Okay, this is what we consider to be a research talking-point. From two Stanford academics, Persi Diaconis and Susan Holmes, and Richard Montgomery from Santa Cruz, University of California…
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.
The research shows that coin-flipping simply isn’t random, but determined instead by the laws of mechanics; if you start with heads facing up you are more likely to end with heads up, and vice versa.
The startling revelation is discussed in a new book by behavioural finance expert David Adler – Snap Judgement: When to Trust Your Instincts, When to Ignore Them, and How to Avoid Making Big Mistakes with Your Money.
The Standford/Santa Cruz team built a flipping machine and filmed the tosses in slow motion. Here’s the machine:
In a Big Money article, Adler notes that while much of the maths and physics behind this discovery are complex, some of the basic ideas are quite simple. For example, if the force of the flip is the same, the outcome is the same. And while people flipping — rather than machine flipping — is less predictable, a slight physical bias is still there.
The true laws of coin tosses show yet again the inadequacy of our intuition (as well as the flawed metaphors favored by economists). We are indeed fooled by randomness. But we are also fooled by nearly random processes that look random, even if they aren’t, because the differences are too subtle for us to notice. And hence we continue to use coin flips as a figure of speech but also in real life, particularly in gambling and professional sports.
So should the call on who bats first at Edgbaston on Thursday be decided another way?
Apparently not, so long as neither Andrew Strauss nor Ricky Ponting knows how the coin is going to start out – heads up, or tails. You can’t be both the tosser and the caller, otherwise the bias offers an edge, albeit just one per cent.