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"Jazz" Is the Hardest Word to Guess in Hangman

Mathematician Jon McLoone calculated the most difficult word to guess in the game of Hangman. It's "jazz". Here's how he arrived at that result:

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."


Link via reddit | Photo by Flickr user quinn.anya used under Creative Commons license

That's if you don't cheat.

From Ken Jennings: "When I was a kid, I remember my brother beat me once at Battleship by simply refusing to put his ships anywhere on his grid. Makes it a lot harder, as you can imagine. And it’s a neat Gordian-knot way to win.I was wondering: is there a similar way to cheat at Hangman? Can you mentally switch words as the other player is guessing, in such a way that they can’t win?

The answer’s yes. Off the top of my head, one good family of words to choose is _ A _ _ L E. The other player will immediately get the E and the A. Let’s be generous and give them the L as well. But then you can decide the word is BABBLE, CACKLE, GAGGLE, WAFFLE, or DAZZLE–all words with no common consonants–depending on what letter the player guesses now. In fact, ?a??le words are pretty good choices in honest Hangman as well, for the same reason. Too many options for the other play to guarantee they’ll get to them all before their man expires."
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There's another problem with this - the simulated runs are being guessed by a computer program. A computer will not guess in the same manner as a human would. (Of course, all humans would guess different, but what 'AI' we've made so far is horrible at thinking like a human.)
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As archibot and video game dork wrote, this is all well and good as long as you're playing against a computer.

I don't think most kids will go the wheel of fortune route and start out with "RSTLNE" and then go from there.

I hope there wasn't a government grant involved with figuring out how to beat the computer at hangman...
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jazz would be hard unless they guessed J, at which point the jig is up

my favorite go-to hangman secret weapon word has always been zephyr
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@video game dork

"Of course, all humans would guess different, but what 'AI' we've made so far is horrible at thinking like a human."

Actually, modeling the way a human guesses letters isn't difficult at all. It just needs to be slightly weighted towards more common letters with a lesser propensity to go for the uncommon ones.

@remf

"I don't think most kids will go the wheel of fortune route and start out with "RSTLNE" and then go from there."

Maybe not as a specific strategy, but those being very common letters, any bright kid will gravitate towards them anyways.

@ted

NAGGERS?
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syzygy actually isn't that hard - usually people guess vowels first and when they are forced to guess Y, it's a giveaway for anyone familiar with the word
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Simulating a more 'human like' guessing can be done that way, but that's not really modeling an AI to think, and thus guess, like a human. The actual human thought process (speaking in terms of information, even leabing out the biological 'mechanics' of it) is WAAAAAAY more complicated than anything we've been able to do in the field of AI thus far. (And the AI subsection of Computer Science is a particular strong suit of mine).
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