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. 2009 Dec 8;181(12):E306-8.
doi: 10.1503/cmaj.091733. Epub 2009 Dec 7.

Holiday review. How random is the toss of a coin?

Matthew P A Clark  1 , Brian D Westerberg
Affiliations

Holiday review. How random is the toss of a coin?

Matthew P A Clark et al. CMAJ. .

Abstract

Background: The toss of a coin has been a method used to determine random outcomes for centuries. It is still used in some research studies as a method of randomization, although it has largely been discredited as a valid randomization method. We sought to provide evidence that the toss of a coin can be manipulated.

Methods: We performed a prospective experiment involving otolaryngology residents in Vancouver, Canada. The main outcome was the proportion of "heads" coin tosses achieved (out of 300 attempts) by each participant. Each of the participants attempted to flip the coin so as to achieve a heads result.

Results: All participants achieved more heads than tails results, with 7 of the 13 participants having significantly more heads results (p<or=0.05). The highest proportion of heads achieved was 0.68 (95% confidence interval 0.62-0.73, p<0.001).

Interpretation: Certain people are able to successfully manipulate the toss of a coin. This throws into doubt the validity of using a coin toss to determine a chance result.

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References

    1. Murray DB, Teare SW. Probability of a tossed coin falling on its edge. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993;48:2547–52. - PubMed
    1. Diaconis P, Homes S, Montgomery R. Dynamical bias in the coin toss. SIAM Rev. 2007;49:211–35.
    1. MacKenzie D. Euro coin accused of unfair flipping. New Sci. 2002. Jan 4, [(accessed 2009 Oct. 22)]. Available: www.newscientist.com/article/dn1748-euro-coin-accused-of-unfair-flipping....
    1. Denny C, Dennis S. Heads, Belgium wins — and wins. The Guardian; [UK]: 2002. Jan 4, [(accessed 2009 Oct. 22)]. Available: www.guardian.co.uk/world/2002/jan/04/euro.eu2.
    1. Kosnitzky G. Murphy’s Magic Supplies. Rancho Cordova (CA): 2006. Heads or tails; p. 6.