Is This Possible?
I was reading something about the possibilities in a deck of cards once shuffled. The person claimed that once properly randomized, it’s most likely that they have never been in that position before in the history of the earth.
Since I love numbers, I thought I would check it out, doing the math myself.
We are trying to reach the number of seconds to match the mathematical possibilities for a shuffled deck of cards.
Here is how it was stated to reach the number of seconds to match the possibilities.
Walk around the earth taking one step every billion years.
I figure a normal step is about one yard. So, it would take about 43,825,760 steps to get around the earth, and it would take 43,825,760,000,000,000 years to get it done.
Once you make it around the earth, take one drop of water from the Pacific Ocean.
Then start all over again, walk around the earth, 1 step each billion years, then take another drop water out of the Pacific Ocean. Do this over and over until you have emptied the ocean.
The Pacific Ocean has about 14,152,000,000,000,000,000,000,000 drops of water, so it would take 620,222,155,420,000,000,000,000,000,000,000,000,000,000 years to get the ocean emptied
Once you have the ocean emptied lay down a single piece of paper, flat on the earth.
Then fill the ocean back up and start all over again. Take one step each billion years, take a drop out of the ocean, empty the ocean again, then lay another sheet of paper flat on the ground.
Continue this process, stacking one piece of paper each time you have emptied the ocean until the paper reaches the Sun! Are you kidding?
I figured the number of sheets of paper to get to the Sun was about 1,472,500,000,000,000. This was figured using 250 sheets per inch.
So, we take this number times the years to get the ocean emptied.
Now guess what?
We haven’t even come close to matching the number of possibilities in a shuffled deck of cards.
So, to pass the remaining time, deal yourself a 5-card poker hand once every billion years.
Each time you get a Royal Flush, buy a lottery ticket.
The odds of getting a Royal Flush in five cards is 649,739 to one. Since you are dealing once every one billion years, it would take 649,739,000,000,000 years to get one. Once you get a Royal Flush, buy a lottery ticket. Keep doing this until you win the lottery.
Once you win the lottery, head to the Grand Canyon and throw in one grain of sand.
Then do it again, deal yourself a 5-card poker hand once every billion years until you get another Royal Flush. Then buy another lottery ticket and continue until you hit the Grand Prize. Then one more grain of sand in the Grand Canyon.
Now, once you get the Grand Canyon full of sand, head over to Mt. Everest
and take away one ounce of earth from it.
You guessed it, start all over again, deal yourself a hand once every billion years until you get a Royal Flush, buy a lottery ticket for each Royal Flush until you hit the main jackpot, then throw a grain of sand into the Grand Canyon for each jackpot until full, once full get another ounce from Mt Everest. Repeat over and over until you have leveled Mt Everest.
So, after walking around the earth at one step each billion years, taking out one drop of water from the Pacific Ocean until emptied, then laying a single piece of paper flat on the ground each time you empty the ocean, until the paper reaches the Sun.
Then dealing yourself, one 5-card poker hand each billion years until you get a Royal Flush. For every royal flush you buy a lottery ticket until you hit the lottery. Once you hit the lottery, throw one grain of sand into the Grand Canyon, repeat until full. Once full take one ounce from Mt. Everest – repeat until Everest is gone. And guess what? According to the article you are still short. You would need to repeat this whole process another 255 times to match the number of seconds in the possibilities of a randomized deck of 52 cards.
According to the article we would still be short on time, but according to my math, we have finally made it. We are now at 4,568,027,063,769,760,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years. Since there are about 31,540,000 seconds in a year, we should have reached the number of possibilities in a randomized deck of cards.
That number is: 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
The blog post that I was looking at, can be found here.
Odds of winning the lottery are 13,986,816 to one.
Using these numbers, it would take 9,087,779,841,024 years to win one lottery
I figured it would take 88,000,000,000,000,000,000,000 grains of to fill up the Grand Canyon.
It would take 799,724,626,010,112,000,000,000,000,000,000,000,000,000,000 years to fill up the Grand Canyon
Per sources, Mt Everest weighs 5,712,000,000,000,000 in ounces.
A side note: I got to thinking last night of all the different casinos around the world and how often they shuffle the cards. Then of all the people that play cards all around the world. Surely with everyone in the world shuffling cards constantly there would be several duplicate shuffles. So I decided to do the math.
Cards have been around for about 500 years and there are about 7,530,000,000 people on earth.
Let’s assume that there have been that many people for the last 500 years and every person in the world shuffled a deck of cards every second. There are 86,400 seconds in one day and 31,536,000 seconds in one year. If you take that times the number of years since cards have been around, you would get 15,768,000,000 seconds for a period of 500 years.
Now take that times 7,530,000,000 and you get 118,733,040,000,000,000,000. That’s how many shuffles you would have if everyone on earth has shuffled a deck of cards every second for the last 500 years.
The odds of anyone shuffling an exact duplicate deck are 1 in 679,323,760,016,115,000,000,000,000,000,000,000,000,000,000,000.
So it’s almost a certainty that no one has ever shuffled a deck of cards randomly and came up with the same order of cards that someone else has ever done on earth for all time!
To take it a little further, let’s say that everyone on earth has been shuffling for every second since the beginning of the universe 13.8 Billion years ago. In that case the probability of having a duplicate shuffle would only be one in 24,613,179,710,728,800,000,000,000,000,000,000,000,000.
Let’s go a little deeper. Let’s say that there are 10 Billion galaxies in the universe. Each galaxy has about 100 billion stars. Let’s say that each star has 10 planets and that each planet has 7,530,000,000 people. Now let’s say that all of these people have been shuffling cards since the beginning of the universe 13.8 Billion years ago. You would have 75,300,000,000,000,000,000,000,00,000,000 people shuffling cards 435,196,800,000,000,000 times. That would equal a total of 32,770,319,040,000,000,000,000,000,000,000,000,000,000,000,000,000 shuffles. The odds of any two being the same would be one in 2,461,317,971,072,880,000. That’s over 2.4 Quintillion.
Still No One Has Shuffled A Duplicate Deck!!!
So just remember, every time you shuffle a deck of cards, they have never been in that exact position before.