Name: ペニーのゲーム - 番号マニア (Penney's Game - Numberphile)
Uploaded: 2021-01-14T10:46:49.000Z
Duration: 9 min 2 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

法助動詞 A2

I'm gonna show you a little bit of a scam, or a trick, that you can try out on people.

to 不定詞

So, what I'm going to ask you to do, is to pick a sequence of three coin tosses.

So, you know, heads-tails-heads, or tails-tails-tails.

Okay. So, Brady's picking tails-tails-heads.

And the game is: we're gonna toss this coin and see who gets that first.

So, let's see who wins. We'll do a best of 5.

let's try game Number 1. All right, here we go.

All right, let's write down this sequence.

Okay, that's pretty good actually; that's good for me.

Yeah, it's good for me, not good for you.

We might have to do a different video about how many heads we can get in a row.

Brady: "In fact, I'm definitely gonna win this next one"

Brady does win that, he had to win that after all those tails coming up. Okay,

Brady: "So, It is bad to choose any two consecutives as you start."

Ahhh cmon cmon cmon you can still win this

Brady: "So, what would you have done if I had not been stupid and not given consecutives as my..."

I can pick a sequence that is more likely to appear before yours.

Brady: "What if I pick the most likely of them all?"

Exactly, what if you pick the most likely of them all?

It goes round in a circle like rock, paper, scissors

Let's say that Brady picks whatever sequence he does pick

I'm going to show you what sequence I should pick so that I can beat him.

Right, or at least with a better chance of beating him.

I'm going to show you the cycle of winning. Let's do that.

Right. So let's say Brady picks heads-heads-heads, right? Three heads in a row.

Then what I should pick is tail-heads-heads.

And tail-heads-heads will beat heads-heads-heads.

then I should pick heads-tails-tails, that will beat Brady.

Incidentally, if he had picked, instead, tails-heads-tails,

you pick this one here, tails-tails-heads. So it's not quite a circle, this.

It has some spikes coming off the side of it.

If Brady had picked tails-tails-tails, you want to choose heads-tails-tails.

then the best choice is heads-heads-tails.

If you had picked heads-tails-heads, I would again pick heads-heads-tails.

If you had chosen heads-heads-tails, Brady, I would have picked tails-heads-heads.

So we have this little circle, but you can see the spikes coming off it as well.

So to read this, Brady's choice would be here, at the pointy end of the arrow.

My choice, the better choice, would be here, so the arrow going towards Brady's choice there.

There is a way to help you to remember this cycle.

The way you do it is, when your opponent picks a sequence, let's say, tails-heads-heads,

what you should do is, in your mind, copy the middle one, so make a copy of that coin,

so I've got another heads there, I'm gonna put it at the front, and flip it over.

So it would become a tails. And then my choice would be tails-tails-heads.

That little way of remembering it is better than just remembering that cycle.

And that will work. That's your best choice to go for.

I should show you the probabilities for each choice.

If Brady picked heads-heads-heads, I would pick tails-heads-heads.

And the chance of beating you is actually pretty good. It's seven eighths. I can tell you that's round about 87.5 percent.

So it's really likely. I'm really likely to win the game.

That's why I did best of five, though, just in case probability let me down.

This probability here, if I wanted to work tails-heads-heads beating heads-heads-tails,

that happens with a chance of three quarters, so it's about 75 percent,

If you wanted to do this one here, heads-heads-tails beating heads-tails-heads,

that happens with a chance of two thirds, so that's, what's that, about 67 percent.

And then, actually the others are similar.

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ペニーのゲーム - 番号マニア (Penney's Game - Numberphile)

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