29: the perfect cribbage hand

The highest possible hand at Cribbage is 29 points (shown above). It comprises all four 5s and the Jack of nobs. It is extremely rare to score a 29 hand in cribbage. In tournament play there is usually a special award for a 29 hand, whether it be cash or merely glory.

Your 29 hand stories

James Gilly

There is a fine tradition of cribbage playing in the US Navy and especially the submarine service. James Gilly writes:

In 1991, whilst under way on USS Simon Lake (AS 33), I was playing in the R-10 division office with one of the nucs; as I recall, I dealt, and after making my discard said something along the lines of "Go ahead - cut me a five. I dare you." And he did...

My camera was locked in my rack at the time, so we noted the score and the hands and then finished the game. I went and got the camera, and we set up the board and cards for pictures - except that I miscounted when placing my rear peg so the photos look like I cheated and pegged 30.

My second 29 came in 2000 or 2001. I was under way again, this time on USS Providence (SSN 719), and was playing on the mess decks with one of the sonar techs. I honestly can't remember which of us dealt that hand. This time, though, I happened to have my camera in my pocket, so we were able to take pictures immediately and then finish the game.

Dale and Helen Moeller

Dale Moeller and his wife Helen were returning from their 50th wedding anniversary vacation when they decided to play a game of cribbage in their hotel. Helen writes:

My husband calmly said, "Helen, I think I have a perfect hand!" What made it even more exciting was the fact that during our initial card-playing, we were surrounded by a group of friendly Shriners from Kansas, there for a golf tournament, and many of them had stopped at our table to introduce themselves and comment on the game of cribbage. One gentleman in particular, a dentist from Wichita, said that he played on-line 3 times a day and was director of the Shriners' cribbage tournaments. He had never even seen a perfect hand before. My husband's great fortune and luck could have happened at our kitchen table in Wisner, NE, but being amid people who really appreciated and understood the odds of a perfect cribbage hand made it even more awesome!

As an added note, Dale won that game by only one peg -- even with THE hand!! We are very competitive and enjoy cribbage very much. It was my idea to get the board & deck of cards from the car (while he enjoyed his beer) -- he said I didn't have to bother, but I did anyway!! Sometimes this wife of 50 years has a good idea!

Indeed she does! We'd love to hear your perfect hand stories. If you have had a 29 hand in cribbage, why not contact us and share the story?

Barry McCormack

Barry McCormack of London, Ontario, recently received a cribbage 29 hand in a friendly game with his son. As his daughter Tiffany wrote to me, it was "the first 29 hand he had ever had or seen in over 40 years of playing the game".

What are the odds of getting a 29 hand in cribbage?

It is possible to work out the exact chances of getting a 29 hand in cribbage. Mathematician David desJardins explains:

You need to be dealt three fives, the jack of the fourth suit, and two other cards neither of which is a five. The total number of such six-card hands is 4*(47*46/2) = 4324, out of (52*51*50*49*48*47/720) = 20358520 possible hands. Given this event, the probability of turning up the fourth five is 1/46. So the probability is:

4324 / 20358520 / 46 = 1 / 216580 (very roughly, 200,000 to 1)

Cribbage master Michael Schell elaborates on this argument, and the corresponding odds in the 3- and 4-handed games, in this Cribbage Forum article. He also notes:

The 1 in 216,580 figure jibes well with the actual incidence rate of 29 hands in sanctioned tournaments in North America. The ACC pays $100 for a 29 hand received in sanctioned play, and thus publishes a "Club 29" list each season. To be exact, the incidence is a tad lower than the odds predict, since the odds assume you keep an eligible hand (5-5-5-J) whenever you can. Since you wouldn't always want to do this (defending in an endgame for example), the actual occurrence of 29 hands among experts will be a bit less frequent than the mathematical calculation predicts.

How many possible ways are there of making a 29 hand in cribbage?

The 29th point comes from the nob Jack, and since you have all four fives, any of the four Jacks will do. Thus there are four possible 29 hands in cribbage, with the Jack of each of the four suits being the turn up card.

A 29 hand and a 28 in the same game

Adam Wigdahl writes:

I had a 29 hand yesterday (picture right). Two hands later my opponent had a 28. I ended up losing the game, and actually there was a chance I would have been skunked if I didn't have a 20 point hand towards the end of the game. Now what are the odds of a 28 and a 29 happening in the same game?

We put this question to Professor Plum, our wizened statistics guru. Professor Plum:

First we need to know the odds of a 28 hand. This is just the four 5s plus any ten-card (not the right Jack!), the odds of which are 1 in 15,028. We already know the odds of a 29 are 1 in 216,580. On average 20 hands are dealt in a game of cribbage, so the chances of both hands appearing in the same game are ( 20 / 15028 ) * ( 19 / 216580 ) = 0.000000117, or 1 in 8,565,169. So about 1 in 9 million is the answer.

Adam's own workings suggest that the likelihood of actually being able to score a 28 and a 29 (as opposed to being dealt them) is about 1 in 10 million (often the last hands of a game are not scored as one player has gone out). But how surprised should we be about such an occurrence?

If we consider only officially sanctioned tournament play in the United States, there is a tournament somewhere almost every day, so let us say 365 tournaments a year of about 30 games each. So we would expect to see about one 29 hand a year in tournament play. I don't have the actual figures, but that sounds about right.

But a 29 and the 28 in the same game are a thousand times as improbable, so we would expect this to occur in tournaments about once every 1,000 years.

It is impossible to know how many games of cribbage are played every day, between friends and families and pubgoers. But there must be thousands of times as many unofficial games as there are tournament games. So we could estimate that a 29+28 combination occurs somewhere in the world maybe about once a year.