May

26

A standard deck of cards contains 52! combinations after riffle shuffling at least 7 times to ensure randomness. Expressed as a number, there are 8.06×10^67 total combinations. To put this in perspective, there are 4.37×10^17 seconds since the big bang. It is estimated there are 5×10^18 grains of sand and 10^50 atoms on earth. There are 10^46 molecules in all of the oceans. The estimated number of stars in the observable universe is 10^23. It’s a certainty that two entire 52 card decks have never ever matched, let alone more than once. They never will. Here’s another way of looking at it, if a billion people shuffled a deck of cards every second since the big bang, it would total 2×10^32 shuffles, which is still 10^22 less than the total. All of that said, there are some elegant propositional bets that can be derived from this material.

Nils Poertner responds:

Yes - incredible numbers. LIfe itself is a miracle (I don't buy into this bing bang thing) - but would not be able to bet against the odds you described here.

Asindu Drileba offers:

Leo Susskind explains that many constants in physics need to be fine tuned for the universe to exist in the way we see it. Some cannot be deviated by as low as 5%. All these constants needed to be fine tuned concurrently. Otherwise, stars would not even form.

Big Al writes:

If you assume that order matters, then when dealing cards for a game of Texas Holdem at a 9-seat table (18 hole cards and 5 community cards), there are 52!/29! possible permutations. That's roughly 9 x 10^36, or 9 x (1 billion)^4. Which means that, though possible, it is highly unlikely that any game (at a fair table) has ever been dealt the same way twice.

The History of Playing Cards


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