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Is it possible that every Bridge hand possible has been dealt somewhere at sometime in history

Discussion in 'Mathematics' started by ian60, Sep 8, 2015.

  1. ian60

    ian60 New commenter

    The number of different ways in which 13 cards could be dealt from a pack of 52 is approx 4 x 10^21.

    A huge number indeed, but given the popularity of the game around the world, and the number of years it has been played, is it possible that every possible hand has been dealt?

    Or are there millions of hands yet to be dealt.

    The number of different ways of dealing 4 hands is 52!, I find it very hard to believe every possible starting game has been played.

    Just musing
  2. maths126

    maths126 New commenter

    Hmm - good puzzle! Some rough thoughts:

    Assume there are 8 billion people in the world, all playing bridge.

    That's 2 billion hands being played (4 people per pack of cards obviously)

    Assume a new hand is dealt every second (they play quickly)

    Assume too that they have been playing like this for 1000 years.

    That gives us 6e19 deals so far.

    There are 8e67 different possible deals.

    We?ve still got a long way to go yet.

    While it may well be that the same 13-card hand has been picked up somewhere before, it would be played differently according to the bidding, the dummy and the play on the table, so the full 52 card deal must be considered rather than just the 13 card hand.
  3. ian60

    ian60 New commenter

    Thanks for your thoughts Maths126.

    I'm not a big card player, and maybe I should ave chosen Whist rather than Bridge.

    But the idea that every time you lift your cards, there is a high probability that no one else has ever had a hand quite like it, fascinates me.
  4. DrFrostMaths

    DrFrostMaths New commenter

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