Bill Morgan had already been dubbed Australia’s luckiest man when, in 1999, he won the lottery for a second time. The truck driver had been in an accident that left him clinically dead for 14 minutes (twice the time needed to declare someone as having died) and then in a coma for 12 days. Against all odds, Morgan made a miraculous recovery. A year later, after he won a car on a scratch-off lottery ticket, his story caught the attention of national news. Then, while recreating the lucky moment for the cameras, Morgan won again, this time to the tune of 250,000 Australian dollars. What are the chances?!

Well, according to mathematician John Edensor Littlewood, it is not quite as unlikely as you might think. Writing in A Mathematician’s Miscellany in 1953, Littlewood demonstrated that ...