Stanford on the coin toss

Discussion in 'General Math' started by snuka, Jan 3, 2005.

  1. snuka

    snuka Guest

    snuka, Jan 3, 2005
    #1
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  2. snuka

    Mike Terry Guest

    Snuka,

    The article says there is a bias towards heads when the coin starts off as
    heads.

    How can this be? Coins are launched with a certain distribution of
    energies, a certain distribution of rotation rates, they're caught after a
    certain distribution of flight times etc. and putting all this together we
    would expect there to be a resulting distribution of heads vs. tails
    outcomes. I would expect this to be very close to a 50% heads/tails split,
    but would not expect it to be exact. (That the difference from 50% is
    supposedly measurable rather surprises me, though...)

    Regards,
    Mike.
     
    Mike Terry, Jan 3, 2005
    #2
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  3. snuka

    mensanator Guest

    Because they don't know how to properly flip a coin.
    That's not surprising since most people don't.

    First, you need a proper coin. Anything smaller than
    a half-dollar should be avoided.

    Second, you hold out a closed fist with the index
    finger wrapped about the tip of the thumb, such that
    the index finger is horizontal.

    Third, the coin is laid flat atop the index finger
    such that the large knuckle supports the weight of
    the coin and the rim not quite touching the thumb.

    Fourth, the hand is smartly pulled downwards while
    simultaneously flicking the thumb.

    Since the hand can accelerate faster than gravity,
    the coin, seperates from the finger and is suspended
    in mid-air (actually in free fall). Thus, when struck
    by the thumbnail, it rings like a bell. If the coin
    is in contact with the finger at the moment of impact,
    the ringing is damped out and you get a clunk.

    With a proper flip, you don't get wobblers. When struck
    in mid-air, the coin pivots about its center. When
    struck while in contact with the finger, the pivot point
    is the far edge not the center, so you get a wobbler.
    You don't need high speed cameras. Any flip that doesn't
    ring must be done over. The other hallmark of a proper
    flip is the absence of a horizontal velocity component.
    A properly flipped coin will go straight up in the air
    and can be caught by merely opening the closed fist and
    waiting for it to drop into your palm. Wobblers sometimes
    fly across the room.

    Unfortunately, the machine pictured emulates an improper
    flip, so whatever his conclusions are, they are irrelevant.
     
    mensanator, Jan 4, 2005
    #3
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