hangman is a weird game you know the game hangman? you know, that
game that you play when youâre 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 Iâve been thinking about hangman a lot recently, and wow hangman is a lot stranger
than youâd think. Iâm jan Misali, and hangman is a weird game. part one: what hangman is letâs start with the basics. hangman is
a pencil and paper game about guessing a word one letter at a time. itâs generally played
with two players, one player guessing a word picked by a second player. itâll be useful
to give these roles names, so Iâm going to call the player who doesnât know the
word the âguesserâ and the player who does know the word the âexecutionerâ. 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 childrenâs 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 thatâs
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 isnât the best idea. as a result, classroom hangman often involves
things like crossing apples off a tree or drawing a stick figure thatâs just like,
chilling there. or a turtle! lesser analysts would stop at the theme, but
come on. everyone knows that hangmanâs theme is weird. itâs honestly the least weird
thing about this game, all things considered. letâs 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 theyâve picked for the guesser
to guess. they then draw the gallows that will serve to keep track of the guesserâs
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 âhangmanâ. 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 âfhqwhgadsâ. at this point, the guesser accuses the executioner
of cheating, claiming that fhqwhgads isnât 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, itâs possible to play the role of the guesser far
more strategically. part two: winning at hangman now, I know what youâre 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, thatâs not really a strategy,
thatâs more like a human intuition thing. thatâs 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 letâs 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 itâs more useful
when the letter isnât 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 donât 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 theyâre 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, letâs compare it to the simple frequency strategy for the word âjoyousnessesâ. for the simple frequency strategy, âjoyousnessesâ
is a very challenging word, as it contains the letter <j>, 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 <j>. 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 <i>, and guesses that first. since joyousnesses doesnât
have an <i> in it, it then only considers twelve letter words that do not contain an
<i>, and finds that the most common letter among those words is <e>. it then continues for the rest of the game
filling out the blanks in the same order as the simple strategy, except that it doesnât
make any incorrect guesses between. as soon as it guesses <o>, 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, itâs 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 doesnât actually encourage learning what words mean, just what letters
are in them. even if what youâre trying to trick your students into studying for is
a spelling test or something, with a small enough list of potential words itâs 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. âwhatâs the hardest word to guess in hangmanâ
is not a very hard question to find answers to. the answer Iâve seen the most is âjazzâ,
a claim that can be traced back to research done by Jon McLoone back in 2010. <j> and
<z> 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, thereâs another word thatâs exactly the same as jazz except that the <a> is replaced
with a less common vowel. so, clearly Jon wasnât using a complete enough dictionary.
if I canât trust Jon McCloone, I guess that means Iâll 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 canât 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 thatâs pretty obvious is that
the harder words to guess are ones that have less common letters. longer words where the
only vowel is <y> are especially difficult, like ârhythmâ and âsymphysyâ. 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 donât 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 âyayâ proved itself a challenge; there are a lot of three letter
words where the middle letter is <a>, as it turns out. âaxâ 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 âfâ
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 itâs
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 âwordâ to guess would just be whatever
letter is the least common! so the âhardest word to guessâ is the
letter j! or just whatever letter the guesserâs strategy
happens to prioritize last. thereâs 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 Iâve 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 <j>. but wait a second, thereâs no way anybody
would actually be okay with that in a real game of hangman, right? Iâm pretty sure
the whole âthe dictionary has a definition for it so itâs a wordâ argument wouldnât
be able to convince a real human guesser that j is a word. and besides, theyâd 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 guesserâs 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 theyâve finished drawing the hangman.
so, how many incorrect guesses does that take? six? ten? fifteen? thereâs a complete lack
of standardization. some players deliberately keep adding detail to the hangman as to give
the guesser extra guesses. an executioner whoâs 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 hangmanâs 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 hangmanâs 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 thatâs not how hangman works, the lack of standardization
means that itâs completely possible for you to convince them that you think that thatâs
how hangman works. to make it extra hard, donât 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 canât 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 âfhqwhgadsâ? was that a valid word to have picked? no, you wonât find
it in a respectable dictionary, but dictionaries arenât authorities on what is or isnât
a quote unquote âreal wordâ, and even if they were, they still wouldnât be authorities
on what is or isnât 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. itâs not just the set of all English words that
can be spelled within the limitations of the basic ruleset; words that are, quote, âforeign,
hyphenated, capitalized, disparaging, derogatory, obscene or offensiveâ are all banned in
competitive Scrabble. hangman, as a pencil and paper game, doesnât
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 itâs not just a matter of what counts
as a real word. what counts as a letter? hereâs a question: does the word âpinĚataâ contain
the letter <n> 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
<n> would be an incorrect guess for the word. but in English, diacritics are often ignored.
âpinataâ is often spelled without the tilde as a perfectly acceptable alternate
spelling. but this isnât about pinata without a tilde, itâs about pinĚata with a tilde.
does that word contain the letter <n>? and if so, how would it work in hangman? does
the diacritic count as a separate letter? if the guesser guesses <n>, does the executioner
write it with the tilde or without it? itâs somewhat common for things that arenât
letters to be included as part of the setup for the word at the start of the game, like
hyphens or spaces. but thereâs definitely an argument you could make, especially if
youâre 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 âthatâsâ, 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 thereâs no specific
rule that says an apostrophe isnât 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 doesnât the executioner always win
in practice? the reason is that winning as the executioner just isnât very fun. part four: hangman is a weird game hangman doesnât exist in a vacuum. itâs
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. thatâs 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
donât 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, theyâd
be incentivized not to draw anything! theyâd just wait out the timer and automatically
win! thatâs no fun at all. and thatâs exactly the reason why it isnât
fun to win as the executioner. of course you want the guesser to win, because thatâs
what makes word guessing games fun! but even then, the way the executioner isnât supposed
to have any real choice during gameplay means that hangman isnât 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 isnât really a word guessing game, in the same sense
that Portal isnât really a first person shooter. so, if itâs not a word guessing game, what
is it? maybe itâs 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 isnât
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 isnât very fun, being good at tic tac toe
is also not very fun. if both players know what theyâre doing, the result is a tie
every single time. but really, the fact is that other pencil
and paper games just donât 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 isnât like that. you canât just decide to keep playing after tic tac toe ends, but
for hangman thatâs seemingly the default way to play. perhaps Iâm looking at this too broadly.
of course there are games that are like hangman. just look at Wheel of Fortune! hugely popular
gameshow thatâs clearly just hangman with prizes attached. right? well, not necessarily. thereâs 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 donât think that âcompetitiveâ is
entirely accurate. due to the asymmetric nature of the game, the two players are better described
as âadversariesâ, not âcompetitorsâ. they are working against each other, but they
arenât 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 guesserâs 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? itâs almost as though they had this idea for a show where
you spin a wheel then sometimes get money but they didnât 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, theyâre very similar
games. thereâs another game that has just as much
in common with hangman: Battleship. Battleship is actually even closer to hangman, since
thereâs more control at the start of the game over the initial setup, and thereâs
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 donât have in common with hangman: both games are
symmetric. the two players are both guessers. and it makes sense, right? otherwise, the
player who isnât 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 otherâs words. you donât even need the hangman to keep track of incorrect
guesses because the winner would just be whoever guesses the other playerâs word first. sure,
itâs definitely further away from the spirit of word guessing games, but as established,
hangman isnât 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. itâs
a game that everyone has played, yet at the same time itâs a game where nobody knows
exactly what the rules are. itâs 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.
itâs completely unlike anything else in its genre. itâs completely unlike anything
else in its medium. hangman is a weird game. thanks for watching. Iâve been jan Misali,
and apostrophes are definitely letters.
That... sounds a lot like most roleplaying games. The executioner is like the GM. They don't want to win outright, because that's not the point. Instead they want to provide a challenge for the other player(s) that is doable, but not guaranteed.
That was weirdly enjoyable good job.