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-