Sunday, October 04, 2015

Pick a card, any card...

Take a pack of cards and shuffle it.  Just an ordinary, everyday activity, and yet you've probably just made history.  The particular arrangement of cards you've ended up with has almost certainly never been seen before.  What am I on about? Well refer back to my posts under the title "How many?" in November and  December 2008 and you will I hope see that the number of ways a pack of cards can end up after a random shuffle is 52! - that is, factorial 52.  Now that's an enormous number
 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 to be exact.  And this is far, far greater than the number of seconds since the earth came into being, so you can see why every shuffle can be considered unique.  In fact, it's not quite as simple as that, because the way most people shuffle cards (the riffle shuffle) is not really random, but will still produce at least 4,503,599,627,370,496 different results and doing it more than once, as most of us do, will quickly produce a number greater than the age of the earth. So like I say, you've almost certainly made history.

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