So exclude 5 required card from the set - we can select our free 2 cards from the set of 52-5 = 47 cards.Ĥ * C (47,2) = 4 * 47!/ (2! * (47-2)!) = 4* 47 * 46 / 2 = 4324 - the number of the good 6-card cribbage hands.
And - 2 free cards left to add to 6 cards totally (except for the one starter card 5 - one for each set). The good hands: there are four 4-card hands.
There is a combinatorics' formula for calculating the number of the all possible combinations of r elements selected from the set of k total elements: So that our goal is to determine the probability that the initial six card hand contains three fives and a jack, all of different suits, but not the remaining five (which needs to be the starter card). Also we know, that there are only 4 hands that give 29 points: How did we calculate it.įirst of all we should remember, what upon dealing a player receives 6 cards, 2 of them will be discarded to the crib later. In our Cribbage Statistics page we stated, that the getting of the best cribbage hand - a 29 hand - odds is 1 to 216580.
