Shuffling a deck of cards may seem like a simple act, but the probability behind it is something that many people are not aware of. With just seven riffle shuffles, a unique sequence of cards can be created. This means that the sequence of cards that is produced has never been seen before and will never be seen again.
To put this into perspective, if someone were to start shuffling a deck of cards at the beginning of the observable universe over 13 billion years ago, and completed a seven-riffle shuffle every second, it is highly unlikely that they would have seen the same deck of cards order twice.
The total number of combinations that can be made through shuffling a deck of cards is 8.0658 x 10^67. This number is significantly larger than the age of the universe, which is only around 1 x 10^18 seconds old. After a true shuffle, the likelihood of finding two decks in the same order is extremely low, making it more probable to become the President of the United States or be struck by lightning.
The probability of correctly guessing the cards in a deck decreases with each riffle shuffle. After one riffle, it is possible to guess about 30 cards correctly, but this number drops to 19 after two riffles, and further drops to 13 after the third riffle. After seven riffles, a deck of 52 cards should be completely random, ensuring fairness and unpredictability in card games.
Ensuring the predictability of a deck of cards is crucial for both game operators and players. The riffle shuffle is considered the best method for randomizing the order of cards in a deck, making it a trusted method for ensuring fairness in gameplay. Additionally, the riffle shuffle is not only effective but also visually appealing, making it a popular choice for shuffling cards.