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Steven Schulman

Steven Schulman's Public Library

  • You can tell if a card is officially rare by looking at the bottom right corner. Black circle means common, black diamond means uncommon, black star means rare.

  • windows key + the R key together, type in "msinfo32" (no quotes) and press OK, you'll see a system summary
Mar 02, 16

"Sarthak Chatterjee, loves math
338.8k Views • Upvoted by Ori Gurel-Gurevich, Level 17 Mathematician
Sarthak has 30+ answers in Mathematics.
Every time you shuffle a deck of cards, it is likely that you've come up with an arrangement that has never been seen before in human history.

Consider a standard deck of 52 playing cards. Choose one card and keep it aside. How many choices do you have? Well, there are 52 cards you can select and hence 52 choices. Select another card. This time you have 51 choices, remember one card has been kept aside. The fundamental principle of counting says that you can do both of these in 52×5152×51 ways. If you continue this procedure, you have 52×51×50×⋯×2×152×51×50×⋯×2×1 ways in which you can arrange your deck. The product of numbers from 52 to 1 is called the 'factorial' of 52, written 52! . This is an inconceivably large number.

52!=80658175170943878571660636856403766975289505440883277824000000000000≈8.0658×106752!=80658175170943878571660636856403766975289505440883277824000000000000≈8.0658×1067

Now how many shuffles have been made in human history? This is well nigh impossible to calculate, but let's take a shot. Assume that 7 billion people (close to the current population of the world) have been shuffling cards once every second since 1300 AD (approximately 700 years), the time when the modern deck of cards appeared. The number of shuffles comes out be roughly (ignoring leap years etc.)

7billion×700×365×24×60×60≈1.546×10207billion×700×365×24×60×60≈1.546×1020

Of course, this is a gross overestimation, but it drives home the point. So, as a fraction of the total number of shuffles possible, the shuffles already done are a paltry

1.546×10208.0658×1067≈1.9×10−481.546×10208.0658×1067≈1.9×10−48

So next time you shuffle a deck of cards and lay them on the table, chances are you're looking at some never-before-seen piece of history.

Source: MW - Shuffling Cards
Image Courtesy: DeviantArt
Written Oct 15 • View Upvotes"

  • Factorials can be used to neatly express periods of time. 10! seconds, or 362880 seconds, is exactly 6 weeks. 8! minutes make 4 weeks, and there are 4! hours in a day.

  • The official UN press release for the International Conference on the Question of Jerusalem noted that “a policy of ethnic cleansing was pushing Palestinians out of the city”.

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