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Old 07-24-2003, 06:36 PM
redsamurai redsamurai is offline
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Join Date: Jun 2003
Location: Seattle
Posts: 29
Default Re: Stuff that\'s tough to believe

No longer having access to a top Mathematics software package I can't do the calculation, but here is the formula. Like in the "birthday" problem we take 1 minus the odds all of the shuffles of a deck are different ( http://www.cs.jcu.edu.au/~david/Tours/birthday.html ). For N shuffles this comes is:
P(@ least on match in N shuffles)
= 1 - ((52!-1)/52!)*((52!-2)/52!)*...*((52!-N)/52!)
= 1 - Product of ((52! - n)/52!) for n=1 to N

Using MatLab or Mathematic someone can likely solve this for P=50%. I estimated this using a different inexact probalistic technique and it came out to approx 1*10^33 (this could be an order or two of ten off). In other words if you shuffled a billion decks each second it would over 10,000,000,000,000,000 (10^16) years to be 50% likely to repeat an exact random shuffling.

All that said hold'em players only care about the position of 25 cards in the deck (10 players with 5 common cards). Anyone care to do that calculation?
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