Can you solve the riddle and escape Hades? - Dan Finkel

翻译人员: Peggy Chen 校对人员: Yolanda Zhang

Maybe the fates got clumsy.

也许是命运的捉弄。

Maybe Poseidon had one of his angry days.

也许是波塞冬生气的一天。

However it happened, the underworld is overcrowded,

然而事情还是发生了， 地狱里的人太多了，

and Zeus has ordered Hades to let some spirits out.

宙斯于是吩咐哈迪斯释放一些鬼神。

Hades arranges all the souls of the dead in a line before Cerberus.

哈迪斯让所有亡灵在 刻耳柏洛斯面前排成一排。

When one of his three heads bites down on the soul in front of it,

当三头狗的其中一个头 咬了它面前的亡灵的时候，

they’ll get returned to the land of the living.

这个亡灵将会回到 他们生活的土地上。

Anyone to the left must get out of line and stay in Hades forever.

任何位于左边的亡灵 都要离开队伍，永远留在地狱。

And everyone else shuffles forward, at which point Cerberus will feed again.

其他亡灵就要继续前进， 三头狗就继续吃掉面前的亡灵。

Each of the dog’s heads has an equal chance of being the one to bite each time,

三头狗的三个头 咬亡灵的概率都是均等的，

and no two ever bite simultaneously.

只有一个头能够伸出来咬亡灵。

Unfortunately, Hades’ minions forgot to tell you what was happening,

不幸的是，哈迪斯的仆人 忘记告诉你这个规则，

and by the time you show up there are only 99 souls left in line.

当你知道发生了什么的时候 队伍里只有 99 个亡灵了。

Hades looks furious and drawing attention to yourself won’t end well.

哈迪斯非常生气，把注意力 吸引到你身上可不会有好结果。

But suddenly, time freezes, and Hermes steps out of the shadows.

但是突然，时间停止了， 赫尔墨斯从影子里走出来。

He tells you he can instantly put you into the line,

他告诉你，他可以 马上将你排入队伍里，

and no one will realize what happened.

并且没有人会发现发生了什么。

But he’ll only grant his grace to someone clever enough

但是他只把这个恩典 赐予足够聪明，

to take full advantage of it.

能够充分利用这个机会的人。

Choose the best place in line and he’ll give you the spot.

只有选择了队伍中最佳的位置， 他才会把这个位置给你。

Choose wrong, and he’ll leave you to rot.

选择错误，你就只能等死。

Which spot should you pick?

【哪一个位置是你应该选择的呢？】

Pause the video to figure it out yourself.

【暂停视频，思考一下吧】

Answer in 3

【答案揭晓 3 】

Answer in 2

【答案揭晓 2 】

Answer in 1

【答案揭晓 1 】

It’s possible to calculate the exact probability of going free

在 100 个位置中 计算出精确的逃脱机率

in all 100 spots.

是有可能的。

But there’s a much simpler path to the solution

但是这里有更简单的解决方法，

that requires surprisingly little calculation.

几乎不需要进行任何计算。

Imagine being anywhere in line.

想象你在队伍中的任意一个位置。

Way up at the front, one of the three heads will pick someone at random,

在队伍的最前面，三头狗的 三个头将随机地咬掉一个亡灵，

and you’ll move forward 1, 2, or 3 spaces.

你将会向前移动一个、 两个，或三个位置。

Since each is equally likely,

因为每一种情况都是等概率的，

your chance of survival from wherever you started

所以你从起点出发的生存几率

is the average of the chances from each of the three spaces in front of you.

就是你前面三个位置的 生存几率的平均值。

And this is where you can find a huge shortcut.

也就是说，你可以从中 找到一个很大的捷径。

Averages must be on or between the extremes of what you’re averaging—

平均数一定就是，或者 在你要平均的极值之间——

they can never be higher than the highest value

平均数不会高于最高值，

or lower than the lowest.

也不会低于最低值。

So whatever your chances of survival are where you start,

所以无论在起始点 你的生存的几率是多少，

one of the three places in front of you is at least as good,

在你前面的三个位置， 至少有一个一样好，

and probably better.

也许更好。

This observation is incredibly powerful.

这一观察结果具有强大的力量。

It means that wherever you are in line,

这意味着， 无论你在队伍的哪个位置，

it’d be wise to trade your place for one of the three spots in front of you.

用你的位置去交换前面 三个位置中的一个都是明智的。

Let’s ignore which for now and think of them as a trio—

让我们先忽略要选哪个位置，然后 把这些位置以三个为一组进行思考——

this trio’s maximum value is better than this trio’s, and so on.

这三个的最高值比这三个高， 以此类推。

Keep going and you’ll reach the front...

继续向前走，你将会来到最前面......

These three spots must contain the extreme values—

这三个位置一定包括了

the best and worst probabilities—

整个队伍中的极值，

for the entire line.

即最好和最差的概率。

In other words, they’re all we need to consider.

换句话说，这些就是 我们需要思考的全部数值。

Place 1 is bad.

位置 1 并不好。

Head one would save you, and the other two doom you forever.

第一个头将会拯救你， 其余的两个将会让你永远消失。

That’s just a 1 in 3 chance to escape.

这里只有三分之一的机会逃离地狱。

Place 2 is better: head two is great,

位置 2 不错：第二个头很好，

head 3 is bad, and head 1 is ok in that it gives you another chance.

第三个头不好，第一个头一般般， 因为它会给你第二个机会。

But place 3 is best, because head 3 saves you

但是第三个位置是最好的， 因为第三个头会拯救你，

while heads 1 and 2 both give you extra chances.

而第一个头和第二个头 只给了你额外的机会。

If you did want to consider the exact probabilities,

如果你不想去思考准确的概率。

the odds of surviving in place 3 are 16 out of 27, or close to 60%.

位置 3 的生存机率是 16 / 27， 或者说接近 60%。

The spots later in line tend to be very close to having a 50% chance of survival.

队伍后面的位置的 生存机率无限接近于 50%。

Why 50%?

为什么是 50%？

Because every time Cerberus sends one soul up to be reborn,

因为每一次三条狗 都让一位亡灵复活，

he leaves 0, 1, or 2 souls in the underworld.

再让 0 个，1 个或者 2 个亡灵留在地狱。

That averages out to one person staying for each one who gets freed.

平均下来，一个人被释放， 就有一个人留下来。

But you can beat those odds handily with what you now know.

但是利用目前已知的信息， 你已经可以轻易地战胜这些机率。

Hermes has places to be, and so do you.

赫耳墨斯有它的位置， 你也一样。

He rewards your insight by sneaking you into the third spot.

他安排你前往第三个位置， 以奖励你的洞察力。

And from there it’ll be just a short wait to learn your ultimate fate.

在那里，只需要短暂的一瞬， 你就会得知自己最后的归宿。