Facts about cribbage.

• The origins of cribbage are uncertain, but the game dates back almost five hundred years.

• The rules of cribbage are simple to learn, but can take a lifetime to master!

• The highest possible hand in cribbage is 29, the perfect cribbage hand.

• There are several 'impossible totals' - point counts which cannot be made with any hand. The lowest such total is 19 - hence the expression 'a nineteen hand', or 'I have nineteen', almost universally (perhaps sarcastically) used to describe a zero-point hand.

• Cribbage has given the English language a number of expressions which it is hard to imagine doing without, including "level pegging", "what a turn-up/a turn-up for the books", "streets ahead", and "pegged out".

• The fact that the crib alternates with the deal means that on average, the lead should also change hands with each deal - which means it ain't over till it's over!

• The biggest possible improvement in your score from the cut is 20 points, when you hold 4-4-6-6 and cut a 5.

• The first dealer in a game wins 55% to 60% of the time.

The distribution of cribbage hands

What is the most common point value of a cribbage hand? What is the average point value?

The MathWorld Cribbage page has a graph showing the frequency of different hand values in cribbage. This shows that the most frequent point value, ignoring the skew effect of the discard, is 4 (closely followed by 2).

Most common cribbage hands

The average point value of a hand is 4.7249. Of course, in real play scores will be slightly higher because of the discard, but the distribution will be similar.

The 5-scores-2 conjecture

Does any hand containing a 5 score at least two points? The answer is yes. This question is addressed in detail here, complete with computer programs in Perl to generate all possible such hands and verify the conjecture:

• Generating all 5-card hands