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Tuesday, August 19, 2014

embaralhar-baralho

Shuffle (almost) always produces unique sequences in the deck

It's easier to win the lottery than shuffling cards in the same sequence twice.
 Seems like overkill? So know that your deck probably has a number unprecedented in history whenever you mix the cards.
 Oh, and do not need to be magical or expert casino.
 The number that makes this statement a fact is great, but the explanation is simple. 
The calculation remembers the birthday paradox, since in a deck of 52 cards, the first card has 52 chances to occupy the first position, but the next has 51, the third 50 and so on
. Multiplying the possibilities of each of the 52 positions (52 x 51 x 50 x 49 x 48 ...) or 52 factor, the result of about 1067 x 8.065817517094 combinations.

 To get an idea of how this number is really big, it's just you remember that it is far more than the number of stars in a galaxy (about 100 billion) and that the chances of someone winning the Mega Sena alone (1 in 50 million). 

And how to know if anyone ever repeated exactly the same sequence?
 Well, statistics show that the probability is very small, after all, the result of 52 factorial (52!)
 Is greater than hypothetically the playing cards have been mixed throughout its approximate 700 years of existence, which makes the chance an identical series of repeating less than 1 followed by 44 zeros.



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