It’s a Miracle!

Imagine you have thee cards of different colors, say red, yellow and blue. You can arrange these cards in a maximum of 6 different ways. Red Yellow Blue, Red Blue Yellow, Yellow Red Blue, Yellow Blue Red, Blue Yellow Red, Blue Red Yellow. Each card can occupy one of three positions position 1, position 2, and position 3. When filling position 1, you have three cards to choose from. Once you have filled position 1, you have two cards to use to fill position 2. Once you have filled position 2, you have one card to use to fill position 3. So you have 3 possibilities multiplied by 2 possibilities multiplied by 1 possibility. or 3 x 2 x 1 = 6 for a total of 6 possible combinations.

If you had four cards you would have 4 x 3 x 2 x 1 = 24 possible combinations. As you can see the number of possible cards has increased by 18 with the addition of of just one card. With a deck of 52 cards there is a huge number is possible combinations. In fact it is approximately 8 with 67 zeroes behind it.* For the sake of simplicity I’ll call this number 8 gazillion. Suppose you shuffle a deck of cards until it is in a completely random order and then you shuffle a second deck of cards until it is in a completely random order. The odds that both decks are in the same order is one in 8 gazillion*.

Now suppose that you shuffled two decks and they both came up in the exact same order. After jumping up and down and screaming and notifying the media, you might start to think, how could this possibly happen? This is a Miracle! But the truth is any arrangement of cards is just a likely as another. Why not be amazed at a deck arranged in any other order?

The same is true of any so-called rare event. Just because it happened only once in all of history doesn’t mean it was a miracle.

* 8.06581751709439e+67