hangman is a weird game
you know the game hangman? you know, that game that you play when you’re in a family
restaurant or in a classroom and in no other environments. 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 stranger than 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 is a pencil and paper game about guessing a word
one letter at a time. it’s generally played with two players, one player guessing a word
picked by a second player. it’ll be useful to give these roles names, so I’m going
to call the player who doesn’t know the word the “guesser” and the player who
does know the word the “executioner”.
the most obviously strange thing about this game is the theme. using a drawing of a person
being hanged to keep track of score is extremely morbid for a children’s game. this is, however,
not unique to hangman. I mean, yes, the specifics of it definitely are, but games for children
have had dark themes as long as children have played games, from Ring Around the Rosie to
Fortnite.
the theme is an aspect of hangman that’s somewhat problematic for one of the main contexts
where the game is played; hangman is often played in classrooms in order to teach children
vocabulary. despite how ubiquitous hangman is, an elementary school teacher drawing a
stick figure being hanged in front of a group of small children isn’t the best idea. as
a result, classroom hangman often involves things 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, but come on. everyone knows that hangman’s theme
is weird. it’s honestly the least weird thing about this game, all things considered.
let’s go through an example game just as a reminder to everybody at home how the game
works. the executioner starts by writing nine blanks, corresponding to the nine letters
in the word they’ve picked for the guesser to guess. they then draw the gallows that
will serve to keep track of the guesser’s incorrect guesses.
for the rest of the game, the executioner takes a more passive role, providing feedback
for the guesser as they guess letters. if they guess a letter that appears in the word,
the executioner fills in the blank where it appears.
if the letter appears multiple times in the word, they fill in everywhere that the letter
appears.
if the guesser guesses a letter that does not appear in the word, the executioner adds
a single line to the gallows drawing, which eventually becomes a drawing of a person being
hanged- the titular “hangman”. if the executioner finishes drawing the hangman before
the guesser can guess the word, the executioner wins. but if the guesser guesses the word
first, the guesser wins.
in this case, the executioner won, so now they reveal to the guesser that the word was
“fhqwhgads”.
at this point, the guesser accuses the executioner of cheating, claiming that fhqwhgads isn’t
a real word. the argument escalates, creating a scene in the middle of the family restaurant.
while in this example game the guesser was guessing letters somewhat arbitrarily, it’s
possible to play the role of the guesser far more strategically.
part two: winning at hangman
now, I know what you’re thinking. playing hangman is so easy! all you need to do is
guess letters in decreasing order of how common they are, right?
well, not quite. sure, that works at first, but eventually you gotta switch from thinking
about individual letters and start thinking about 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 strategy is 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 you know how long the word is, but each letter
you guess tells you more about the word. this is obvious in the case when the letter is
in the word, but sometimes it’s more useful when the letter isn’t in the word.
I conjecture that the perfect strategy for the guesser, therefore, can be precisely defined
like this:
consider all words that it could be, given the information you already have (how long
it is, where specific letters are, and specific letters 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 possible words would still be on the table if that
were the case select whichever letter minimizes this number
how well does this strategy work? well, I wrote some code and tested it out.
if you guess letters randomly, with no strategy beyond just making sure that you don’t guess
the same letter twice, you end up making about sixteen incorrect guesses on average.
guessing letters in order of frequency is much 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 involves shouting out more than half the alphabet before
you get it, and even though guessing by frequency is an improvement over that, not adjusting
what letters are prioritized as more of the word is revealed means that it practically
assumes that every word contains every vowel at 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 only make one incorrect guess!
as an example of just how good the perfect strategy 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 in the fewest words in the word list I used.
this strategy will always blindly guess every single 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 does is notice that the word is twelve letters
long. it understands that for twelve letter words, the most common letter is , and
guesses that first. since joyousnesses doesn’t have 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 game filling out the blanks in the same order as
the simple strategy, except that it doesn’t make any incorrect guesses between. as soon
as it guesses , it already knows exactly what word it is.
and so the perfect strategy gets to the answer with only one incorrect guess. incredible!
one slight problem is that the perfect strategy only works if you have a perfect knowledge
of what words the executioner could have selected beforehand. in practice, no human player would
be able to use this strategy. that is, except in one specific case. you know how hangman
is sometimes played in a classroom to teach children vocabulary? well, in that situation,
the guesser can be expected to know every single word that the executioner could have
selected. simply by memorizing the given list of words, it’s entirely feasible for a guesser
playing classroom hangman to play perfectly optimally.
this fact is, I believe, the reason why hangman is 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 letters are in them. even if what you’re trying
to trick your students into studying for is a spelling test or something, with a small
enough list of potential words it’s not really necessary to know exactly how to spell
any of the potential words to be able to use this strategy, just what letters are in them.
while the guesser has many possible strategies that they can use, the executioner, in their
more passive role, seems to be far more limited in 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 is unlikely the guess them, so a word that contains
both letters would naturally be pretty hard to guess.
but is it the hardest word to guess? after all, there’s another word that’s exactly
the same as jazz except that the is replaced with 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 to a full second for my laptop to do all the
regex calculations necessary to do my conjectured perfect hangman strategy, I can’t just check
every single English word; that would take longer than I have the patience for. instead,
I had to rely on looking for trends among the words in the random sample that I was
able to check.
one thing that’s pretty obvious is that the harder words to guess are ones that have
less common letters. longer words where the only vowel is are especially difficult,
like “rhythm” and “symphysy”.
however, long words in general are not, as it turns out, necessarily more difficult to
guess than short words. the most important factor is actually the total number of unique
letters in the word, where words with fewer unique 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 they make is to be correct. And of course real
human guessers don’t generally guess letters at 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 words that I was able to throw at my perfect strategy,
it would appear that the answer is some word with only two unique letters, arranged in
a pattern that could fit as many words as possible. the word “yay” proved itself
a challenge; there are a lot of three letter words where the middle letter is , as it
turns out. “ax” is a hard word for a similar reason.
but is that the limit? are there words with fewer 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 look up.
if every letter could be a word, that means that the executioner can pick one of those,
and no matter what the guesser does it’s impossible for them to get any useful information
about the word unless they happen to guess what letter it is. so then the most difficult
“word” to guess would just be whatever letter is the least common!
so the “hardest word to guess” is the letter j!
or just whatever letter the guesser’s strategy happens to prioritize last. there’s actually
not any one clear consensus on what the least common letter is in English. it depends on
a lot of different factors. however, within the text file I’ve been using as my reference
list of English words, only considering how many words a letter appears in at all and
not how many times it appears total, and also not considering how common words are relative
to each other, the least common letter, and therefore the hardest letter to guess, is
.
but wait a second, there’s no way anybody would actually be okay with that in a real
game of hangman, right? I’m pretty sure the whole “the dictionary has a definition
for it so it’s a word” argument wouldn’t be able to convince a real human guesser that
j is a word.
and besides, they’d totally just accuse the executioner of cheating. how do they know
that the executioner actually picked j at the start of the game? for all the guesser
knows, the executioner could have just waited until 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-game is the most powerful technique that the executioner
can use, and following the standard rules of hangman there is literally nothing stopping
them from doing so. if done well, the executioner can use this strategy without the guesser
noticing anything.
suppose that the executioner starts the game by putting down six blanks. they can then,
by not having actually picked a word at the start, claim that the guesser’s first five
guesses are all incorrect no matter what they are, and only then actually select a word.
to do this, all you need is to simultaneously have six words in mind that have no letters
in common, then after their first five guesses pick one of them.
this is far from the only exploit that the executioner 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 lack of standardization. some players deliberately
keep adding detail to the hangman as to give the 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, retroactively decide that the noose is actually the hangman’s
head and draw a suspiciously shaped body connected to it.
after their second incorrect guess, draw a leg coming from the middle of the body.
then after their third incorrect guess, draw the hangman’s arms, t-posing, and confidently
declare yourself the winner.
congratulations, you have now drawn the hangman in a way that only gives the guesser three
incorrect guesses! when the guesser predictably calls you out and says that that’s not how
hangman works, the lack of standardization means that it’s completely possible for
you to convince them that you think that that’s how 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 of the 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 with the word “fhqwhgads”? was that a valid
word to have picked? no, you won’t find it in a respectable dictionary, but dictionaries
aren’t authorities on what is or isn’t a quote unquote “real word”, and even
if they were, they still wouldn’t be authorities on what is or isn’t a valid word to pick
in hangman.
consider Scrabble, another word game. Scrabble is often played competitively, and Scrabble
competitions do, in fact, have standard rules for which words are legal to play. it’s
not just the set of all English words that can be spelled within the limitations of the
basic ruleset; words that are, quote, “foreign, hyphenated, capitalized, disparaging, derogatory,
obscene or offensive” are all banned in competitive Scrabble.
hangman, as a pencil and paper game, doesn’t have 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 any string of characters to be played as a word,
putting players in the same situation as the end of the example game from the beginning,
left to decide among themselves weather or not the word the executioner picked was valid.
but it’s not just a matter of what counts as a real word. what counts as a letter? here’s
a question: does the word “piñata” contain the letter in English? in Spanish, the
answer would be no. n-tilde is considered a 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 alternate spelling. 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? does the diacritic count as a separate letter?
if the guesser guesses , does the executioner write it with the tilde or without it?
it’s somewhat common for things that aren’t letters to be included as part of the setup
for the word at the start of the game, like hyphens or spaces. but there’s definitely
an argument you could make, especially if you’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 guessing randomly still has a 1/26 chance of getting
it immediately. the word “that’s”, on the 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 specific rule that says an apostrophe isn’t a letter.
in fact, go right ahead and get into a heated debate over weather or not apostrophe is a
letter in general. you have my support.
the thing is, all of these ways for the executioner to cheat and win are like, kinda obvious.
so why doesn’t the executioner always win in 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’s an important part of the word guessing game
genre. yet, as a word guessing game, hangman is clearly an odd one out.
take Pictionary, for example. that’s a pretty typical word guessing game. in a round of
Pictionary, one player is randomly assigned a word, then they have to communicate with
their team members what that word is by drawing a picture of it. their team wins the round
if they can guess the word within a time limit.
most word guessing games follow this basic format. players are put into teams, and players
who know the word try to help guessers guess the word under some restriction. crucially,
players who know the word and players who don’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 well you 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’d be incentivized not to draw anything! they’d
just wait out the timer and automatically win! that’s no fun at all.
and that’s exactly the reason why it isn’t fun to win as the executioner. of course you
want the guesser to win, because that’s what makes word guessing games fun! but even
then, the way the executioner isn’t supposed to have any real choice during gameplay means
that hangman isn’t designed for the limited communication antics that make up most word
guessing games. so, even though it is definitely a game about guessing words, hangman isn’t
really a word guessing game, in the same sense that Portal isn’t really a first person
shooter.
so, if it’s not a word guessing game, what is it? maybe it’s more helpful to consider
the medium rather than the genre.
hangman is a pencil and paper game. pencil and paper games are categorically extremely
simple. their rules are passed down through oral tradition, and are minimal enough that
they only take seconds to learn. this isn’t unique to pencil and paper games. there is
definitely something to be said about the elegance of games like rock paper scissors,
or even tag.
pencil and paper games are like a halfway point 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 and crosses.
while tic tac toe and hangman are in completely different genres, they do have at least one
thing in common beyond their medium. just like how winning as the executioner in hangman
isn’t very fun, being good at tic tac toe is also not very fun. if both players know
what they’re doing, the result is a tie every single time.
but really, the fact is that other pencil and paper games just don’t have the same
amount of open-endedness as hangman. pencil and paper games have simple rules with unambiguous
wins states for both players, and hangman just isn’t like that. you can’t just decide
to keep playing after tic tac toe ends, but for 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 popular gameshow that’s clearly just hangman with
prizes attached. right?
well, not necessarily. there’s some pretty fundamental differences. first of all, there
are multiple guessers competing against each other. this is kinda like classroom hangman,
where a teacher takes the role of the executioner and an entire classroom of students are the
guesser.
how do you turn hangman into a competitive game? you could argue that hangman is already
competitive, as the guesser and executioner are competing against each other. however,
I don’t think that “competitive” is entirely accurate. due to the asymmetric nature
of the game, the two players are better described as “adversaries”, not “competitors”.
they are working against each other, but they aren’t competing.
anyway, to turn hangman from an adversarial game into a competitive game, one easy thing
to change is to have multiple guessers take turns guessing letters, and say that whoever
gets the final letter wins. this is good enough for most variants of classroom hangman, but
Wheel of Fortune has a few more specific fundamental differences.
first, Wheel of Fortune is actually about guessing 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 infinite amount. 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 players to make more informed guesses.
the second fundamental change is the way scoring works. for each correct guess, a guesser is
awarded an amount of money determined randomly by 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 element of randomness adds a level of excitement and
uncertainty.
the third fundamental change is a restriction on what guesses are allowed and when. at the
start of a guesser’s turn, they spin the Wheel 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 common letters in English, limiting when they can
be guessed adds a layer of strategy to the game.
these major changes seem to have been made specifically to make it more difficult to
rely entirely on knowledge of letter frequency to win. the randomness of the Wheel means
that even a player who somehow knows exactly what the phrase is before any letters have
been revealed has a slim but non-zero chance of never getting a single opportunity to guess
anything.
but like, why? why does hangman need to be adjusted to make it harder for more skilled
players to win in order for it to work as the basis of a game show? it’s almost as
though they had this idea for a show where you spin a wheel then sometimes get money
but they didn’t want it to just be televised gambling so they had to attach it to some
sort of skill based game, and hangman was just the first thing they thought of.
maybe hangman would fit in more in the genre of guessing game. take, for example, Guess
Who. like hangman, a player selects one from a set of possible options at the start of
the game, and then the other player gathers information by guessing individual segments.
at an abstract level, they’re very similar games.
there’s another game that has just as much in common with hangman: Battleship. Battleship
is actually even closer to hangman, since there’s more control at the start of the
game over the initial setup, and there’s more clear limits for what things can actually
be guessed.
there is one thing Guess Who and Battleship have in common with each other that they don’t
have in common with hangman: both games are symmetric. the two players are both guessers.
and it makes sense, right? otherwise, the player who isn’t guessing would have nothing
to do for the whole game.
say, that gives me an idea for how we could make 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 letters in each other’s words. you don’t even
need the hangman to keep track of incorrect guesses 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 adversarial pencil and paper word guessing game. its position
in pop culture is completely unique. it’s a game that everyone has played, yet at the
same time it’s a game where nobody knows exactly what the rules are. it’s a game
where one player needs to have an understanding of letter frequency to succeed, while the
other player has nothing preventing them from cheating, 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 anything else in its medium.
hangman is a weird game.
thanks for watching. I’ve been jan Misali, and apostrophes are definitely letters.