hangman is a weird game

hangman is a weird game you know the game hangman? you know, thatgame that you play when you’re in a family restaurant or in a classroom and in no otherenvironments.

have you ever like, really thought about hangman, like from a game design perspective?because I’ve been thinking about hangman a lot recently, and wow hangman is a lot strangerthan you’d think.

I’m jan Misali, and hangman is a weird game.

part one: what hangman is let’s start with the basics.

hangman isa pencil and paper game about guessing a word one letter at a time.

it’s generally playedwith two players, one player guessing a word picked by a second player.

it’ll be usefulto give these roles names, so I’m going to call the player who doesn’t know theword the “guesser” and the player who does know the word the “executioner”.

the most obviously strange thing about thisgame is the theme.

using a drawing of a person being hanged to keep track of score is extremelymorbid for a children’s game.

this is, however, not unique to hangman.

I mean, yes, the specificsof it definitely are, but games for children have had dark themes as long as children haveplayed games, from Ring Around the Rosie to Fortnite.

the theme is an aspect of hangman that’ssomewhat problematic for one of the main contexts where the game is played; hangman is oftenplayed in classrooms in order to teach children vocabulary.

despite how ubiquitous hangmanis, an elementary school teacher drawing a stick figure being hanged in front of a groupof small children isn’t the best idea.

as a result, classroom hangman often involvesthings like crossing apples off a tree or drawing a stick figure that’s just like, chilling there.

or a turtle! lesser analysts would stop at the theme, butcome on.

everyone knows that hangman’s theme is weird.

it’s honestly the least weirdthing about this game, all things considered.

let’s go through an example game just asa reminder to everybody at home how the game works.

the executioner starts by writing nineblanks, corresponding to the nine letters in the word they’ve picked for the guesserto guess.

they then draw the gallows that will serve to keep track of the guesser’sincorrect guesses.

for the rest of the game, the executionertakes a more passive role, providing feedback for the guesser as they guess letters.

ifthey guess a letter that appears in the word, the executioner fills in the blank where itappears.

if the letter appears multiple times in theword, they fill in everywhere that the letter appears.

if the guesser guesses a letter that doesnot appear in the word, the executioner adds a single line to the gallows drawing, whicheventually becomes a drawing of a person being hanged- the titular “hangman”.

if theexecutioner finishes drawing the hangman before the guesser can guess the word, the executionerwins.

but if the guesser guesses the word first, the guesser wins.

in this case, the executioner won, so nowthey reveal to the guesser that the word was “fhqwhgads”.

at this point, the guesser accuses the executionerof cheating, claiming that fhqwhgads isn’t a real word.

the argument escalates, creatinga scene in the middle of the family restaurant.

while in this example game the guesser wasguessing letters somewhat arbitrarily, it’s possible to play the role of the guesser farmore strategically.

part two: winning at hangman now, I know what you’re thinking.

playinghangman is so easy! all you need to do is guess letters in decreasing order of how commonthey are, right? well, not quite.

sure, that works at first, but eventually you gotta switch from thinking about individual letters and start thinkingabout what words it might be based on the pattern of blanks.

of course, that’s not really a strategy, that’s more like a human intuition thing.

that’s like saying that the best chess strategyis to think about what moves will make you likely to win the game and then do those.

so let’s make it more rigorous.

as the guesser, each letter you guess is a chance to get information from the executioner.

at the start, all youknow how long the word is, but each letter you guess tells you more about the word.

thisis obvious in the case when the letter is in the word, but sometimes it’s more usefulwhen the letter isn’t in the word.

I conjecture that the perfect strategy forthe guesser, therefore, can be precisely defined like this: consider all words that it could be, giventhe information you already have (how long it is, where specific letters are, and specificletters that are not in the word) for each letter you have not guessed yet, assume that the word does not contain that letter, and determine how many of the possiblewords would still be on the table if that were the caseselect whichever letter minimizes this number how well does this strategy work? well, Iwrote some code and tested it out.

if you guess letters randomly, with no strategybeyond just making sure that you don’t guess the same letter twice, you end up making aboutsixteen incorrect guesses on average.

guessing letters in order of frequency ismuch better, resulting in around ten incorrect guesses on average.

both of these strategies are incredibly simple, and predictably they’re both pretty bad at hangman.

guessing at random usually involvesshouting out more than half the alphabet before you get it, and even though guessing by frequencyis an improvement over that, not adjusting what letters are prioritized as more of theword is revealed means that it practically assumes that every word contains every vowelat once, wasting a lot of guesses.

my conjectured perfect strategy, on average, only needs two incorrect guesses, and in fact the most common result was for it to onlymake one incorrect guess! as an example of just how good the perfectstrategy is, let’s compare it to the simple frequency strategy for the word “joyousnesses”.

for the simple frequency strategy, “joyousnesses”is a very challenging word, as it contains the letter , the letter that appears inthe fewest words in the word list I used.

this strategy will always blindly guess everysingle letter in the alphabet before it guesses .

in total, it makes nineteen incorrect guesses.

now compare this to how the perfect strategy does.

the first thing the perfect strategy doesis notice that the word is twelve letters long.

it understands that for twelve letterwords, the most common letter is , and guesses that first.

since joyousnesses doesn’thave an in it, it then only considers twelve letter words that do not contain an, and finds that the most common letter among those words is .

it then continues for the rest of the gamefilling out the blanks in the same order as the simple strategy, except that it doesn’tmake any incorrect guesses between.

as soon as it guesses , it already knows exactlywhat word it is.

and so the perfect strategy gets to the answerwith only one incorrect guess.

incredible! one slight problem is that the perfect strategyonly works if you have a perfect knowledge of what words the executioner could have selectedbeforehand.

in practice, no human player would be able to use this strategy.

that is, exceptin one specific case.

you know how hangman is sometimes played in a classroom to teachchildren vocabulary? well, in that situation, the guesser can be expected to know everysingle word that the executioner could have selected.

simply by memorizing the given listof words, it’s entirely feasible for a guesser playing classroom hangman to play perfectlyoptimally.

this fact is, I believe, the reason why hangmanis a popular game for teaching vocabulary.

one minor issue with it as a teaching method, however, is that it doesn’t actually encourage learning what words mean, just what lettersare in them.

even if what you’re trying to trick your students into studying for isa spelling test or something, with a small enough list of potential words it’s notreally necessary to know exactly how to spell any of the potential words to be able to usethis strategy, just what letters are in them.

while the guesser has many possible strategiesthat they can use, the executioner, in their more passive role, seems to be far more limitedin their options, not having any real choice outside of what the initial word is.

“what’s the hardest word to guess in hangman”is not a very hard question to find answers to.

the answer I’ve seen the most is “jazz”, a claim that can be traced back to research done by Jon McLoone back in 2010.

and are two of the least common letters used in the English language, so the guesser isunlikely the guess them, so a word that contains both letters would naturally be pretty hardto guess.

but is it the hardest word to guess? afterall, there’s another word that’s exactly the same as jazz except that the is replacedwith a less common vowel.

so, clearly Jon wasn’t using a complete enough dictionary.

if I can’t trust Jon McCloone, I guess that means I’ll have to do the math myself! unfortunately, given that it can take up toa full second for my laptop to do all the regex calculations necessary to do my conjecturedperfect hangman strategy, I can’t just check every single English word; that would takelonger than I have the patience for.

instead, I had to rely on looking for trends amongthe words in the random sample that I was able to check.

one thing that’s pretty obvious is thatthe harder words to guess are ones that have less common letters.

longer words where theonly vowel is are especially difficult, like “rhythm” and “symphysy”.

however, long words in general are not, asit turns out, necessarily more difficult to guess than short words.

the most importantfactor is actually the total number of unique letters in the word, where words with fewerunique letters are more challenging to guess.

consider the random guesser.

statistically, the more unique letters there are in the word, the more likely any individual guess theymake is to be correct.

And of course real human guessers don’t generally guess lettersat random; the more of the word is revealed the more well informed their guesses become.

so then, what is the hardest word to guess? well, based on the random sample of wordsthat I was able to throw at my perfect strategy, it would appear that the answer is some wordwith only two unique letters, arranged in a pattern that could fit as many words aspossible.

the word “yay” proved itself a challenge; there are a lot of three letterwords where the middle letter is , as it turns out.

“ax” is a hard word for a similarreason.

but is that the limit? are there words withfewer unique letters than that? well, Marriem-Webster helpfully lists six definitions for “f”as a noun.

clearly, f is a word.

in fact, the same holds true for any letter you lookup.

if every letter could be a word, that meansthat the executioner can pick one of those, and no matter what the guesser does it’simpossible for them to get any useful information about the word unless they happen to guesswhat letter it is.

so then the most difficult “word” to guess would just be whateverletter is the least common! so the “hardest word to guess” is theletter j! or just whatever letter the guesser’s strategyhappens to prioritize last.

there’s actually not any one clear consensus on what the leastcommon letter is in English.

it depends on a lot of different factors.

however, withinthe text file I’ve been using as my reference list of English words, only considering howmany words a letter appears in at all and not how many times it appears total, and alsonot considering how common words are relative to each other, the least common letter, andtherefore the hardest letter to guess, is .

but wait a second, there’s no way anybodywould actually be okay with that in a real game of hangman, right? I’m pretty surethe whole “the dictionary has a definition for it so it’s a word” argument wouldn’tbe able to convince a real human guesser that j is a word.

and besides, they’d totally just accusethe executioner of cheating.

how do they know that the executioner actually picked j atthe start of the game? for all the guesser knows, the executioner could have just waiteduntil they ran out of guesses and then retroactively decided what the letter was.

which brings us to.

.

.

part three: cheating at hangman dynamically changing what the word is mid-gameis the most powerful technique that the executioner can use, and following the standard rulesof hangman there is literally nothing stopping them from doing so.

if done well, the executionercan use this strategy without the guesser noticing anything.

suppose that the executioner starts the gameby putting down six blanks.

they can then, by not having actually picked a word at thestart, claim that the guesser’s first five guesses are all incorrect no matter what theyare, and only then actually select a word.

to do this, all you need is to simultaneouslyhave six words in mind that have no letters in common, then after their first five guessespick one of them.

this is far from the only exploit that theexecutioner can use.

remember, the executioner wins when they’ve finished drawing the hangman.

so, how many incorrect guesses does that take? six? ten? fifteen? there’s a complete lackof standardization.

some players deliberately keep adding detail to the hangman as to givethe guesser extra guesses.

an executioner who’s in it to win, however, can do the opposite of that.

before the game starts, draw the gallows, including a noose.

after their first incorrect guess, retroactivelydecide that the noose is actually the hangman’s head and draw a suspiciously shaped body connectedto it.

after their second incorrect guess, draw aleg coming from the middle of the body.

then after their third incorrect guess, drawthe hangman’s arms, t-posing, and confidently declare yourself the winner.

congratulations, you have now drawn the hangmanin a way that only gives the guesser three incorrect guesses! when the guesser predictablycalls you out and says that that’s not how hangman works, the lack of standardizationmeans that it’s completely possible for you to convince them that you think that that’show hangman works.

to make it extra hard, don’t even write down their wrong guesses, force them to keep track of that themself.

but say it was decided before the start ofthe game how many guesses are given, so you can’t actually do any of that.

no worries, you can still bend the spirit of the game quite a bit.

remember the example game at the start withthe word “fhqwhgads”? was that a valid word to have picked? no, you won’t findit in a respectable dictionary, but dictionaries aren’t authorities on what is or isn’ta quote unquote “real word”, and even if they were, they still wouldn’t be authoritieson what is or isn’t a valid word to pick in hangman.

consider Scrabble, another word game.

Scrabbleis often played competitively, and Scrabble competitions do, in fact, have standard rulesfor which words are legal to play.

it’s not just the set of all English words thatcan be spelled within the limitations of the basic ruleset; words that are, quote, “foreign, hyphenated, capitalized, disparaging, derogatory, obscene or offensive” are all banned incompetitive Scrabble.

hangman, as a pencil and paper game, doesn’thave an official guide to what words are legal, which implies that everything is fair game.

in fact, many digital implementations of hangman seemingly embrace this freedom and allow anystring of characters to be played as a word, putting players in the same situation as theend of the example game from the beginning, left to decide among themselves weather ornot the word the executioner picked was valid.

but it’s not just a matter of what countsas a real word.

what counts as a letter? here’s a question: does the word “piñata” containthe letter in English? in Spanish, the answer would be no.

n-tilde is considereda completely separate letter from n in Spanish, and therefore in Spanish language hangman would be an incorrect guess for the word.

but in English, diacritics are often ignored.

“pinata” is often spelled without the tilde as a perfectly acceptable alternatespelling.

but this isn’t about pinata without a tilde, it’s about piñata with a tilde.

does that word contain the letter ? and if so, how would it work in hangman? doesthe diacritic count as a separate letter? if the guesser guesses , does the executionerwrite it with the tilde or without it? it’s somewhat common for things that aren’tletters to be included as part of the setup for the word at the start of the game, likehyphens or spaces.

but there’s definitely an argument you could make, especially ifyou’re trying to win as the executioner, that these should be counted as separate letters, and that the guesser needs to actually guess them.

j is a hard word to guess, but someone guessingrandomly still has a 1/26 chance of getting it immediately.

the word “that’s”, onthe other hand, if presented as a six letter word, might be literally impossible to guess.

and if the guesser accuses you of cheating, feel free to argue that there’s no specificrule that says an apostrophe isn’t a letter.

in fact, go right ahead and get into a heateddebate over weather or not apostrophe is a letter in general.

you have my support.

the thing is, all of these ways for the executionerto cheat and win are like, kinda obvious.

so why doesn’t the executioner always winin practice? the reason is that winning as the executioner just isn’t very fun.

part four: hangman is a weird game hangman doesn’t exist in a vacuum.

it’san important part of the word guessing game genre.

yet, as a word guessing game, hangmanis clearly an odd one out.

take Pictionary, for example.

that’s a prettytypical word guessing game.

in a round of Pictionary, one player is randomly assigneda word, then they have to communicate with their team members what that word is by drawinga picture of it.

their team wins the round if they can guess the word within a time limit.

most word guessing games follow this basicformat.

players are put into teams, and players who know the word try to help guessers guessthe word under some restriction.

crucially, players who know the word and players whodon’t are working towards the same goal; word guessing games are fundamentally cooperative.

they can of course be played competitively, but always as a competition to see how wellyou can cooperate.

imagine if Pictionary worked like hangman.

instead of the word being randomly selected for the artist, the artist picks it themself, and the artist wins if the guesser fails to guess the word.

under these rules, they’dbe incentivized not to draw anything! they’d just wait out the timer and automaticallywin! that’s no fun at all.

and that’s exactly the reason why it isn’tfun to win as the executioner.

of course you want the guesser to win, because that’swhat makes word guessing games fun! but even then, the way the executioner isn’t supposedto have any real choice during gameplay means that hangman isn’t designed for the limitedcommunication antics that make up most word guessing games.

so, even though it is definitelya game about guessing words, hangman isn’t really a word guessing game, in the same sensethat Portal isn’t really a first person shooter.

so, if it’s not a word guessing game, whatis it? maybe it’s more helpful to consider the medium rather than the genre.

hangman is a pencil and paper game.

penciland paper games are categorically extremely simple.

their rules are passed down throughoral tradition, and are minimal enough that they only take seconds to learn.

this isn’tunique to pencil and paper games.

there is definitely something to be said about theelegance of games like rock paper scissors, or even tag.

pencil and paper games are like a halfwaypoint between games that use nothing other than the human body and proper board games.

the most well known pencil and paper game is tic tac toe, also known as naughts andcrosses.

while tic tac toe and hangman are in completelydifferent genres, they do have at least one thing in common beyond their medium.

justlike how winning as the executioner in hangman isn’t very fun, being good at tic tac toeis also not very fun.

if both players know what they’re doing, the result is a tieevery single time.

but really, the fact is that other penciland paper games just don’t have the same amount of open-endedness as hangman.

penciland paper games have simple rules with unambiguous wins states for both players, and hangmanjust isn’t like that.

you can’t just decide to keep playing after tic tac toe ends, butfor hangman that’s seemingly the default way to play.

perhaps I’m looking at this too broadly.

of course there are games that are like hangman.

just look at Wheel of Fortune! hugely populargameshow that’s clearly just hangman with prizes attached.

right? well, not necessarily.

there’s some prettyfundamental differences.

first of all, there are multiple guessers competing against eachother.

this is kinda like classroom hangman, where a teacher takes the role of the executionerand an entire classroom of students are the guesser.

how do you turn hangman into a competitivegame? you could argue that hangman is already competitive, as the guesser and executionerare competing against each other.

however, I don’t think that “competitive” isentirely accurate.

due to the asymmetric nature of the game, the two players are better describedas “adversaries”, not “competitors”.

they are working against each other, but theyaren’t competing.

anyway, to turn hangman from an adversarialgame into a competitive game, one easy thing to change is to have multiple guessers taketurns guessing letters, and say that whoever gets the final letter wins.

this is good enoughfor most variants of classroom hangman, but Wheel of Fortune has a few more specific fundamentaldifferences.

first, Wheel of Fortune is actually aboutguessing phrases and not single words.

this is a pretty minor change all things considered, but it crucially increases the total number of possibilities by a functionally infiniteamount.

to counter this, a general category is given to the guessers right at the start.

this piece of information provides a little bit of context to the round, and allows playersto make more informed guesses.

the second fundamental change is the way scoringworks.

for each correct guess, a guesser is awarded an amount of money determined randomlyby the titular Wheel of Fortune, multiplied by how many times it appears in the phrase.

this awards players who reveal more of the phrase throughout the round, while the elementof randomness adds a level of excitement and uncertainty.

the third fundamental change is a restrictionon what guesses are allowed and when.

at the start of a guesser’s turn, they spin theWheel and guess a consonant.

if they guess correctly, they can choose to spin again, buy a vowel, or attempt to guess the entire phrase.

since vowels are among the most commonletters in English, limiting when they can be guessed adds a layer of strategy to thegame.

these major changes seem to have been madespecifically to make it more difficult to rely entirely on knowledge of letter frequencyto win.

the randomness of the Wheel means that even a player who somehow knows exactlywhat the phrase is before any letters have been revealed has a slim but non-zero chanceof never getting a single opportunity to guess anything.

but like, why? why does hangman need to beadjusted to make it harder for more skilled players to win in order for it to work asthe basis of a game show? it’s almost as though they had this idea for a show whereyou spin a wheel then sometimes get money but they didn’t want it to just be televisedgambling so they had to attach it to some sort of skill based game, and hangman wasjust the first thing they thought of.

maybe hangman would fit in more in the genreof guessing game.

take, for example, Guess Who.

like hangman, a player selects one froma set of possible options at the start of the game, and then the other player gathersinformation by guessing individual segments.

at an abstract level, they’re very similargames.

there’s another game that has just as muchin common with hangman: Battleship.

Battleship is actually even closer to hangman, sincethere’s more control at the start of the game over the initial setup, and there’smore clear limits for what things can actually be guessed.

there is one thing Guess Who and Battleshiphave in common with each other that they don’t have in common with hangman: both games aresymmetric.

the two players are both guessers.

and it makes sense, right? otherwise, theplayer who isn’t guessing would have nothing to do for the whole game.

say, that gives me an idea for how we couldmake hangman more fun for both players.

just make it like Battleship! make it symmetric!at the start of the game, both players pick a word, then they take turns guessing lettersin each other’s words.

you don’t even need the hangman to keep track of incorrectguesses because the winner would just be whoever guesses the other player’s word first.

sure, it’s definitely further away from the spirit of word guessing games, but as established, hangman isn’t like other word guessing games.

part five: conclusion hangman is a two player asymmetric adversarialpencil and paper word guessing game.

its position in pop culture is completely unique.

it’sa game that everyone has played, yet at the same time it’s a game where nobody knowsexactly what the rules are.

it’s a game where one player needs to have an understandingof letter frequency to succeed, while the other player has nothing preventing them fromcheating, something which they will only take advantage of to prevent themself from winning.

it’s completely unlike anything else in its genre.

it’s completely unlike anythingelse in its medium.

hangman is a weird game.

thanks for watching.

I’ve been jan Misali, and apostrophes are definitely letters.

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