Can you solve the pirate riddle

你能解决海盗之谜吗

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It's a good day to be a pirate.

Amaro and his four mateys,

Bart, Charlotte, Daniel, and Eliza

have struck gold:

a chest with 100 coins.

今天海盗们的幸运日。

阿马罗和他的四个好伙伴，

巴特、夏洛蒂、丹尼尔和伊莱莎

发现了宝藏：

一个装满了100个金币的宝箱。

But now, they must divvy up the booty according to the pirate code.

As captain, Amaro gets to propose how to distribute the coins.

Then, each pirate,  including Amaro himself,

gets to vote either yarr or nay.

If the vote passes, or if there's a tie, the coins are divided according to plan.

But if the majority votes nay,

Amaro must walk the plank

and Bart becomes captain.

现在他们必须根据海盗规定 将战利品均分。

阿马罗作为船长， 由他提出分配方案。

包括阿马罗在内的每个海盗，都需要投票同意或反对。

如果赞成数过半或平票， 金币就会按照此种方法进行分配。

但如果多数人投反对票，

阿马罗必须跳海，

巴特就会成为新船长。

Then, Bart gets to propose a new distribution

and all remaining pirates vote again.

If his plan is rejected, he walks the plank, too,

and Charlotte takes his place.

This process repeats, with the captain's hat moving to Daniel and then Eliza until either a proposal is accepted or there's only one pirate left.

巴特再次提出新方案，

包括巴特在内的全体海盗继续投票。

如果方案被否决， 巴特也需要跳海。

夏洛蒂会成为船长。

这个步骤一直重复下去，直到提议通过，或只剩下一个海盗，否则船长之位还会传给丹尼尔，然后是伊莱莎。

 

Naturally, each pirate wants to stay alive while getting as much gold as possible.

But being pirates,  none of them trust each other,

so they can't collaborate in advance.

And being blood-thirsty pirates,

if anyone thinks they'll end up with the same amount of gold either way,

they'll vote to make the captain walk the plank just for fun.

Finally, each pirate is excellent at logical deduction

and knows that the others are, too.

What distribution should Amaro propose to make sure he lives?

Pause here if you want to figure it out for yourself!

Answer in: 3

Answer in: 2

Answer in: 1

毫无疑问，每个海盗都不想死， 同时尽可能获得最多金币

但身为海盗，他们并不信任彼此，

因此他们不会事先结盟合作。

同时作为残忍的海盗，他们认为：如果自己不管怎样 都会得到相同的金币，

他们也会投反对票让船长跳海， 只是为了找乐子。

最后，每个海盗都善于逻辑推理，

并且清楚其他海盗也如此。

阿马罗应当提出何种方案以确保活命呢？

如果你想自己思考，请在此暂停一会儿

倒计时：3

倒计时：2

倒计时：1

If we follow our intuition,

it seems like Amaro should try to bribe the other pirates with most of the gold to increase the chances of his plan being accepted.

But it turns out he can do much better than that. Why?

Like we said, the pirates all know each other to be top-notch logicians.

So when each votes, they won't just be thinking about the current proposal,

but about all possible outcomes down the line.

And because the rank order is known in advance,

each can accurately predict how the others would vote in any situation

and adjust their own votes accordingly.

根据我们的直觉来看，

似乎阿马罗应该用 最多的金币贿赂其他海盗这样才能提高方案通过的几率。

事实上存在更好的方案。为什么？

如我们之前所说，海盗们知道彼此擅长逻辑。

因此当每个人进行投票时， 他们不仅思考当下的方案，

也要考虑所有可能方案的结果。

由于人员排序是提前确定的，

每个人都可以预测其他人的投票，

并因此做出调整。

Because Eliza's last, she has the most outcomes to consider,

so let's start by following  her thought process.

She'd reason this out by working backwards from the last possible scenario with only her and Daniel remaining.

Daniel would obviously propose to keep all the gold

and Eliza's one vote would not be enough to override him,

so Eliza wants to avoid this situation at all costs.

因为伊莱莎排在最后一位， 她需要考虑的结果最多，

我们从她的思路入手。

她可以通过最后一种情况，即只剩下她和丹尼尔，进行反向思考。

丹尼尔很可能会提议他获得全部金币，

而伊莱莎只有一票，无法胜出，

因此伊莱莎要尽可能避免这种情况。

Now we move to the previous decision point

with three pirates left  and Charlotte making the proposal.

Everyone knows that if she's outvoted, the decision moves to Daniel,

who will then get all the gold while Eliza gets nothing.

So to secure Eliza's vote,

Charlotte only needs to offer her slightly more than nothing, one coin.

Since this ensures her support,

Charlotte doesn't need to offer Daniel anything at all.

现在我们再退回到前一次投票，

即剩下三个海盗，且由夏洛蒂提出方案。

每个人都清楚，如果她的提议被否决， 决定权就会到丹尼尔手上，

而丹尼尔会保留全部金币，伊莱莎一无所获。

为了保住伊莱莎的选票，

夏洛蒂只需要给伊莱莎一个金币。

因为这样就能够确保伊莱莎的支持票，

所以夏洛蒂不需要给丹尼尔任何金币。

What if there are four pirates?

As captain, Bart would still only need one other vote for his plan to pass.

He knows that Daniel wouldn't want  the decision to pass to Charlotte,

so he would offer Daniel one coin for his support

with nothing for Charlotte or Eliza.

有四名海盗时情况又会怎样呢？

作为船长，巴特需要额外一张支持票确保方案通过。

他清楚丹尼尔不会想要让夏洛蒂做船长，

因此，他需要给丹尼尔一个金币，

不给夏洛蒂和伊莱莎任何金币。

Now we're back at the initial vote with all five pirates standing.

Having considered all the other scenarios,

Amaro knows that if he goes overboard,

the decision comes down to Bart,

which would be bad news  for Charlotte and Eliza.

So he offers them one coin each, keeping 98 for himself.

Bart and Daniel vote nay,

but Charlotte and Eliza  grudgingly vote yarr

knowing that the alternative  would be worse for them.

现在我们再回到一开始的场景，

五名海盗都在场。

考虑到了所有的情况后，阿马罗知道，如果他的提议被否决，

决定权就会转移给巴特，

这对于夏洛蒂和伊莱莎来说将是个坏事。

因此他可以给夏洛蒂和伊莱莎每人一个金币， 而自己保留98个金币。

巴特和丹尼尔会投票反对，

但夏洛蒂和伊莱莎只能不情愿地投票同意，

因为她们清楚其他情况会更恶劣。

The pirate game involves some interesting concepts from game theory.

One is the concept of common knowledge

where each person is aware of what the others know

and uses this to predict their reasoning.

And the final distribution is an example of a Nash equilibrium

where each player knows every other players' strategy

and chooses theirs accordingly.

海盗游戏包含了博弈论中一些有趣的概念。

其中一个概念是公共知识，

即每个人都清楚其他人也知道某信息，

并以此进行推断。

海盗们最后形成的分配称为纳什均衡，

每个海盗都清楚其他海盗的策略，

并以此选择自己的方案。

Even though it may lead to a worse outcome for everyone than cooperating would,

no individual player can benefit by changing their strategy.

So it looks like Amaro gets to keep most of the gold,

and the other pirates might need to find better ways to use those impressive logic skills,

like revising this absurd pirate code.

虽然这样做的结果对每个人来说都比相互合作更差，

但没有参与者会通过改变策略而获益。

似乎阿马罗可以保留大部分金币，

而其他海盗则需要寻找更好的途径去运用自己高超的逻辑能力，

比如修改这荒谬的海盗规定。