Best possible Cribbage hand
The best hand is 3 fives and a Jack, with the remaining five being turned up and belonging to the same suit as the Jack.
|Jack with each five (four 15s)||8|
|4 permutations of 3 fives (another four 15s)||8|
|Jack of cut suit (one for his nob)||1|
There are 4 possible ways of getting a hand like this (depending on the cut suit) making the chances of being this lucky are 1 in 216,580!
You can read lots more about cribbage statistics on Wikipedia at Wikipedia: Cribbage Statistics or, if you're new to the game, see how it's played at Wikipedia: Cribbage Rules and how to play well at Wikipedia: Cribbage Strategy.
To keep up our hopes, we have a cribbage board like the one depicted.