The Unbeatable Game from the 60s: Dr NIM

I’m gonna show you a game which seems difficult But! I’f you learn one simple trick, and i’m serious it’s genuinely this one simple trick The game becomes, so easy! Most people can be beaten by a piece of plastic, From the sixties. -music- Here’s the game of Dr.Nim I managed to find and buy online It came in a fantastic original 1960s box check that
out You can tell us nineteen sixties America
because there’s a wholesome family having fun with guns in the background! The game
starts with the row Marbles along the top of the board there, and the goal is
to take the last marble, whoever gets that one there wins the game, and each
time you have a go you can choose to take one two or three
marbles. but who am I going to play against? well
for dr.Nim you play, the piece of plastic itself
there are levers and things that toggle and bars underneath it will make its own
moves and in theory it will always beat me as the human i get the luxury of
going first there’s a little toggle down here it is on the left and means it’s Dr.Nim’s go, if it’s on the right it’s my go as a human and whenever I
want to release a ball i just hit the button on the side there there goes the first one and you know
what, i’m going to do two marbles on my first go so now I move the lever over to Dr.Nim’s
side and to set Dr.Nim going you hit the button once and it will choose
how many marbles that wants to take so here we go, going for one, oh wait it’s
gone for a second one oh! So it took two marbles and then moved
the lever back over to indicate it’s now my go well I only want one, so there’s my one
and it’s made it through, ever so often we get stuck I now go fine, dr.
Nim all yours I took one, what are you going to do?
that’s going for one, going for a second one its gone for a third one, and then switched
it back to my go okay there are four left, I think dr.
Nim may have me in a corner here, i’m going to take, oh goodness I’ll go with two again there’s- actualy you know what? Just one, I’ll do one, and gonna go straight back to dr.Nim, and you’re on dr.Nim one second, one and the winning third one and just to
rub it in as it winds it puts the lever back over, to say it’s now my go… …to suck… No matter how many times you play doctor
Nim, the plastic jerk as long as the human goes first as long
as you play by all the rules and don’t cheat it will beat you every single time this is based on a mathematical game
called unsurprisingly, NIM, and this is a plastic computer that has been built to
be any human in a simplified version of NIM, NIM is a great game to play it like
this piece of plastic you’re a big fan of beating other people
and i’m going to teach you how to always win at NIMH so you can use it to annoy your friends
and family, – music- the game of NIM has been known about
and studied by mathematicians for, well over a century, although people believe it
predates that by a long way specifically what we’re looking at here
is a version of NIM called single pile NIM,for dr.Nim all the marbles
came off one row the version i’m going to show you, all these coins will be in a
single line technically proper NIM can have more
than one pile, but believe me the strategies for multi pile NIMH get a lot more
complicated as very much another game for another video the way I would normally play NIMH in a bar
or similar setting against friends strangers you know, chumps, would be to
use something like 12 coins we start from one end each player can take one
two or three coins whoever takes the last coin wins while I
absolutely never encourage any form of gambling if you were the kind of person
who would like to do that you and your opponent can both put some money on the
game put it under the last coin or token and
whoever takes that one gets the cash, in a similar vein many years ago we were
involved in setting up something called mass of asking where we went outside and
did busking with mathematics on the street one of the routines involved putting 12
pigs on one of our buskers the 12 peg had 20 pounds underneath it very importantly 20 pounds of our money
but we knew if we played the correct strategy we would always be able to win
the game and keep money some people found that pretty annoying
they would go away come up with strategies come back trying to beat us, in
fact there are a few ways people can try and get you in a corner where you can no
longer win but I’ll get to that in a moment to start with here’s how you win 12 coin NIMH, a nice
way to start is by looking at the end game i got myself in before with dr.Nim
i had for marbles left or in this case for coins it was my go, and i knew i couldn’t
possibly win, and if you get your opponent in this situation you can always win
because if they take one you take three if they take to you take two they take
three you take one and they can’t take four according to the rules, so the goal of the game is to get
them into this situation but how do you guarantee that situation well imagine it earlier in the game and
there are eight remaining and it’s their go you’ve got the same deal going on with
just these four to leave these four left if they take one you take three they
take to you take two they take three you take one as long as
between them and you you take for away you’ll be left in that end game we can now go one step back to the very
beginning of the game where there are 12 coins all together you’re thinking of them in lots of four
for there for there for at the end for each round of full the other person goes
first you go second you need to make sure you
take enough coins after their go so between you you have taken four in
total once you know what’s going on it’s a very straightforward game to win
they take one you take three they take to you take two they realize
they can’t win they get annoyed you get the money the only problem arises when people
realize the trick themselves and this is what we had when we were basking people
would go away work it out come back and then they
would insist that we go first instead of them, so what you do is if any
of your friends caughten on to what you’re doing the next time you reset it you do what
we used to do you just take out an extra coin and put it on the end we would
suddenly increase the number of pegs to be greater than 12 you go first and you bring it down to
the now multiple of 4 it’s they go and you’re right back in
your winning situation -Some Extra Radical Music- so how does dr.Nim the piece of plastic
play by those rules with the top we have the 12 marbles as we would expect and then underneath that we have a
series of these little toggling plastic Levers, they keep track of how many
models have gone through the game so far and you can think of them as kind of
like a binary counter but it’s not true binary it’s more of a tally system that
keeps track of the marbles you start with the leftmost one up and
the other two flat down the first model release drop the left one that raises
the center one if I then send a second one it drops the things one raises the
right one the third marble just restore the right
one to being flat only when there’s a fourth marble your
left my one get raised back up again and we’re right back to where we started
that repeats every set of four marbles after they’ve gotten through what are
now calling the paddles the marbles can go one of two different ways they can
either go to the left or they can go to the right, if its Dr.Nim’s turn and
the switches over on their side any marbles which go to the left will
bump the switch over ending dr.Nim’s go any marbles which go to the right hit the button and release another
marble so we need to save from the different arrangements of the top three
paddles and it keeps track from each set of 4 is the first second third or fourth
ball do they cause dr.Nim’s go to end? or do
they cause them to take another marble let’s have a look i’ll just cycle
through a few marbles and will keep track first Marvel out ends dr. names go
second marble you take another ball third marble take another ball fourth
model and the go and it carries on like that first one will end his go on the
left second one goes to the right take another one third one go to the right
take another one for one goes to the left ending their go so what does this mean for dr.Nims
strategy where you can imagine all 12 marbles at the beginning works in their
groups of four and for each one it’s dr. him get to go on the first
fourth model they’re going to call their go to an end if they get to have a go on the second
or third they’re always going to carry on to another one when i first got the
game and I was investigating how it works actually found that a little bit odd
because dr.Nim doesn’t have to end their go on the first marble in theory
the human is always going to have the first model from each set of 4 why is it designed to go to the left is
it just easier to build that way It turns out if you read the admittedly
casually racist instruction manual you see they’re acting all different
ways of playing doc turn in their options for dr. need to go first and you
can do the same trick you can give them extra marbles the doctor named will just take straight
away in there are other versions where you have a fighting chance there are some versions of this game
where you can actually beat dr.Nim and that’s what this little paddle here is
for is called the equalizer paddle and you can set that so initially doctor
named doesn’t play with perfect strategy you get a chance at the beginning to
beat it but if you make one mistake it will take
over return to perfect play and you’re not going to win, and that’s why dr.Nim
has to end its go on the first position as well as the fourth position it would
only end in the fourth position there are some versions of the game
where you may have ended at a whole round of four in that case dr.Nim would take four
marbles that’s against the rules and it will have cheated and whoever designed
the dr.Nim game to their credit they made in such a way
that it will never cheat it will always play within the rules
admittedly in such a way that it would normally kick your ass so they are that is the game of dr.Nim, I find it absolutely fascinating as an example of a very early computing
based game the instructions for all their drawbacks
to go into a surprising amount of detail of the theory behind how dr.Nim
actually plays so you can see here there’s a whole section next to that
fantastic caricature which talks all about whether or not machines can
actually think, if you like this kind of real-world ridiculous physical computing
then you’re going to love my Domino computer check it out – thousand dominoes arranged in a pattern
such as they can do binary arithmetic if you like this general concept of
fascinating mathematics of course make sure you subscribe to my stand-up mass
channel and if you like winning drinks money or just admiration of your friends
when you do that how to playing them and please do go beat them -Last bit of Epic Music-