|
Flint, here's what I'm thinking:
There are 52! (52 factorial) ways that the first shuffle can come out.
The probability of the second shuffle exactly matching the first is 1/52!.
The third shuffle has a 1/52! chance of matching the first shuffle, and a 1/52! chance of matching the second shuffle, so by the third shuffle, there's a 3/52! chance of two shuffles being the same.
The 4th shuffle has a 1/52! chance of matching the first shuffle, and a 1/52! chance of matching the second shuffle, 1/52! chance of matching the 3rd shuffle, so by the 4th shuffle, there's a 7/52! chance of two shuffles being the same.
Etc...
The question should be, "how many shuffles would be required to have an X % chance of two shuffles matching?"
|