# Probability of shuffling a deck of cards the same way twice

**The**

**probability**

**of**being dealt a royal flush is the number of royal flushes divided by the total number of poker hands. We now carry out the division and see that a royal flush is rare indeed. There is only a

**probability**

**of**4/2,598,960 = 1/649,740 = 0.00015% of being dealt this hand. Much like very large numbers, a

**probability**that is this.

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**The**two players with the two lowest

**cards**play against the two players with the two highest

**cards**.

**The**player with the lowest

**card**deals first. For drawing, the

**cards**rank: K (high), Q, J, 10, 9, 8, 7,

**A**. Players drawing equal

**cards**must draw again. Partners sit opposite each other. The Shuffle and Cut. The dealer has the right to shuffle last.

**deck**but

**the**

**deck**now holds only 51

**cards**, so your odds of drawing a spade on the.

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**card**stud with 8 players playing up to the last

**card**, or 5

**card**draw with all the players switching their entire hands, you will notice that the initial

**deck**

**shuffling**matters. Calculating possible distinct shuffles over a set is done by using factorial. When you shuffle a

**deck**

**of**

**cards**again, your odds of getting a new combination again are basically 100% because your odds of getting the

**same**combination

**twice**in a row are 1 in 80 658 175 170 943 878 571 660 636 856 403 766 975 289 505 440 883 277 824 000 000 000 000. Every time you shuffle the

**deck**again, you increase that 1 by 1, and

**the**. So here is the fact: Every time you shuffle a

**deck**.

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**shuffling**100 times a second for 100 trillion years.