What are the odds of shuffling a deck of cards into the right order?

Wednesday 22nd July 2009
Submitted by Robert Matthews
Chris Nicolson, Isle of Skye

It depends on how you shuffle them and the cards' order when you start. If you truly randomise the deck, the chances of the cards ending up in perfect order - spades, then hearts, diamonds and clubs - are around 1 in 10 to the power 68 (or 1 followed by 68 zeros). That's a huge number, roughly equal to the number of atoms in our galaxy. Yet card players report it happening. The reason is fresh packs of cards come in perfect order and if they're not shuffled well, can end up back in order. For example, if a dealer riffle shuffles a fresh pack - splitting the deck in two and interleaving the cards together - the pack can end up back where it was after just eight shuffles. Thus, paradoxically, people who aren't very good at shuffling can do a better job of jumbling a pack than those who are.

Is there a formula for generating random numbers?
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