Who gives a toss: the statistics of coins

Spring is here in Melbourne, and a time for fashionable horse racing, including The Melbourne Cup in November., once attended by Mark Twain. Australia is also home of the “two-up” coin tossing game (descended from the British pitch and toss), played in outback pubs, hidden city lanes and now Australian casino’s, described in great old Australian novels such as Come In Spinner, and the eerie book and 1971 movie Wake in Fright (aka Outback).

In the 18th century, the Comte de Buffon obtained 2048 heads from 4040 tosses, while more recently and not to be outdone the statistician Karl Pearson obtained 12,012 heads out of 24,000 tosses (The Jungles of Randomness by Ivars Peterson, 1998). Of course a misunderstanding of the law of large numbers or so-called law of averages, makes the uninitiated think that if there’s say seven heads in a row, a cosmic force will decide “hang on that coin is coming up heads more than 50%, better make the next one a tail”).

While it doesn’t look at two-up, “Digital Dice” by the always entertaining Paul Nahin (2008) examines a tricky coin-tossing problem posed in 1941 and not solved until 1966. Prof Paul shows how to solve it using a computer-based Monte Carlo method, itself named after that famous casino in Monaco, where James Bond correctly observed that “the cards have no memory”.

And who says stats isn’t relevant?!