Martin writes:

I am an avid cribbage player and have enjoyed the game for close to fifty years. I've never had a perfect twenty-nine hand but I've had three twenty-eight hands. I know that the odds of getting the twenty-nine hand are approximately one in a little over three million [ Actually, it's one in about 200,000 - Ed ]. Recently something very strange occurred to me. I dealt the first hand of a new game and here is how the scoring went:

The cut was not a jack

The laying down phase of the hand yielded the mandatory one point on a "go"

My regular hand yielded zero points

My crib hand yielded zero points

I have never heard of anyone else accomplish this feat. As you are aware the dealer of a hand will always score at least one point on a "go" or a "last card". So I am wondering - what are the odds of such an event occurring? I'm pretty decent with math problems however I'm not sure I even know exactly what equations are required to calculate the odds of getting a perfect "imperfect" hand. Can you help me figure out the end result?

To work out the odds of a zero-scoring cribbage hand (apart from the mandatory one point for go), we need to calculate how many such hands there are, and then divide that into the number of all possible cribbage hands. It is a tricky problem because we need to make no points in the play, assuming correct play. Anyone care to tackle it?