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Maybe the fates got clumsy. Maybe Poseidon had one of his angry days.
也许是命运的捉弄。也许是波塞冬生气的一天。
However it happened, the underworld is overcrowded, and Zeus has ordered Hades to let some spirits out.
然而事情还是发生了，地狱里的人太多了，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, they'll get returned to the land of the living.
当三头狗的其中一个头咬了它面前的亡灵的时候，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, and no two ever bite simultaneously.
三头狗的三个头咬亡灵的概率都是均等的，只有一个头能够伸出来咬亡灵。
Unfortunately, Hades' minions forgot to tell you what was happening, and by the time you show up there are only 99 souls left in line.
不幸的是，哈迪斯的仆人忘记告诉你这个规则，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. But suddenly, time freezes, and Hermes steps out of the shadows.
哈迪斯非常生气，把注意力吸引到你身上可不会有好结果。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, and no one will realize what happened.
他告诉你，他可以马上将你排入队伍里，并且没有人会发现发生了什么。
But he'll only grant his grace to someone clever enough to take full advantage of it.
但是他只把这个恩典赐予足够聪明，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. Choose wrong, and he'll leave you to rot.
只有选择了队伍中最佳的位置，他才会把这个位置给你。选择错误，你就只能等死。
It's possible to calculate the exact probability of going free in all 100 spots.
在100个位置中计算出精确的逃脱机率是有可能的。
But there's a much simpler path to the solution that requires surprisingly little calculation. Imagine being anywhere in line.
但是这里有更简单的解决方法，几乎不需要进行任何计算。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, and you'll move forward 1, 2, or 3 spaces.
在队伍的最前面，三头狗的三个头将随机地咬掉一个亡灵，你将会向前移动一个、两个，或三个位置。
Since each is equally likely, your chance of survival from wherever you started is the average of the chances from each of the three spaces in front of you.
因为每一种情况都是等概率的，所以你从起点出发的生存几率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 -- they can never be higher than the highest value or lower than the lowest.
平均数一定就是，或者在你要平均的极值之间--平均数不会高于最高值，也不会低于最低值。
So whatever your chances of survival are where you start, one of the three places in front of you is at least as good, and probably better.
所以无论在起始点你的生存的几率是多少，在你前面的三个位置，至少有一个一样好，也许更好。
This observation is incredibly powerful. It means that wherever you are in line, it'd be wise to trade your place for one of the three spots in front of you.
这一观察结果具有强大的力量。这意味着，无论你在队伍的哪个位置，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 -- this trio's maximum value is better than this trio's, and so on.
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--这三个的最高值比这三个高，以此类推。
Keep going and you'll reach the front... These three spots must contain the extreme values -- the best and worst probabilities -- for the entire line.
继续向前走，你将会来到最前面...这三个位置一定包括了整个队伍中的极值，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. Head one would save you, and the other two doom you forever. That's just a 1 in 3 chance to escape.
位置1并不好。第一个头将会拯救你，其余的两个将会让你永远消失。这里只有三分之一的机会逃离地狱。
Place 2 is better: head two is great, head 3 is bad, and head 1 is ok in that it gives you another chance.
位置2不错：第二个头很好，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 while heads 1 and 2 both give you extra chances.
但是第三个位置是最好的，因为第三个头会拯救你，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, the odds of surviving in place 3 are 16 out of 27, or close to 60%.
如果你不想去思考准确的概率。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. Why 50%?
队伍后面的位置的生存机率无限接近于50%。为什么是50%？
Because every time Cerberus sends one soul up to be reborn, he leaves 0, 1, or 2 souls in the underworld.
因为每一次三条狗都让一位亡灵复活，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. But you can beat those odds handily with what you now know.
平均下来，一个人被释放，就有一个人留下来。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. He rewards your insight by sneaking you into the third spot.
赫耳墨斯有它的位置，你也一样。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。
