...in the history of card shuffling, after having been properly shuffled, assuming that every deck ever used was a standard 52-card deck?
The answer is below so you won't automatically see it in case you want to think about first.
The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is ‘52 factorial’ otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
Many casinos use the child's approach to shuffling with new decks of cards, i.e. spreading all the cards out on the table and jumbling them before collecting them back into a deck. This is called 'washing' the deck or the 'Corgi' shuffle; casinos or tournaments often use it when introducing a new pack to initially randomise it. If you can riffle shuffle cards perfectly – i.e. ABABAB, as some casino dealers can – it actually makes the order slightly less random than if you shuffled the cards imperfectly.
To mix up a pack of cards thoroughly you need at least seven imperfect riffle shuffles. Any less and there is still a vestige of order; any more and the rewards of the extra shuffle are small. For some games like blackjack, where suits don’t matter, you only need about four shuffles.
Here's the link I got the above explanation from: http://qi.com/infocloud/playing-cards
The answer is below so you won't automatically see it in case you want to think about first.
The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is ‘52 factorial’ otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
Many casinos use the child's approach to shuffling with new decks of cards, i.e. spreading all the cards out on the table and jumbling them before collecting them back into a deck. This is called 'washing' the deck or the 'Corgi' shuffle; casinos or tournaments often use it when introducing a new pack to initially randomise it. If you can riffle shuffle cards perfectly – i.e. ABABAB, as some casino dealers can – it actually makes the order slightly less random than if you shuffled the cards imperfectly.
To mix up a pack of cards thoroughly you need at least seven imperfect riffle shuffles. Any less and there is still a vestige of order; any more and the rewards of the extra shuffle are small. For some games like blackjack, where suits don’t matter, you only need about four shuffles.
Here's the link I got the above explanation from: http://qi.com/infocloud/playing-cards
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