The coin toss: not 50-50 after all

Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more likely to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up.

How much more likely? At least 51 percent of the time, the researchers claim, and possibly as much as 55 percent to 60 percent — depending on the flipping motion of the individual.

In other words, more than random luck is at work.

Reporting by Mercury News. Hat tip (second in a row!) to Meaningfulness.

Paper is here.

Randomistas: I’m told that Microsoft Excel’s random number function is also… not random. Anyone have hard information on this?

10 thoughts on “The coin toss: not 50-50 after all

  1. Not just excel, any programmed random function is just pseudo random at best…
    one of the key differentiators between humans and machines is the inherent randomness of human character. Excel just uses a timestamp based seed to generate a combination from around 2E11 possibilities…

  2. You can’t randomize using an deterministic algorithm. So, if you use a very long series of numbers generated in excel, at some (long) time you will see a pattern. Look here:
    http://en.wikipedia.org/wiki/Pseudorandom_number_generator
    But this is not a concern for short series (say, one hundred thousand numbers, even one million numbers).

    I didn’t see the paper, but I do not think this is a suprise. You should google “random walk first return”. It is a well established result in stochastic process that if you flip a coin, say, 10000 times, most of time it will show one of the sides leading (ie. more landing of one side than the other). A very good discussion you can find in the famous Feller’s book. ( An Introduction to Probability Theory and Its Applications)

  3. Manoel,

    Well, yeah. Heads – Tails will approximately distributed as Normal( 0 , t/2) after t trials, which goes to infinity in both directions as t gets large

    . But the actual proportion Heads/(Heads+Tails) will go to Normal(1/2, 1/(4*t)), which should tend to 1/2 pretty quickly. The only way you’d see divergence is if the probability is truely something else other then 1/2.

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  6. At least we could *once* have taken some comfort from the eminently plausible proposition that the side of the coin facing up at the start of the flip was independent of anything that mattered.

    But now that you’ve brought this to the attention of the coin flippers, there goes that too. Thanks alot, guys. Now I gotta go out and find only illiterate coin flippers who have no friends who read statistical computing blogs. Where on *earth* am I supposed to find *them*?

  7. “Random numbers are based on a predictable algorithm. If you know the previous number and the algorithm, you can predict the next number(s) generated by the random function. This sounds counter-intuitive, but that’s because random numbers which are generated by computers are not truly random. […] You can test this for yourself. […]”

    http://www.mrexcel.com/forum/showpost.php?p=391514&postcount=7