Hangman’s Most Difficult Word

Hangman — a short, easy to play game: all one needs is a pencil, piece of paper, and a friend.  A staple of bored schoolchildren everywhere, the game has origins dating back to the early 1900s.

But what’s the hardest word to guess?

Jon McLoone built a computer game — with a series of algorithms — to figure out that exact question.  It rests on a key assumption: the guesser will pick common letters (e.g. vowels) measurably and proportionally more often than exceptionally rare ones (Q, X, Z, J).  McLoone then simulated fifty Hangman runs for every single word in the dictionary.   That’s 90,000 words, totaling nearly 5 million games on Hangman.

Some words were easily guessed, typically requiring fewer than five incorrect letters offered.  For example, the word “difficult” proved easy — in its 50 trials, the simulator guessed, on average, only 3.3 incorrect letters.  Allowing for eight incorrect ones before our stick figure meets an untimely death, the word “difficult” only caused one stick-death.  Allowing for ten?  Mr. Stick had a 100% survival rate.

Having gathered all this data on 90,000 words, McLoone selected the 1,000 most promising and then ran the game 3,000 times using just those thousand.  All said and done, McLoone “played” nearly 8 million games of Hangman in order to determine that the hardest Hangman word to guess — regardless of whether the guesser has 8, 9, 10, or even up to 13 guesses, is “jazz.”

Bonus fact: It took one person with a computer to figure out the above.  But it took 35 computer-years to determine that every single possible position of a Rubik’s Cube — all 43,252,003,274,489,856,000 of them — is solvable in 20 moves or fewer.

Related: Like a Rubik’s Cube, but gone crazy.