Odds Of Being Dealt All Penalty Cards In Hearts

957941745812300000000000000:1

One of the rules stipulates that a penalty card cannot be discarded on the first trick. Based on the odds it is very unlikely that a player would not be able to follow this rule. As a matter of fact my online version of the game does not even account for this possibility. So if you are ever playing this game and get an all penalty deal, take a screen shot and send it to me.

There are 5.3645 X 10 28 possible deals in game of hearts. ( I will publish an article on that calculation in the future. )

There are 14 possible hands that contain all penalty cards:

-all hearts
-the queen plus all hearts except the 2
-the queen plus all hearts except the 3
-the queen plus all hearts except the 4
-etc....

There are 4 players who can potentially be dealt one of those hands for a total of 56 possible deals out of 5.3645 X 10 28 total possible deals which gives us:
9.579417458123 X 1026 :1