I've got a magic trick for you Brady. I have
to say I'm not much of a magician but
but we're gonna try okay? So here you go,
here's the cards, one from ten of hearts
I'll show them to you so you see there's nothing
strange, they're not marked or anything.
So I'm going to shuffle them, just
shuffle them a few times okay? I've been
I've been practicing this for like three
days, three days straight just just for
you just to get this trick ready for you.
What I want you to do is just choose a
card and just don't show it to me,
show the viewers but just don't show
it. - (Brady: I'm gonna take this card.)
Okay; and I'm gonna try to read your mind. I'm gonna try
to read your mind and see what what card
that is. Is it the four of Hearts? Sweet,
we're done, that's it, that's all I
wanted to show you. - (Alright, thanks man, see you later!)
I'm such a bad magician I'm actually gonna tell you
what I- how I did this, okay? You know I
guess a good magician isn't supposed to
reveal the tricks but I'm gonna, I'm
gonna tell you how this works. So here's
the cards in order and this might seem a
little bit weird but I'm actually gonna
take the ten out and put a joker back in;
and we'll talk about why I do this
in a minute. This is just to
explain a little bit better how the
trick works, okay? So actually the trick
is very simple, I mean you practice it
for an afternoon you're gonna be able to
do it. So all I do is just each time I'm
gonna cut the deck exactly in half-
(There are 10, are there?) - There's ten cards, so I put 5
here 5 here, and I just make sure that
the shuffle goes perfectly like left,
right, left, right, left, right. So you see I
I go like this left, right, left, right,
left, right, left, right, left, right - and
that's what I've been practicing- you
know I was practicing on the train on
the way here everything- - (I have to say,)
(with all due respect, you weren't very)
(fast at it. Presumably a good magician can-)
Yeah yeah yeah, I mean if if you guys
practice you're gonna be much better
than me at this okay? But so let's talk
about what I did here, okay, so you know
we started with the cards in the order,
and I'm actually I'm gonna call the
Joker a zero okay - just to get it in. 0,
1, 2, 3, 4, 5, 6, 7,
8, 9 okay? So then what I did is
that I cut exactly in half, right, so cards
0, 1, 2, 3, & 4 on the left and then 5, 6, 7, 8 & 9
on the right. Okay? And then
like I said I made sure to just alternate
left, right, left, right, left, right,
left, right. - (And this is called a perfect shuffle?)
It's called a perfect shuffle. And so these are still cards 0, 1, 2, 3 & 4;
these are cards 5, 6, 7, 8 & 9,
okay. And so if I did this right, which I
hope I did, then when we look at the
cards they should be in the order that
we just did it here. So cross your
fingers, or cross my fingers: 0, 5,
1, 6, 2, 7, 3, 8, 4, 9.
So that's what I did, this is the perfect
shuffle. And now what I want to show you
is actually a different way of seeing
this; in mathematics a very common idea
is to try to see the same object in a
few different ways, and so I actually
want to do the same thing graphically. So
let me start again with the cards in
order, and now let me just draw
graphically what happened here.
So I'm just gonna write this order into
this picture, so I'm just gonna say- this
is the order that the cards are in right
now, right? Let's put them over here
so the cards are in the order of this
shuffle: 0, 5, 1 - these
are the new positions - and now what I
want to do is that I want to represent
graphically this perfect shuffle. Card
0: stayed in position 0. Right,
it stayed on top? The card 1 went
to position 1, card 2 went to position
2...card 4 went over here. Card 5
went up here and-
Okay? So you're basically seeing
here graphically the the trail that the
cards were taking, right? And so this
is kind of a little picture of what
happened and here you already start
seeing more structure than maybe what
you would have expected, right? For
example you notice that the top and the
bottom cards never change positions;
there's also this nice symmetry right?
You see that this thing, at least the
picture, looks the same if you flip it upside down.
Yeah? And that's something that's not at
all clear when you when you do that.
Okay so let's go back to the
cards, so I did one perfect shuffle and
now they're in this order, but let me now
do a second perfect shuffle. Here we go...
See that was faster - I should have done it faster like that.
(That's not bad! Still a bit slow, not bad.)
A different way of doing this is actually just to follow
the picture, right? So if I draw the same
picture and just string it along here
then I'm gonna be able to see what
happens to this shuffle. - (So draw that)
(same pattern again?) - Exactly so I'm going
to take this pattern and just transcribe
it directly right next to it, okay.
(You don't even need to look at the cards?)
That's right,
because, you know, this is the one thing
that I have to be careful is that I'm
always doing the same perfect shuffle
and if I do the same perfect shuffle
then the picture is gonna tell me
exactly what I'm doing. And so here I'm
seeing graphically what the shuffle is
doing and so if I'm doing everything
correctly this is exactly the order that
the cards should be in. Okay so now I
wanna keep doing this and the other
thing that I have to do in this trick is
make sure that I do it the right number
of times. I just needed to make sure to
do this six times, okay? I prepared the
trick that way, I need to do it six times.
Now the nice thing is that we can just
do everything at a time; so this one is
gonna go straight here, this card for
example it keeps going like this.
Seven goes like this;
this one is easier.
I keep thinking I should make a- make a
carpet out of this or something like
that. - (The perfect shuffle carpet.)
The perfect shuffle carpet, exactly.
So now I'm gonna make sure to do it also
with the cards, so we already did two
perfect shuffles and now I'm gonna do four more.
Okay so here's one, okay, here's another
one two...four.
So the Joker is supposed to be on top,
that's not too hard I must have gotten
that right - there's the joker, okay? Now
let's follow the path of the 1, okay so
the one started on top, and then it it
went over here, and then down here, and
and then all the way down here,
over here;
and according to this the 1 went all the way down
and then went back up. So if I did this
right then this should be the number 1,
the ace. Let's follow the 2; so the 2
started up here, then it came down here,
maybe you'll start seeing what that's going
to happen, right? So the card 2, it went
all the way down and then it ended up in
the next position so again if I did this
right it should be the number 2. I mean,
one thing you'll notice here actually is
that if you follow the path of the 1 and the 2
they're very similar to each other; and
you might think that's always gonna
happen but it actually turns out that's
not what's gonna happen. So if you look
at the 3, comes down here and then it
goes back up. See it keeps bouncing up
and down? - (Kind of oscillate a bit didn't it?)
Yeah so it has a very different
behavior but the outcome is the same
that, you know, the 3 jumps down, up,
down, up, down, up; and it also lands in the
correct position. So again if I did this
correctly it should be right there. Follow
the 4, real quick, and it lands over
here, okay, so card number 4 ends in
position number four. And so again if I did
this right it should be right there, okay?
And I could keep doing this but I can
also take advantage of what I notice at
the beginning that there's this
symmetry actually, this picture is the
same upside down. And that means that if
the cards 1, 2, 3 and 4 ended
up in the right position then so should
the other ones, right? You know there's a 5,
there's the 6, there's the 7,
there's the 8, there's the 9. So
you see what I'm doing is not any kind
of feat of memory or anything like this,
it's actually very simple;
I just shuffled carefully in a way that
when I'm done doing six perfect shuffles
the cards are back in the order where
they started. We went like this and then
you took- you took this one out and then
I knew that I just needed to count from
here. Joker, 1, 2, 3 and whatever
the missing one is the 4. That's the trick.
[Extras] Okay that's the trick and, you know, I
like it I think it's surprising;
especially because I mean there's a lot
of possible combinations in in a deck of
cards and it's surprising that it comes
back so quickly. And actually after after
I realized this I thought, well, why does
it come back so quickly? Only- it's only
in six steps. And so I thought about this
a little bit harder and I found an even
better explanation for what's going on.