Shuffling a deck of cards the same way twice is almost impossible.
I don't mean really difficult, I mean IMPOSSIBLE*
*Disclaimer: It isn't actually impossible, but it is FAR less likely than winning the lottery multiple times per day, every day of your life.
The odds of shuffling a deck of cards and having it end up the same way twice are
1:80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
*Disclaimer: It isn't actually impossible, but it is FAR less likely than winning the lottery multiple times per day, every day of your life.
The odds of shuffling a deck of cards and having it end up the same way twice are
1:80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
That number written out in words is:
eighty unvigintillion, six hundred fiftyeight vigintillion, one hundred seventyfive novemdecillion, one hundred seventy octodecillion, nine hundred fortythree septendecillion, eight hundred seventyeight sexdecillion, five hundred seventyone quindecillion, six hundred sixty quattuordecillion, six hundred thirtysix tredecillion, eight hundred fiftysix duodecillion, four hundred three undecillion, seven hundred sixtysix decillion, nine hundred seventyfive nonillion, two hundred eightynine octillion, five hundred five septillion, four hundred forty sextillion, eight hundred eightythree quintillion, two hundred seventyseven quadrillion, eight hundred twentyfour trillion. 
Now check this out!Knowing what you know about the odds of shuffling, is there ANY way that this is realistically possible??

That number is ridiculously large and incredibly difficult to comprehend. So let's tell a story to try to get an idea of just HOW large this number is:
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters.Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water.Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three leftmost digits haven’t even changed. You still have 8.063e67 more seconds to go.1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.
And you thought Sunday afternoons were boringTo pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands.If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds.You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt. Exercise for the reader: at what point exactly would the timer reach zero?
Back here on the ranchOf course, in reality none of this could ever happen. Sorry to break it to you. The truth is, the Pacific Ocean will boil off as the Sun becomes a red giant before you could even take your fifth step in your first trek around the world. Somewhat more of an obstacle, however, is the fact that all the stars in the universe will eventually burn out leaving space a dark, everexpanding void inhabited by a few scattered elementary particles drifting a tiny fraction of a degree above absolute zero. The exact details are still a bit fuzzy, but according to some reckonings of The Reckoning, all this could happen before you would've had a chance to reduce the vast Pacific by the amount of a few backyard swimming pools.
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters.Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water.Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three leftmost digits haven’t even changed. You still have 8.063e67 more seconds to go.1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.
And you thought Sunday afternoons were boringTo pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands.If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds.You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt. Exercise for the reader: at what point exactly would the timer reach zero?
Back here on the ranchOf course, in reality none of this could ever happen. Sorry to break it to you. The truth is, the Pacific Ocean will boil off as the Sun becomes a red giant before you could even take your fifth step in your first trek around the world. Somewhat more of an obstacle, however, is the fact that all the stars in the universe will eventually burn out leaving space a dark, everexpanding void inhabited by a few scattered elementary particles drifting a tiny fraction of a degree above absolute zero. The exact details are still a bit fuzzy, but according to some reckonings of The Reckoning, all this could happen before you would've had a chance to reduce the vast Pacific by the amount of a few backyard swimming pools.