I love improbable events and also love demonstrating mathematically why many or most are not as improbable as they seem. Last month, the New York Times’s puzzle, Wordle, offered me another chance at both pleasures—an eye-popping 1-in-2309 occurrence that, upon further thought was really far likelier than that.
My interest in not-as-rare-as-they-seem occurrences isn’t simply idle amusement. The tendency of humans (including “experts”) to overestimate the rarity of surprising events can lead to awful actions, as described in my earlier essay, “Experts with Statistics: Chimps with Machine Guns.” Among other things, that piece told how a statistician wrongly persuaded a British jury to convict a grieving mother of murdering her children and how a California doctor wrongly persuaded his patient that he almost certainly had AIDS. Panic can ensue when coincidental geographical clusters of cancer patients are misinterpreted as causally linked. (Other improbability essays of mine include: “Impossible Things before Breakfast,” “The Improbable Book,” “Coincidentally …,” “Why Impossible Things Are Everywhere,” and “The Double World of François Brunelle.”)
But today’s offering doesn’t involve cancer, murder, or AIDS. It merely reflects a really surprising puzzle result and some idle vacation time to ponder whether it was all that unlikely.
Explaining Wordle
To explain the game to the uninitiated, here’s the not-at-all improbable sequence my companion, Melanie, and I made on August 26. Wordle players seek to identify a particular five-letter word (reportedly out of a 2,309-word list) within six attempts. Wordle accepts a larger pool of 12,966 five-letter words as guesses, but for various reasons (e.g., plurals, past tenses, obscenities) most will never be offered as solutions. (Some websites offer different numbers of words, but I’ll use these.)
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