Author's note: While I find this information of great value, those of you not familiar with the great game of cribbage might find it extremely dry. I recommend reading the rules of cribbage as an introduction, if you're interested.
The more one delves into the game of cribbage, the more one realizes that there is a great deal of math involved, at least if you're interested in getting better. I therefore offer up to the E2 crowd some of the more helpful cribbage statistics I've collected/compiled over the years.
Pegging It is generally known that the dealer outpegs the nondealer (or "pone," as he is often known) during the average hand. In this area, the experts generally agree on the margin of this advantage: the dealer pegs an average of 3.5 points per hand, while pone pegs an average of only 2.1 points.
Much of this advantage is the result of a structural advantage the dealer has: he can never be held to zero pegging points (he will always receive at least one go point), while pone is often shut out. A relatively basic analysis reveals only 18 legal ways to play two four-card cribbage hands (three of which result in pone receiving no go points). This at first may seem like too few; however, consider that the first three cards must always be Pone-Dealer-Pone, since you cannot possibly reach a "go" point with fewer than three cards.
If we assume (and we probably shouldn't) that occurences of these 18 patterns are evenly distributed, the dealer averages 1.28 "go" points (0.46 standard deviation) and pone averages 0.94 "go" points (0.54 standard deviation) Therefore, the dealer has an absolute advantage of only 0.34 points per hand.
Hands Prof. Steven Lumetta of the University of Illinois has computed that, including the turn-up card, there are 12,994,800 possible cribbage hands. The average score is calculated as 4.77 points (3.13 standard deviation). This is of little value other than as curiosity, since cribbage players have some control over their hands through the discard, and are not often stuck with complete dogs.
Not surprisingly, the average hand for the dealer (who has the advantage of being able to discard to his own crib) is somewhat lower than the average hand for pone. Some authorities suggest that the numbers are the same--an average of 8 points whether you are dealer or pone--but experience speaks against this. My own analysis (examining 3,551 hands) seems to confirm DeLynn Colvert's numbers: 7.96 points for dealer (3.93 standard deviation) and 8.12 points for pone (3.64 standard deviation).
Cribs This is a lot more straightforward. Authorities generally fall in a range of 4.5-4.8 as the average crib score. Again, my analysis (involving 1,675 cribs) supports Colvert, and I hold the crib average to be 4.67 points, with a standard deviation of 3.14
In sum, the dealer can expect to score about 16 points on each hand (including crib and pegging), and pone can expect to score approximately 10 points (including pegging). Thus, the total score for a cycle as dealer and pone is equal to about 26 points (some authorities suggest that this number averages 25 of fourth street, due to heightened defense).