[Cryptography] are flipped coins unbiased? (was: Re: Photon beam splitters for "true" random number generation ?)

Jonathan Thornburg jthorn at astro.indiana.edu
Thu Dec 24 17:13:42 EST 2015

On Thu, Dec 24, 2015 at 07:23:50AM -0500, Richard Outerbridge wrote:
> Once upon a time I asked the Royal Canadian Mint whether our National
> $1.00 coin, the Loonie,
> flipped at the start of all professional CFL football games, was certified
> to be unbiased.
> They sniffed at me that was not one of the qualities they tested their
> coins for.

For a detailed analysis of coin tossing, see

   Persi Diaconis, Susan Holmes, and Richard Montgomery
   "Dynamical Bias in the Coin Toss"
   SIAM Review, 49(2):211-235 (2007)

      We analyze the natural process of flipping a coin which is caught
      in the hand. We show that vigorously flipped coins tend to come
      up the same way they started. The limiting chance of coming up
      this way depends on a single parameter, the angle between the
      normal to the coin and the angular momentum vector. Measurements
      of this parameter based on high-speed photography are reported.
      For natural flips, the chance of coming up as started is about .51.

(For those who may not know of him, Persi Diaconis is a very well-regarded
professional mathematician, former professional magician, and expert card


-- "Jonathan Thornburg [remove -animal to reply]" <jthorn at astro.indiana-zebra.edu>
   Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
   (presently at home in western Canada)
   "There was of course no way of knowing whether you were being watched
    at any given moment.  How often, or on what system, the Thought Police
    plugged in on any individual wire was guesswork.  It was even conceivable
    that they watched everybody all the time."  -- George Orwell, "1984"

More information about the cryptography mailing list