It’s a rainy day in the 1500s, and the King’s Justice slides a noose around your neck. He tightens it, steps around the wobbly stool beneath your feet and looks you square in the eye. “I’m thinking of a four-letter word,” he grunts. “If you can guess it in ten tries, I’ll let you go free.”
Ah… A classic game of Hangman.
Fortunately for most of us, the letter-guessing classroom game rarely involves such high stakes. But let’s say you did have a very important reason to win. What word should you pick to give your opponent, statistically, the lowest odds of victory?
Mathematician Jon McLoone’s daughter asked him this same question in 2010 and, being a professional numbers whiz for Wolfram, McLoone decided to find an answer that could be supported by nearly five million data points. McLoone designed a Hangman computer game meant to simulate how real human players might actually guess. Working off the assumption that the average person would guess common letters like R, S, T, and the five vowels more often that rare letters like Q, Z, J, and X, McLoone simulated 50 games of Hangman for every word in his 90,000 word dictionary. Nearly five million games of Hangman later, McLoone was ready to answer his daughter.
So, what makes a word hard to guess? For one, the shorter a word is, generally, the trickier it is to solve. This might seem counter intuitive at first, but consider the probability: In a four-letter word like “ball” or “poor” there are only three possible letters that will save the stickman from the gallows. Guessers therefore have a 23/26 chance of picking incorrectly with each guess. If the word is composed of rare letters like J, Q, and Z, guessing correctly becomes even harder. (You’ll never guess the most complicated word in English. Hint: it’s only three letters long.)
Such was the case with McLoone’s top 25 list of unguessable words, which was filled with tricky words like fizz, buzz, jink, hajj, and quiz. But one word reigned supreme, no matter if the computer was allowed 8, 9, 10, 11, 12, or even 13 guesses. The hardest word to guess in hangman, according to science, is: Jazz.
Composed of 75 percent uncommon letters (J and Z) and allowing only three chances at picking correctly, jazz is the perfect storm of Hangman trickery. It’s kind of fitting, really. They say jazz is all about the notes they don’t play. And in the game of hangman, winning is all about the letters they don’t pick.