Card Shuffling

Every time you shuffle a deck of cards that combination of cards has likely never existed before!

The number of possible card shuffles is:

52! = 8.06581752 × 10^67 (google calculate this)

If you shuffled a deck of cards every second for a million years you would only get 3.1556926 × 10^13 combinations

31,556,926 second in a year

31,556,926 * 1,000,000 = 3.1556926 × 10^13

If you shuffled a deck of cards every mili-second (1,000 times a second) for a trillion years (longer than the earth is estimated to have existed) you would only get 3.1556926 × 10^22 combinations. That's not even .01 percent of the total possible shuffles.

1,000 milliseconds in a second

31 556 926 000 milliseconds in year

1,000,000,000,000 * 31556926000 = 3.1556926 × 10^22

If the entire human race shuffled a deck of cards every millisecond for 1 trillion years there would only be 2.11652087 × 10^32. That's still not even .01 percent of the total possible shuffles.

world population: 6,706,993,152

6,706,993,152 * 1,000,000,000,000 * 31,556,926,000 = 2.11652087 × 10^32

If the entire human race shuffled a deck of cards every millisecond for 100 quattuordecillion years there would be 2.11652087 × 10^67 different shuffles

10^47 years = 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (100 quattuordecillion )

100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 * 6,706,993,152 * 31,556,926,000 = 2.11652087 × 10^67

Then you would be at about 25% of all possible shuffles!

Names for big numbers

  • thousand
  • million
  • billion
  • trillion
  • quadrillion
  • quintillion
  • sextillion
  • septillion
  • octillion
  • nonillion
  • decillion
  • undecillion
  • duodecillion
  • tredecillion
  • quattuordecillion = 10^45
  • quindecillion = 10^48
  • sexdecillion = 10^51
  • septendecillion = 10^54
  • octodecillion = 10^57
  • novemdecillion = 10^60
  • vigintillion = 10^63
  • unvigintillion = 10^66 (close to the number of possible shuffles)
  • duovigintillion = 10^69
  • ...
  • Googol = 10^100 (a 1 followed by 100 zeros)

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