Is a Shuffled Deck of Cards Unique?

According to the laws of probability, it would be nearly impossible for any person to shuffle a deck of cards and have it end up in the same order as any other shuffled deck in history. This fact takes into account a deck of 52 properly shuffled cards, meaning that the cards were truly shuffled in order to create randomization. For example, a perfect shuffle — in which a deck is separated exactly in half and all of the cards are alternatively interlaced in order — is commonly used for magic tricks and would not have randomization. It is commonly accepted protocol that a deck of cards requires seven shuffles to have proper randomization.

More about probability:

  • A two-sided coin might not have an equal chance of landing on each side after being flipped. Research has suggested that 51% of the time, the coin will land with the same side up as when it was flipped.

  • In a group of 23 people, there is a 50% chance that two of them will have the same birthday.

  • It would take about eight perfect shuffles of a deck of cards to get it back to its original order.
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Discussion Comments


This statement requires, begs, a statement of what the odds are. As stated, and then followed by the statement about 8 perfect shuffles to return to a perfect order, seems counter-intuitive and less that logical.


If a deck returns to its original not order after eight perfect shuffles, then on that eighth shuffle it would be returning to the same order as a previous(the first)deck. That's a contradiction.


I have never understood any reasoning - mathematical or otherwise - why it's a 50 percent chance of two people in a group of 23 sharing the same birthday. As far as I'm concerned there are 365 days in a year and therefore a one in 365 chance of it being any day. The next person has 363 chances about it being different against one the same and so on. Assuming the 22 previous were different, why doesn't the 23 have 342 chances for it to be different and 22 the same or about 17 to 1?

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