Suppose you raised pre-flop with the AK and have one caller, so you go heads-up to the flop. On the flop comes QKA which are all spades. This is clearly a very draw-heavy board, and your two pair AK will not be good all the time.
When you bet and you get raised, is there a situation where it is justified to just call instead of raising or folding?
Suppose the opponent is a tight/passive player. In this situation he probably already made a straight of flush and folding is the best option. He will not be semi-bluffing in this situation very often and certainly will not try this with just an ace. The only possible hand which he could have an you can beat would be AQ, which he will not have the majority of the time.
If the player is quite aggressive, there is quite a large change he has a draw and tries to semi-bluff. If you just call you give him the opportunity to make his hand. Moreover, when faced a large bet/raise on the turn you have no idea where you are at (it might still be possible he made his hand on the flop). I think raising would be the best option, but you would probably have to invest allot to give him proper odds to fold a draw, so folding might still be a valid option.
But what if you know the player is a novice and might even pull of this kind of play with just an Ace, which he thinks is very good because he does not think about draws and board texture. Would it be a good idea to just make the call? A downside of this play is you gain very little information, but he might even call a raise with what he thinks is a strong hand.
If you can think of other situations besides the situations described where it may be good play to just flat call, it would be very appreciated.