hello everyone now today we've got a
very special guest with us and we've got
things bigger holter now David will you
for the benefit are people you watch we
touch the full title of your job here
I am the Winton professor of the public
understanding of risk in the University
of Cambridge okay so try and imagine
getting that onto a business card okay
now this is going to be one of the most
highly qualified videos ever seen on
YouTube with the two of us here now we
are going to teach you a new game today
this game will it'll help you beat your
friends and then we're going to help you
beat them again and then finally I'm
going to teach you a brand new game a
game that I've invented which will help
you beat two of your friends at the same
time
now David I've got three colors dice
here three didn't dice
they're not like regular dice so we
haven't got the regular numbers on them
so if for example this one here has a
threes and sixes on it
this this has twos and fives and this
has got ones and four so they're not
regular long will die so first of all I
want you to pick one of these - take a
look at them how you think carefully
pick a good dice for you I will have the
other one okay a yellow one for David
and what I'm going to do is I'm going to
pick the red dice now we can get rid of
this one because we don't need it for
now so I'll get rid of that and what
we're going to do is we're going to play
ten games we're going to roll the dice
ten times and whoever gets the highest
number wins that's the idea it's best of
ten you can score most out of ten volts
so here we go is game the move by all
right I've got a three zone thing
giggling - - I got three so we're even
students five five Seletar david
schwimmer head - two three again we're
even so - I put a three song head mouse
five five a three over battle off five
five three days boom head two to three
years because he's coming down to the
water
so three for me sharp up ahead by five
or six if I'm right by ten rolls which
means I won ah-ha-ha-ha-ha right so what
David didn't know of course what you
didn't know is that whatever dice David
picks I can always pick a dice with a
better chance of beating yours
as we have seen the red dice will beat
the other dice in the manga the yellow
dice in fact beats the green does so you
might expect then that the red dice will
beat the green dice the red dice is the
strong one the green dice is the weak
one so we would think that the red dice
beats the green dice and if this was
true this would be called a transitive
game because the property is transferred
via the yellow dice in the middle but
this is more like rock paper scissors in
fact these go round in a circle so the
red dice beats yellow dice yellow dice
beach green dice and green dice beans
red dice and this is called a non
transitive game now like I said you can
make these for yourself I invite you to
do so but how does this work well I'm
going to pass over to David now who's
going to explain
let's just look at how we can work out
the probability of red dice beating the
yellow dice now red actually had five
faces with three on it and one face with
six women so when we throw the red
there's a five six chance was getting a
three and a 1/6 chance of u6
now when the yellow is thrown that's got
three faces with two and three faces
with five so it's a half a chance on
getting a two and a half chancellor five
and that's the same no matter what the
red was thrown and so when we look at
this combination that was red beach
yellow so that's a red-winged rare in
this case yellow will win in this case
six be two red will win in this case six
beats five so red will win against as
three possible outcomes will red will
win now what's the probability of one of
those occur well to get the probability
of a particular combination we multiply
the probabilities along the tree so the
chance of this combination is five six
times 1/2 is five twelfths chance of
that happening this one is 1/6 times 1/2
and that's a 1/12 chance that happening
down here a 1/6 times 1/2 another 12 now
so the chance of any one of these
happening is the sum of these
probabilities we add about and we get
seven plus one thing is that's bigger
than 1/2 so an average red is going to
be yellow we can do exactly the same to
show that on average yellow will be
green and then the remark rather
remarkable thing is that we can do the
same to show that on average Green will
be red
since we both know how it works we're
gonna play this again but this time
you're gonna be in charge so I'm going
to you're stooped right so well first
thing I'm going to have to do is pick
one of these colors just right so I
don't know those I'm going to pick Yeah
right yeah there's my favorite color I'm
gonna pick yeah I know the right thing
to do so I get a bit red so you're
picking red bit I'm going to switch the
rules on you right and this time what
we're going to do is we're going to play
this game with two sets with two dice if
we have two dice the incredible thing is
that the order of the chain which we saw
before where the red dice beats the
yellow dice the L dice which the green
dice the green dice needs the red dice
that chain actually flips the order of
the Lea chain flips around so now the
red dice beats the green dice the green
dice beats the yellow dice and the
yellow dice beats the red - that's the
amazing thing
now this isn't always true this is true
for all sets of non-transitive dice it's
true for this set and here's another set
you can buy these on the internet for
these this is a set of four non trusted
- the called Efron dice they're named
after the statistician Brad Ephram and
this will work again in a chain in the
same sort of way that we saw before I'll
put up the instructions on the screen
but this would not flip with two sets of
- you have to be careful about this what
we're going to show you next is a new
game that I've invented which will mean
that you can beat two players at the
same time
so I'm quite excited by this because
this is going to be an exclusive okay so
this is the world premiere these are a
set of five non-transitive dice here
I've colored them in the sort of colors
of the rainbow so we've got Richard of
York gave battle in Wayne so we've got
the colours of the rainbow and as
traditional here we've got the red dice
peach yellow yellow beets green green
bees blue blue beets white and in the
white beets
red in in a big circle the sort of thing
we've seen before but in fact there's
actually a second chain inside this
because at the same time red beets green
green beets white white beets yellow and
yellow beets blue and then blue beet red
against a lower two chains in this game
but and this is the excitement now this
isn't always true and I had to pick my
dice carefully when I made these but
with two sets of dice we've seen the
idea that the chain flips we've seen
this sort of thing already well in this
case the first chain stays the same so
for two sets of dice red beads yellow
beets green beans blue beads white beads
red again that's the same as before but
the second chain Phillips the second
chain now flips so now we have red beets
blue blue beads yellow yellow beets
white white beads green and green beets
red so the idea with this then this
should mean that you can play this game
with two of your friends they can pick
any color that they want and you should
be able to pick a color that will beat
or have a better chance of beating both
them if you get to pick the rules of the
game by the rules of the game I mean if
you can pick if you're paying a one dice
version of the game or a two dice
version of the game
so for this David has invited along a
friend of his at David who assists oh
this is the Cambridge professor of
pathology right okay so we've got three
players now now first of all this is how
it's going to work these are my two
Stooges they are going to pick a dutch
for themselves so you're going to pick a
comma so if little David which club
would you I will choose yellow and
professor
Oh green Bruce message he picks green so
in this case what I'm going to do is I'm
going to pick the red dice now in this
case if I just pick the red dice and a
single dice version of the game I should
expect to beat both professors here I
should beat them both at the same time
and but let's say you pick something
else perhaps you don't pick that so what
would you pick this time uh well I'm
going to choose a white this time and
green again green green green in for the
professor and I'm going to pick in this
case I'm going to pick yellow but I'm
going to pick the two dice version of
the game and in this case now I should
have a better chance of beating both
place so do try them out do you make
them at post any successes or failures
on my comments and until next time if
you have been thanks for watching