As I reported in this 2009 StatsMadeEasy blog, math and stats experts Persi Diaconis, Susan Holmes and Richard Montgomery long ago worked out that “vigorously flipped coins tend to come up the same way they started.”* Based on principles of physics, the “DHM” model predicts about a 0.51 chance that a coin will come up as started. That is not a big difference over 0.50 but worth knowing by its cumulative impact over time providing an appreciable winning edge.
Now in a publication revised on June 2nd the DHM model gains support by evidence from 350,757 flips that fair coins tend to land on the same side they started. All but three of the 50 (!) co-authors—researchers at the University of Amsterdam—flipped coins in 46 different currencies and finally settled on 0.508 as the “same-side bias,” thus providing compelling statistical confirmation for the DHM physics model of coin tossing.
This finding creates many potential repercussions, for example on NFL football games going into overtime, particularly under the old rules when a team that won the coin toss could immediately win with a touchdown. The current rules provide one chance for the opposing team to tie under these circumstances. Nevertheless, it seems to me that referees should randomly pull their coin out without knowing which side came up, keep it covered up from sight of the caller and then flip it.
Let’s keep things totally fair at 50/50. (But do sneak a peek at the coin if you can!)
*Dynamical Bias in the Coin Toss, SIAM (Society for Industrial and Applied Mathematics) Review, Vol. 49, No. 2, pp. 211–235, 2007.