn (possibly lead turn, possibly check turn depending on reads, board)
You are not likely to be able to put your opponent on AA vs. QQ/TT/JJ etc. anyway given the pot size and all, but since so many players will not continue to bluff AK on a blank turn you may be able to get more information on his hand on the turn.
Also, there is some chance that a 3rd spade falls on the turn and scares some opponents into slowing down, allowing you a cheaper showdown if you feel that you might be beat.
Not the only lines you could take but a good subset...I think check-folding the flop is indicative that you are playing scared in some manner (due to prior bad beats, running into AA with KK a few times recently, getting setted on with overpairs recently and paying off and whatnot).
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