# Rare event in Pinochle game

Discussion in 'Probability and Statistics' started by jk91977, Feb 13, 2019.

1. ### jk91977

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Feb 13, 2019
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I am not an extremely experienced Pinochle player, but I would estimate that I have played thousands of hands. What I am asking about seems extremely unlikely, and the answer that I got for this question from another source seems dubious so....

I'm trying to determine the odds of a seemingly ultra rare event in a Pinochle game. I just don't know how to go about finding the answer.

For clarification in case you are unfamiliar with the game, the deck consists of 80 cards: four each A, 10, K, Q, J in each of the four suits for a total of 20 clubs, 20 diamonds, 20 hearts and 20 spades. A "run" is A, 10, K, Q, J in the same suit.

What are the odds, with 4 players that one player is dealt a double run (i.e.two runs of the same suit), and another player is dealt a run in the same suit in the same hand?

In all the Pinochle hands that I have played, I can't remember anyone even getting a double run, let alone someone else also getting the same run.

This is not for any academic work. This is just a unbelievable situation that happened in a card game with some friends.

I wouldn't mind an explanation of the procedure to determine the answer if you have the time.