Hey! DataLeap!
Andrew here and
we are in a fight
we are in an outright quarrel.
We are at WAR
it is a cold war: a lot of Speak Softly and Carry a large stick style but
we are beefing nonetheless
You see, in the cold quarantined afterscape of the
pandemic some of us are not who we say we are... Some of us
are imposters
Consider liking and subscribing :)
Oh yes i'm talking about the meme-y social deduction game that is sweeping the
internet with its meme-y little fingers like a plague:
Among Us. Now i'm not being sponsored by the game at all but it does beg the question
How the heck do you win this game?
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and now back to Among Us
Thanks Andrew. In order to win this game it's a surprising combination
of social deduction and game theory that will cause you
to like math and i'm gonna explain it with an old game show host
a couple of goats and a million dollars plus this
shoot it's a charcuterie board of hedgehogs
but first special agent let's have a brief briefing about the game itself
in this game you can have up to 10 players two of which can be
impostors and if you're an innocent crewmate you have no idea
who anybody else is except yourself imposters can go around and assassinate
other crewmates in cold blood or warm blood whatever it is that pumps through
their impostory veins so the crewmates are
gonna have to think quick let's imagine a game with you and three
other players now four is the minimum number so that's how many people are
gonna be playing this game four you included and let's say
that you are not the imposter all right take a nice breath of relief
from your human squishy lungs but not for long because you need to decide
which one out of your three space compatriots
is the imposter i'll let you pick out of these three
pick someone yet this is basically a question
asked supposedly by monty hall a game show host from the 60s game show
let's make a deal in the game monty the host allows you to pick between three
doors now behind two of these doors is a goat and behind one of these doors
is a brand new car or in our case it's a million
dollars in this case the analogy means that if you pick the million dollars you
are picking the imposter out of your three space
compatriots once again your options were red yellow
and white so without any information it seems like
you have a one in three chance of getting it right
well that's 33 so the game is done well actually the game is far from over
because you have the ability to gain more information
about the innocence of some of your compatriots proof of innocence can
include diligently doing tasks so the taskbar
goes up or certain task animations that only
trigger for innocent people in this theoretical game show a
very real game theory question is asked let's say you
get a little more information you get exactly a third of the
information answered monty opens one of the doors and says
hey it's not this one monty opens the door
and says it's not white
behind that door is a goat let's say that you originally picked
the red one well he gives you a choice you can either
switch from the red one to the yellow one
or stay with your choice what do you do i'll pause here to see
what you might think drop a like down below if you like this
question because this question ultimately ends up being a
little bit of decision theory a little bit of game theory
but all statistics which is why you are going to end up liking
math remember we're beefing here we don't trust each other
so back to the question so the first time you had a choice
you had a one-third chance you had exactly one in three but this time
do you have a different chance do you have
a one in two chance since there's only two possible candidates left
for the imposter or is it even higher what if i told you that by staying with
the original choice you had you still have a one-third chance but if you
switch to the other candidate then you
are actually twice as likely to pick the imposter
this question was originally asked by steve selvin in 1975
as a letter to the american statistician a good number of people end up sticking
with the original choice after all lightning only strikes once and to admit
that you are wrong in any part of this game
is to admit that your guesses are folly something that is difficult for a lot of
us to do but why is it that there is twice as
much likeliness that we choose the right
imposter if we switch after finding out that
someone someone who we didn't choose ended up being innocent
let's bring these bad boys back up and ask the question
again when you originally picked your first guess you had exactly
one in three chants it's either red yellow
or white that means that you had a one in three chance of being right
and a two and three chance of being wrong however
when i knocked one of your choices off of the board
that you didn't get to choose that means suddenly by switching to the other
crewmate you had a inverse of what you originally
chosen chance of being right your first choice is the one that
matters because you're either right or wrong there's only two
ways that this could play out for example only one person
is the imposter which means that you had a 33 percent chance
that it was the one you chose and a 66 chance that it was within
the second group let's play in a different way let's say that you're
trying to find the imposter out of red yellow and white and i gave you the
choice of either picking red as the imposter or someone
out of white and yellow as the imposter well if you chose the first option you
have a one in three chance of being right
if you chose the second option you would have two out of three chances being
right because it it's twice as likely that it's one of
these two people than it is just this one person after all everybody
has a one in three chance of being the imposter right well
now it's the same exact choice all i'm saying is that you don't even need
to worry about this guy now it's the same exact choice except
you don't even have to worry about the hamster i just knocked off
it's either red who you had a one in three chance of getting right
or it's everyone except red which means it's the same
two out of three chances of being right if you still don't believe me
let's have one more explanation let's say that it's
red or everybody in town that's not red so let's say that there's 99 or
999 or 9999 other civilians in this spaceship that's
not red well if you still guessed red on the
very first try and then i knocked off everybody and
said these people are innocent except sushi cat now
what do you think is it red the one that you had
one out of 10 000 choices or is it sushi cat where by not choosing
red you had a 999
out of 10 000 chance of being right what do you think sushi cat you would
switch because the chance that you were right
the very first choice was 1 out of 10 000 but once i
eliminated every other option and allowed you to still
pick someone from the other group that is the exact same
as saying i want to choose everyone except red as a possible candidate
and you would be right 9 999 out of 10 000 choices so how do you win
among us a strategically dominant number of times
well have someone in your mind a hypothesis
and when it turns out that you have innocent people that start to become
revealed that wasn't your original pick make sure
to switch because you statistically
will be right more often than not if you want to try this at home and send
in a video or an image of you trying this three-door
monty hall problem with a couple of goats and a couple of
cars already in the right positions and your friend revealing one of the
goats i'm going to add some math and description
and some instructions on how you can test it at home
and see how often you are right if you switch and how often you are right if
you don't and stay safe out there
are you peace about when you originally picked