Can you solve the pirate riddle

你能解決海盜之謎嗎

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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.

今天海盜們的幸運日。

阿馬羅和他的四個好伙伴，

巴特、夏洛蒂、丹尼爾和伊萊莎

發(fā)現(xiàn)了寶藏：

一個裝滿了100個金幣的寶箱。

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.

現(xiàn)在他們必須根據海盜規(guī)定 將戰(zhàn)利品均分。

阿馬羅作為船長， 由他提出分配方案。

包括阿馬羅在內的每個海盜，都需要投票同意或反對。

如果贊成數(shù)過半或平票， 金幣就會按照此種方法進行分配。

但如果多數(shù)人投反對票，

阿馬羅必須跳海，

巴特就會成為新船長。

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，

包括巴特在內的全體海盜繼續(xù)投票。

如果方案被否決， 巴特也需要跳海。

夏洛蒂會成為船長。

這個步驟一直重復下去，直到提議通過，或只剩下一個海盜，否則船長之位還會傳給丹尼爾，然后是伊萊莎。

?

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

毫無疑問，每個海盜都不想死，?同時盡可能獲得最多金幣

但身為海盜，他們并不信任彼此，

因此他們不會事先結盟合作。

同時作為殘忍的海盜，他們認為：如果自己不管怎樣 都會得到相同的金幣，

他們也會投反對票讓船長跳海， 只是為了找樂子。

最后，每個海盜都善于邏輯推理，

并且清楚其他海盜也如此。

阿馬羅應當提出何種方案以確?；蠲兀?/p>

如果你想自己思考，請在此暫停一會兒

倒計時：3

倒計時：2

倒計時：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.

根據我們的直覺來看，

似乎阿馬羅應該用 最多的金幣賄賂其他海盜這樣才能提高方案通過的幾率。

事實上存在更好的方案。為什么？

如我們之前所說，海盜們知道彼此擅長邏輯。

因此當每個人進行投票時， 他們不僅思考當下的方案，

也要考慮所有可能方案的結果。

由于人員排序是提前確定的，

每個人都可以預測其他人的投票，

并因此做出調整。

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.

因為伊萊莎排在最后一位， 她需要考慮的結果最多，

我們從她的思路入手。

她可以通過最后一種情況，即只剩下她和丹尼爾，進行反向思考。

丹尼爾很可能會提議他獲得全部金幣，

而伊萊莎只有一票，無法勝出，

因此伊萊莎要盡可能避免這種情況。

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.

現(xiàn)在我們再退回到前一次投票，

即剩下三個海盜，且由夏洛蒂提出方案。

每個人都清楚，如果她的提議被否決， 決定權就會到丹尼爾手上，

而丹尼爾會保留全部金幣，伊萊莎一無所獲。

為了保住伊萊莎的選票，

夏洛蒂只需要給伊萊莎一個金幣。

因為這樣就能夠確保伊萊莎的支持票，

所以夏洛蒂不需要給丹尼爾任何金幣。

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.

有四名海盜時情況又會怎樣呢？

作為船長，巴特需要額外一張支持票確保方案通過。

他清楚丹尼爾不會想要讓夏洛蒂做船長，

因此，他需要給丹尼爾一個金幣，

不給夏洛蒂和伊萊莎任何金幣。

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.

現(xiàn)在我們再回到一開始的場景，

五名海盜都在場。

考慮到了所有的情況后，阿馬羅知道，如果他的提議被否決，

決定權就會轉移給巴特，

這對于夏洛蒂和伊萊莎來說將是個壞事。

因此他可以給夏洛蒂和伊萊莎每人一個金幣， 而自己保留98個金幣。

巴特和丹尼爾會投票反對，

但夏洛蒂和伊萊莎只能不情愿地投票同意，

因為她們清楚其他情況會更惡劣。

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.

海盜游戲包含了博弈論中一些有趣的概念。

其中一個概念是公共知識，

即每個人都清楚其他人也知道某信息，

并以此進行推斷。

海盜們最后形成的分配稱為納什均衡，

每個海盜都清楚其他海盜的策略，

并以此選擇自己的方案。

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.

雖然這樣做的結果對每個人來說都比相互合作更差，

但沒有參與者會通過改變策略而獲益。

似乎阿馬羅可以保留大部分金幣，

而其他海盜則需要尋找更好的途徑去運用自己高超的邏輯能力，

比如修改這荒謬的海盜規(guī)定。