At each stage, we compare all of the possible moves to a dictionary of all possible words, and filter out all of the words it can’t be: after our first guess in the diagram above, if we guess “A” and the board now shows “_ A _”, then we know that of the 600+ three-letter words in the English language, we’re dealing with one of only about 134. Then for each of those results, we’re considering what guesses we could make next, and so on. What we’re actually doing here is a filtering exercise: of all of the possible letters we could choose, we’re considering what possible results that could have. There are billions of possible states of game play, but you can narrow them down quickly with strategic guessing. But what if our first guess is right? Well, then we’ve got an “A” in one or more positions on the board, and we need to work out the next best move: it’s unlikely to be “E” – very few three-letter words have both an “A” and an “E” – and of course what letter we should guess next depends entirely on what positions the letters are in. And then, if our guess is wrong, the next best letter to guess is E. We know from Nick’s article that the best letter to guess is A. Suppose our opponent has chosen a three-letter word, and has drawn three dashes to indicate this. Based on the assumption that the “executioner” player is choosing words randomly, and that no clue is given as to the nature of the word, we can determine the best possible move for all possible states of the game by using a data structure known as a tree. Nowadays, very few people die as a result of the game.įirst, though, we need to understand how hangman is perfectly played. In short: hangman’s a more-complex game than you probably thought it was! I’d like to take his work a step further, and work out which word is the hardest word: that is – assuming you’re playing an optimal strategy, what word takes the most-guesses? The rules of hangman used to be a lot more brutal. He also showed that the first guesses should be adjusted based on the length of the word (the most common letter in 5-letter words is ‘S’, but the most common letter in 6-letter words is ‘E’). He showed that the best guesses to make to get your first “hit” in a game of hangman are not the most-commonly occurring letters in written English, because these aren’t the most commonly-occurring letters in individual words. Last year, Nick Berry wrote a fantastic blog post about the optimal strategy for Hangman. What’s the hardest word to guess, when playing hangman? I’ll come back to that.
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