# Stanford on the coin toss

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

1. ### snukaGuest

snuka, Jan 3, 2005

2. ### Mike TerryGuest

Snuka,

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

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

3. ### mensanatorGuest

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