Hi there, everyone.
Now I've got a video coming up, probably next week, in
which I wanted a short clip of a Yahtzee being rolled.
A Yahtzee is when you roll five dice and they all come up
with the same number.
So it could be five ones, five fours, five sixes.
You get the idea.
Now, I know there are lots of ways I could cheat, and I
don't really have to film it, but I've got the
idea in my head now.
So I've set everything up here, and what I'm going to do
is I'm going to keep rolling these dice
until I roll a Yahtzee.
I've actually got my old counting machine here, and I'm
going to use that to count up the numbers.
I've got a few cameras here, so hopefully when the golden
moment arrives, I'll have some footage of it.
So I'll get these cameras rolling.
And let's see how many rolls it takes me.
So there's one thing that's pretty obvious.
And that's just the straight probability.
Let's quickly talk about that.
I'm rolling five dice.
When the first one comes out, that can be a one, two, three,
four, five, or six.
It doesn't really matter.
I've decided any combination is going to be fine.
So the probability of that first one's irrelevant.
But the second dice has to match.
So it's a one in six.
Then the next one has to match.
The next one, and the next one.
All one in six.
Multiply them all together.
And we've got a one in 1,296 chance of
me rolling a Yahtzee.
That's what I'm up against.
Let's give it a go.
[DICE ROLLING]
[CLASSICAL MUSIC PLAYING]
Do you know what's funny?
Part of me was convinced that I'd get it really early.
That it wouldn't take as long as it should really take.
I guess that's why casinos make so much money.
[DICE ROLLING]
People always think they're going to beat the odds.
[CLASSICAL MUSIC PLAYING]
It's a funny thing because each time I roll, I know I am
getting closer to the finish.
Because I am getting closer to the point where
it's going to happen.
But I have the same chance each roll.
It's not like the probability is getting better.
The dice don't have memory.
[CLASSICAL MUSIC PLAYING]
So that's 50 rolls.
Now I have spoken to some of the maths guys about all this
and asked them about what my probabilities are.
And I was told there's a 63% chance that I'll do it within
that 1,296 rolls.
That also means there's a 37% chance that I'll get to 1,296
and I still won't have rolled a Yahtzee.
[CLASSICAL MUSIC PLAYING]
There was another number I was given.
And that is to have a 90% chance of rolling a Yahtzee, I
would have to do 2,920 rolls.
I'm on 160.
[CLASSICAL MUSIC PLAYING]
I know I'm supposed to be a numbers man, but it just seems
counter-intuitive.
This is so difficult.
[CLASSICAL MUSIC PLAYING]
We will be going into probability a lot more on
Numberphile, I think, in the second half of the year.
So don't treat this as some authoritative video about
probability.
It really is just me rolling dice because I
want that one shot.
[DICE ROLLING]
Of course in the real game of Yahtzee you don't have to
throw an exact Yahtzee.
You get three throws.
And you can keep dice you want to keep in the playing area.
I think the probability of getting a Yahtzee that way
drops to something like about 4%.
Or should I say, increases to 4%.
Not really sure what I should say.
[DICE ROLLING]
[CLASSICAL MUSIC PLAYING]
That battery's gone.
So it's time for a camera change.
[DICE ROLLING]
[CLASSICAL MUSIC PLAYING]
If anyone wants to email me legitimate footage of them
throwing a Yahtzee, I will also use that in my video and
be quietly impressed.
There's the email address.
[DICE ROLLING]
[CLASSICAL MUSIC PLAYING]
So I've reached that point now where I no longer even think
I'm going to roll one.
That kind of hopefulness is gone.
That optimism.
Now I'm just facing the reality of probability.
[DICE ROLLING]
[CLASSICAL MUSIC PLAYING]
[DICE ROLLING]
I have done it.
This tape's about to end, but I've done it.
I have rolled a Yahtzee.
There we go.
Five threes, it was.
And it took me 627 rolls, so I came in--
well, I came in a lot quicker than I probably should have.
So maybe I am lucky after all.
[CLASSICAL MUSIC PLAYING]
Cheers.