You are playing no-limit hold 'em and open for a raise with AK. A tight player in the big blind re-raises. Let's assume you are somehow almost positive he has pocket Jacks, Queens, Kings, or Aces and that you call his re-raise. (Under certain circumstances, the better play would be to fold or to put in four bets. But, that's a topic for another day.)
If there was no further betting, you will win about 37% of the time. Of the 12 times he has Jacks or Queens, you win about 5.5. Of the 3 times he has Kings, you win about .9. Of the 3 times he has Aces, you win about .3. Thus, if he will re-raise with those pairs and never with anything else, you are usually getting good enough odds to call.
What about the money that will be bet after the flop? Does that help or hurt you? If it is a small amount, it almost definitely hurts. That’s because he will always bet the flop and you will always call. Essentially, this extra money could have all been bet before the flop, thereby cutting down your odds. If there is a larger amount to be bet post flop, it may help you. This is especially true if your opponent is not tricky.
Suppose he has enough money to bet the size of the pot no matter what comes and he will always do that. Obviously, your counter strategy will usually be to call if an Ace or a King flops and not otherwise. Using very rough math, let us see whether that $100 bet possibility is better than being all-in before the flop.
The worst thing about that bet is that it will make you fold hands that might have drawn out. Assume there is $100 in the pot pre-flop. His ability to knock you out will cost you the pot about 15% of the time. That’s a $15 negative EV. On the other hand, if an Ace or King flops, his bet will usually make you extra money. When a King flops, he has 4 combinations that beat you and 12 that don't. He will sometimes draw out on you. But, you are still at least 70% to win. That $100 bet in that situation is a $40 positive EV and it will occur about 15% of the time. That's $6 for you.
When an Ace flops, you only lose if he has Aces or if he draws out. You win at least 85% of the time, which is a $70 EV, and that happens about 15% of the time. That is another $10.50 for you.
Thus we see that if we can count on a pot sized bet or more, no matter what he has, or if we can win that much on the flop or the turn no matter what he has, that is an extra reason to call pre-flop.
Suppose he has far more than a pot sized bet available to him. Now, it can get tricky. But, only if he is tricky. If he will always bet the flop, but then shut down unless he has top pair beaten, your play is probably to call on the flop and then fold the turn if he bets again. Perhaps you think the better play is to raise when an Ace or King flops since you are the favorite to have him beat. That might be ok when the top card is an Ace. But, definitely not if the top card is a King. Yes, you are a 12 to 4 favorite. And, yes if you just call, you give him a chance to spike a set. But, unless you think he will call your raise with the under pair, the risk isn't worth the reward. Not against someone who will never bet the turn without having you beaten.