Randomness of different card shuffling techniques [OC] : dataisbeautiful

Randomness of different card shuffling techniques [OC] : dataisbeautiful

The number of possible shuffles of a standard deck of cards (52 cards) is 52 * 51 * 50 * … * 1, or otherwise written as 52!. This number is approximately 8 * 1067 (an 8 followed by 67 0’s).

Imagine you shuffle a deck of cards once per second, every second. You shuffle 86400 times per day.

You start on the equator, facing due east. Every 24 hours (86400 shuffles), you take one step (one metre) forward. You keep shuffling, second after second, each day moving one more metre. After about 110 thousand years, you will have walked in a complete circle around the Earth (I know: you can’t walk on water. Just ignore that part).

When you have completed one walk around the Earth, take one cup (250mL) of water out of the Pacific Ocean. Then, start all over again, shuffling, once per second, every second, taking a step every 24 hours. When you get around the Earth a second time (another 110000 years), take another cup of water out of the Pacific Ocean.

Eventually (after approximately 313 quadrillion years, or so, about 22 billion times longer than the age of the universe), the Pacific Ocean will be dry. At that point, fill up the Pacific Ocean with water all over again, and place down one sheet of paper. Then, begin the process all over again, second by second, every 24 hours walking another metre, every lap around the Earth another cup of water, every time the Pacific Ocean runs dry, refilling it and then laying down another sheet of paper.

Eventually, your stack of sheets of papers will be tall enough to reach the Moon. I think it goes without saying that, at this point, the numbers become very difficult to comprehend, but it would take a very very very very very long time to do this enough to get a stack of paper high enough to reach the Moon. Once you get a stack of papers high enough to reach the moon, throw it all away and begin the whole process again, shuffle by shuffle, metre by metre, cup of water by cup of water, sheet of paper by sheet of paper.

Once you have successfully reached the Moon one billion times, congratulations! You are now 0.00000000000001% of the way to shuffling 8 * 1067 times!