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# What are the chances of dealing out cards that have been shuffled well in exact order?

Updated: 4/28/2022

Wiki User

13y ago

The odds are... remote. This is a factorial problem to calculate the answer you take how many options the first "dealt" card has of being. In this case the first card has a 1-in-52 chance of being the Ace of Spades (the "highest" card in a deck.) The next card has a 1-in-51 chance of being the Two of Spades, and so on. You calculate the odds of this happening my multiplying 52 by 51.

So, the odds are 52 times 51 times 50 times 49 times 48 times... yadda yadda yadda until you get to one. The answer?

The odd of taking a shuffled deck of cards, reshuffling it, and the dealing the cards back in the correct order are 1 in 806,581,751,709,439x10 to the 54th power. (septendecillion.)

Or 80 unvigintillion. (80 followed by 66 zeroes). For the sake of comparison, conservative estimates put the number of stars in our galaxy at 100 Billion (100 followed by 9 zeroes) and the number of galaxies in the universe at the same number, making the number of potential stars in the universe at 10 sextilion (a 10 followed by 21 zeroes.)

Wiki User

13y ago

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Q: What are the chances of dealing out cards that have been shuffled well in exact order?
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