Is it possible for a deck of cards to be shuffled accidentally into perfect order?

Sophia Williams Sophia Williams Mar 21, 2022 · 2 mins read
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Deck of cards shuffling is a fundamental concept in the world of playing cards. The randomness of a shuffled deck ensures that games are fair and enjoyable for all players involved. However, some have asked whether it could be possible for a deck of cards to be accidentally shuffled into perfect order.

The answer? No, it’s not possible for a deck of cards to be shuffled accidentally into perfect order.

There are 52 factorial ways to shuffle a standard deck of cards, which means 52 multiplied by 51, multiplied by 50, and so on, until one. This number is approximately 8.0658 x 10^67, which is an unfathomable number of possible shuffles. In short, there are too many possible permutations of a shuffled deck for it to accidentally fall into perfect order.

To put it into perspective, let’s assume that a person could shuffle a deck of cards once every second. It would take that individual around 2.5 x 10^60 years to shuffle the deck of cards enough times to go through all the possible combinations. To give another example, if every person on Earth shuffled a deck of cards every second since the beginning of time, the possibility of one of those decks landing in perfect order would still be virtually impossible.

Moreover, a deck of cards falling into perfect order is not just improbable but impossible. A perfect order means that all 52 cards in the deck are arranged in descending order of suit and value, starting from Ace to King. Achieving this perfect order would require someone to go through each card and arrange them in that precise order, which can only be done manually. It’s highly unlikely for a shuffled deck to accidentally end up in that order.

In conclusion, the likelihood of a deck of cards being accidentally shuffled into perfect order is so infrequent that it can be considered impossible. The concept of shuffling is in place to introduce randomness and unpredictability to the game, ensuring fairness and entertainment for all players. Trying to achieve a perfect order by shuffling is like trying to win the lottery. Sure, it’s possible, but the likelihood is so low that it’s essentially impossible.

Sophia Williams
Written by Sophia Williams
Always exploring new horizons and pushing the boundaries.