Broadly speaking, pairs can expect to win one of three ways:
Playing a pair in hopes of hitting a set is a lot like playing the lottery: You win if your number comes up, and if it doesn't then you have a losing ticket. Unlike the lottery, however, you often will be getting correct odds to play, especially at low limits. The odds against hitting your set are about 7.5 to 1, so assuming your set is a lock to win you'd still need most of the table to play -- except for implied odds. Because a flopped set is pretty well concealed, chances are good that you'll be paid off for multiple bets. Expert authors believe that around 5 opponents are enough to pay off for set value alone, and at low limits that's not rare at all.
When you miss your lottery numbers, you're left with a worthless ticket. When you miss your set, your pair may still be valuable as an overpair, or less likely as a non-overpair.
Whereas each pair has the same probability of hitting its set, regardless of rank, obviously the probability of flopping as an overpair differs immensely. This is really what gives the monster pairs like AA and KK most of their value -- the possibility that after the flop they'll still be ahead of anyone with top-pair-good-kicker, and hence will potentially be paid off rather handsomely. Plainly, your pocket 7s or 8s are going to be in that same position only on the rare times that the flop contains only low cards. Even then, a flop like 2-3-6 is much more likely to make a straight for someone. And finally, overpair-versus-overpair is substantially more common than set-over-set, so the risk of flopping a second-best overpair is greater the farther down the food chain you go.
Holding a pocket pair with larger cards on the board is a disappointing situation. Oftentimes you'll have to fold your pair to any significant action. This is especially true if there is a King or Ace on board since those cards are more likely to have been played by your opponents. The usual line for a middle or low pair versus overcards is to check/fold the flop. Your chance of hitting a set on the turn or river is remote and you will rarely be getting proper pot odds to call.
|PokerWiki's guide to limit hold 'em preflop play|