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How to calculate cribbage 29 hand odds
In our Cribbage Statistics page we stated, that the getting of the best cribbage hand - a 29 hand - odds is 1 to 216580. How did we calculate it.
First of all we should remember, what upon dealing a player receives 6 cards, 2 of them will be discarded to the crib later. Also we know, that there are only 4 hands that give 29 points:
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).
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:
In cribbage it means we select 6 cards from the 52-card pack
C(52,6) = 52! /(6! * (52-6)!) = 52! / (6!*46!) = 52*51*50*49*48*47 / 720 = 20358520 - the total number of 6 card hands
Now we have 4324 from 20358520 without a cut card.
Therefore, the probability of getting a 29 hand in 6 card cribbage is 1 to 216,580 or 0.000004617
This article appeared as a result of the question of Ron Smyrski about the best cribbage hand odds - thank you, Ron.