Shuffling Cards - Against All Odds

 This is from club member Dr. Tim Scott.

 

The next time you thoroughly shuffle a deck of cards, you’ll almost certainly have landed on a combination that’s never been created before — and may never be created again. This may sound unlikely or even impossible, given that each deck contains just 52 cards, but there are more ways to shuffle a deck of cards than there are atoms on Earth. The exact number of possible card combinations is 8 x 10 to the 67th power, which is an 8 followed by 67 zeroes — an almost unfathomably large number. If you were to go back in time to the beginning of the universe and rearrange a deck of cards into a new permutation every second, the universe itself would come to an end before you were a billionth of a way to one of those arrangements repeating itself.

As for how many atoms there are on the planet, most estimates put the number at 1.3 x 10 to the 50th power or 130,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. This is obviously a vast figure in its own right, but it’s still dwarfed by the potential groupings of a deck of cards. The good news for the math-averse among us is most of us will never have to deal with such impossibly immense figures in our day-to-day lives — or in our next bridge game.