Maybe Poseidon had one of his angry days.

也許波塞冬也有生氣的一天。

However it happened, the underworld is overcrowded,

不管發生了什麼，冥界都是人滿為患。

and Zeus has ordered Hades to let some spirits out.

宙斯已經命令哈迪斯放出一些靈魂。

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

哈迪斯將所有死者的靈魂在地獄犬面前排成一排。

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

當他的三個頭顱中的一個咬住前面的靈魂時。

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

他們會被送回活人的土地。

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

左邊的人一定要出線，永遠留在閻王殿裡。

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

而其他人也都向前洗牌，這時地獄犬會再次進食。

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

每個狗頭每次咬人的機會都是相等的。

and no two ever bite simultaneously.

而且沒有兩個人同時咬。

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

不幸的是，哈迪斯的爪牙忘了告訴你發生了什麼。

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

而當你出現的時候，只有99個靈魂在排隊。

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

冥王看起來很憤怒，引起別人的注意不會有好下場。

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

但突然間，時間凝固了，赫爾墨斯從陰影中走了出來。

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

他告訴你，他可以瞬間把你放到線。

and no one will realize what happened.

沒有人會意識到發生了什麼。

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

但他只會把他的恩典賜給足夠聰明的人。

to take full advantage of it.

以充分發揮其優勢。

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

選擇最好的地方排隊，他會給你名額。

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

選錯了，他就會讓你爛掉。

Which spot should you pick?

你該選哪個點？

Pause the video to figure it out yourself.

暫停視頻，自己想辦法。

Answer in 3

3個回答

Answer in 2

答覆2

Answer in 1

回答1

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

可以計算出自由的確切概率。

in all 100 spots.

在所有100個名額中。

But there's a much simpler path to the solution

但有一個更簡單的途徑來解決這個問題。

that requires surprisingly little calculation.

竟然不需要什麼計算。

Imagine being anywhere in line.

想象一下，在任何地方排隊。

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

前面的路上，三個頭目中的一個會隨機選人。

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

你就會向前移動1、2或3個空格。

Since each is equally likely,

既然每個人都有同樣的可能性。

your chance of survival from wherever you started

生存機會

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

是前面三個空格中每個空格的機會的平均值。

And this is where you can find a huge shortcut.

而這也是你可以找到一個巨大的捷徑。

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

平均數必須在你所做的平均數的極值上或極值之間。

they can never be higher than the highest value

它們不能高於最高值

or lower than the lowest.

或低於最低的。

So whatever your chances of survival are where you start,

所以不管你的生存機會在哪裡，你都要從這裡開始。

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

前面的三個地方，至少有一個是好的。

and probably better.

而且可能更好。

This observation is incredibly powerful.

這個觀察力非常強大。

It means that wherever you are in line,

意思是，無論你在哪裡排隊。

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

用你的位置換取你前面三個位置中的一個是明智的。

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

我們先不說是哪一個，就把他們當成一個三人組吧。

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

這個三人組的最大值比這個三人組的好，以此類推。

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

繼續往前走就能到前面... ...

These three spots must contain the extreme values—

這三個點必須包含極值--。

the best and worst probabilities—

最佳和最壞的概率-

for the entire line.

為整條線。

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

換句話說，這些都是我們需要考慮的。

Place 1 is bad.

地方1是壞的。

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

頭一個會救你，而另外兩個會讓你永遠完蛋。

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

那只是三分之一的機會，逃過一劫。

Place 2 is better: head two is great,

2號地比較好：二號頭很好。

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

第3個頭是壞的，第1個頭是好的，因為它給你另一個機會。

But place 3 is best, because head 3 saves you

但3號位是最好的，因為3號頭可以讓你省心

while heads 1 and 2 both give you extra chances.

而頭1和頭2都給你額外的機會。

If you did want to consider the exact probabilities,

如果你真的想考慮確切的概率。

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

第3名的生存機率是27人中的16人，也就是接近60%。

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

後期的點位往往非常接近有50%的生存機會。

Why 50%?

為什麼是50%？

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

因為每次地獄犬都會送一個靈魂上去重生。

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

他在冥界留下0、1、2個靈魂。

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

平均每釋放一個人，就有一個人留下來。

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

但你可以用你現在所知道的東西，輕而易舉地擊敗這些賠率。

Hermes has places to be, and so do you.

愛馬仕有地方要去，你也一樣。

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

他獎勵你的洞察力，把你偷偷送進第三名。

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

而從那裡知道你最終的命運，也只是短暫的等待。