If you could do me something, do me a favor.

So, you know, flipping a coin, heads or tails.

All right.

So I want you to be a coin flipper in your mind.

And I want you to flip a coin in your mind randomly 20 times and write down the result here, but don't show me.

Wait.

Ready for what?

You've done 20.

Okay, Now, I don't want to see, but what's gonna happen is I'm gonna try and make money off your list.

So what I'm gonna do is I'm gonna give you a bunch of pennies, and you don't have to pay me back.

They're yours.

And he's mine.

I bet to play.

And if I win, you give me that amount.

And if I lose, you keep that amount.

All right.

So I'm just gonna put a penny down one penny riding on this.

Okay, So my first prediction is that you flipped ahead.

Yes.

Yes.

So he says head.

So I'm gonna take one of your coins from your stack.

Okay.

I gave them to anyway.

So you shouldn't be too miffed.

Put another coin in.

Okay, I'm gonna predict tiles.

No.

Woo.

So you've said head.

I kind next.

I'm gonna predict tails, not tails.

Next, I'm going to predict tails, and I'm going to bet $20 that on, right?

What did you What was it?

Heads or tails?

It was tires.

You owe me 20 bucks.

Okay, so I'm just gonna put that aside, All right?

Should we keep playing?

I'm gonna bet another coin.

Just remember, you owe me 20 us.

I wanted in us, if that's okay.

Okay.

I got a better mother, but I'm gonna predict tails.

It is tails I can't tells.

It is.

All right.

So I get another coin there.

I'm gonna predict heads.

I'm going to predict tails.

Tails it is.

So that was another coin from you.

Heads?

No.

Okay, so you get to keep that tails, it's ahead.

So you get that.

Heads heads.

It is.

All right.

So I get another coin from you.

This is turning out.

All right.

Your mommy got the 22.

Give me.

Okay.

I'm gonna predict tails.

It is a tale.

So, like another coin from your heads, it is ahead.

Okay, I'm gonna predict a tale is a detail tail.

Okay, I'm gonna predict ahead.

Okay.

You get that coin, I'm gonna predict another head.

It was a head.

So I get a coin from you.

Tail was a tail.

And predict another tale.

No, it's a head.

So I'm gonna predict ahead.

Last one, Um, for 100 bucks tail?

Yeah.

It is a tale that was expensive.

You shouldn't listen to the way I said this.

You've done something fantastic for me.

You have been really bad at creating random sequences.

As I can see here, the longest run that you've had is right.

At the beginning, it was three heads, and then you've pretty much alternated between 1000 heads.

1000 heads.

The most run that you've had of tails or heads is to arrive, and you showed a pattern there.

This demonstrates something called the Gambler's Fallacy.

With gambler's fallacy.

It says that what's happened before has an impact of what will happen next.

If we were using a coin every time you flip it, there's an equal probability that even we get ahead or a tail.

Now, lot of people think Well, how does that work?

Because you know you're flipping coins.

Surely it's not very likely to have, you know, five heads and a rose six heads in a row.

But this is the nature of randomness.

Randomness is very lumpy, right?

And lumpiness means that you do get streaks, which is part of the gamblers.

Lexicon, you know, is like we have a gambling strick.

So you actually have not produced a very good random sequence.

He didn't put enough streaks in night.

This this is actually would be termed homogeneous because it's actually quite mixed the number of ways that we can have 20 heads or tails.

The number of permutations we can have is pretty big, so we can basically get ahead or a tail in each position.

And there's 20 positions.

So the total number of permutations, not combinations like fixed order, is two to the power 20.

And that turns out to be a 1,048,576 because you've done a permutation which has a maximum streak of either three heads or three tiles.

He only had one little tiny street right in the beginning was quite interesting.

That is a subset of every single permutation But this is actually representative the way you think.

And not just you, Brady.

A lot of people think exactly like you.

If they were to do random, they think mixed up right?

That's what people think.

But random isn't mixed up it.

Random is what's random.

In actual fact, it has a different nature to the idea of being mixed up, because if it was evenly mixed up, as I've just shown, I've made a lot of money off here, you end up being predictable and randomness is unpredictable.

So I've actually crunched the numbers, and I can tell you how many permutations have a maximum off three heads or three tails as a streak.

200 for 2830.

So you can see that's a much smaller number than this.

And in actual fact, it turns out to be 23.2% off all possible permutations if less than 1/4.

So, out of all the possible permutations, you can have the pool that you would choose from okay, only is, you're only getting one and four, so you can see just by that logic alone, why this before it's not random all right?

Of course, someone I wasn't consciously limiting myself to the streets.

And three, I guess my brain was somehow Well, that's a natural thing to do because we think streaks unlikely.

We tend to think very small mindedly so if you were just dealing with, say, four in a row, having foreheads or four tails in a row is actually in the minority, because there's only one way you can get four heads in a row, and only one way you can get 4000 right?

But we did 20 and so straight after you did foreheads or four taels.

Imagine if, after that you did head tails, Head tells Head tells, is a whole heap of different permutations you can get, which at the beginning have foreheads or four taels.

Now that's part of how randomness works, is the fact that sure, if you're dealing with a small sample, uh, you can expect things to be quite mixed up.

But that's because there's not many permutations.

Head, tail, head tie, hotel head, tail head is actually, you know, in the same ballpark number as big streaks.

But when you're dealing with very long streaks, then you could have head, head, head, head, head, head, head.

And then you've still got all the permutations left to go, which is still a huge number.

It's not just in that position.

You could get a streak of six heads in a row or 6000 row at any point.

And if you do that, you end up with a whole bunch of permutations, which have a streak of six heads or a streak of six tails.

I've done this with school kids plenty of times.

And what has happened in my empirical evidence, all right is that you do have kids putting in a streak of foreheads or four tails, but only once.

That led me to a maximum of one.

So I actually crunched the numbers and I wanted to work out.

If how many's how many permutations of 20 heads or tails where you had a maximum of three heads or three tiles and just one streak of four?

It's basically what you've done.

Plus, you also allow foreheads or four taels only once.

That's basically all of this, plus one streak off foreheads or four tails.

I really had to crunch the numbers for this.

I'm telling you.

So the total number is 478,000, 520 and that corresponds to 45.6% off all permutations.

It is bigger, but it's still less than half.

So this is kind of the limit of what you're normally mathematically literate.

Person thinks about randomness.

They actually over over 20 flips of heads or tails will actually cut out half of all permutations as possibilities.

Now half is pretty significant.

When we're talking about probability, right?

It's like, puff, you get, you get rounded down.

So you're telling me that over half of all the times I do this with a coin, I will have a streak of four exactly exactly or more streaks of four in a row and longer streaks.

It's because I've chosen quite a lengthy number of flips have done 20.

If what, 16.

It doesn't work.

That nature of randomness really presents itself in the length of the number of flips.

The way we can think about it is how predictable is your sequence.

Really, all you need to know is is there a way that you can write your sequence down of heads and tails.

Is there a way to do it that it's simpler?

And if there is some sort of order or patent to it, then you can actually make it simpler.

But if your sequence is actually very complicated, it's actually harder to write it any smaller than it is.

And there is a way of categorizing around them sequence by saying the easiest way to write this sequence down is just right.

The DNA sequence, which makes up me and the fabulous person you are Brady is actually a near random sequence.

Because the delay sequence contained so much information, it actually, in a way contains lots of patents.

So the way you can think of randomness is it's something that actually has patterns on patterns on patterns on patents and actually fits in very much with way gamblers think where they say, Oh, I can see a pattern here.

I can predict what's gonna happen next, but that's that's just randomness of work.

Randomness, shows, patterns.

But there's no logic to it.

It's not following rules of science or physics or anything.

It's the way randomness is.

I just wish if I just let that last one ahead over one yet if I just made the lost I have just been a streak free.

Yeah, well, because you know well, because you you proved to me that that you weren't going to do it again.

I think you started.

He started big.

This is basically you did.

This is like a Hollywood script.

You start with a big action sequence of the beginning, and then it becomes for me like video.

Thanks.

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Yeah, yes, yeah.

Where's my money?