So much for symmetric bets---Dynamical Bias in the Coin Toss

[g charles-cadogan]

Dynamical Bias in the Coin Toss

Persi Diaconis, Susan Holmes, Richard Montgomery

 

Abstract

We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias 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.

http://comptop.stanford.edu/u/preprints/heads.pdf

[Hammond, Peter]

Two reactions:

1) This may not be the right kind of physics for producing symmetric bets. For an electronic alternative that has been around in the UK since the late 1950s, see

http://en.wikipedia.org/wiki/Premium_Bond

Other lotteries seem to use many numbered balls. And I heard that recently the Coptic Church in Egypt had a blindfolded boy choose one ball from 5 or so in an urn of some sort in order to determine their next Pope.

2) Whenever I was tossing up to determine who would choose whether to bat or bowl first in a cricket match, the coin was always spun vigorously and allowed to land on the pitch, where it does not bounce. I think it is the same for other UK and international sports, such as most codes of football. Does this make any difference? Probably not, because the key issue seems to be that the coin should not bounce.

But it is good to see this work in more accessible form after a related talk I heard Persi give some years ago at a memorial conference for Amos Tversky.

Peter Hammond
Dept. of Economics
Stanford University
579 Serra Mall
Stanford, CA 94305-6072
USA
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+1 (650) 799-2906
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home page: www.stanford.edu/~hammond

Peter J. Hammond, FBA
Department of Economics
University of Warwick
Coventry CV4 7AL
UK
phone: 024765 23052
fax: 024765 23032
e-mail: p.j.h...@warwick.ac.uk
home page: http://go.warwick.ac.uk/pjhammond