It's a good day to be a pirate.
今天是海盗们的幸运日。
Amaro and his four mateys, Bart, Charlotte, Daniel, and Eliza have struck gold: a chest with 100 coins.
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.
现在他们必须根据海盗规定将战利品均分。
As captain, Amaro gets to propose how to distribute the coins.
阿马罗作为船长，由他提出分配方案。
Then, each pirate, including Amaro himself, gets to vote either yarr or nay.
包括阿马罗在内的每个海盗，都需要投票同意或反对。
If the vote passes, or if there's a tie, the coins are divided according to plan.
如果赞成数过半或平票，金币就会按照此种方法进行分配。
But if the majority votes nay, Amaro must walk the plank and Bart becomes captain.
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.
巴特再次提出新方案，包括巴特在内的全体海盗继续投票。
If his plan is rejected, he walks the plank, too, and Charlotte takes his place.
如果方案被否决，巴特也需要跳海，夏洛蒂会成为船长。
This process repeats, with the captain's hat moving to Daniel
这个步骤一直重复下去，船长之位还会传给丹尼尔，
and then Eliza until either a proposal is accepted or there's only one pirate left.
然后是伊莱莎，直到提议通过，或只剩下一个海盗。
Naturally, each pirate wants to stay alive while getting as much gold as possible.
毫无疑问，每个海盗都不想死，同时尽可能获得最多金币。
But being pirates, none of them trust each other, so they can't collaborate in advance.
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。
And being blood-thirsty pirates, if anyone thinks they'll end up with the same amount of gold either way,
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，
they'll vote to make the captain walk the plank just for fun.
他们也会投反对票让船长跳海，只是为了找乐子。
Finally, each pirate is excellent at logical deduction and knows that the others are, too.
最后，每个海盗都善于逻辑推理，并且清楚其他海盗也如此。
What distribution should Amaro propose to make sure he lives?
阿马罗应当提出何种方案以确保活命呢？
If we follow our intuition, it seems like Amaro should try to bribe the other pirates with most of the gold
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，
to increase the chances of his plan being accepted.
这样才能提高方案通过的几率。
But it turns out he can do much better than that. Why?
事实上存在更好的方案。为什么？
Like we said, the pirates all know each other to be top-notch logicians.
如我们之前所说，海盗们知道彼此擅长逻辑。
So when each votes, they won't just be thinking about the current proposal, but about all possible outcomes down the line.
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。
And because the rank order is known in advance,
由于人员排序是提前确定的，
each can accurately predict how the others would vote in any situation and adjust their own votes accordingly.
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.
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。
She'd reason this out by working backwards from the last possible scenario with only her and Daniel remaining.
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。

Daniel would obviously propose to keep all the gold and Eliza's one vote would not be enough to override him,
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，
so Eliza wants to avoid this situation at all costs.
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.
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。
Everyone knows that if she's outvoted,
每个人都清楚，如果她的提议被否决，
the decision moves to Daniel, who will then get all the gold while Eliza gets nothing.
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。
So to secure Eliza's vote, Charlotte only needs to offer her slightly more than nothing, one coin.
为了保住伊莱莎的选票，夏洛蒂只需要给伊莱莎一个金币。
Since this ensures her support, Charlotte doesn't need to offer Daniel anything at all.
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?
有四名海盗时情况又会怎样呢？
As captain, Bart would still only need one other vote for his plan to pass.
作为船长，巴特需要额外一张支持票确保方案通过。
He knows that Daniel wouldn't want the decision to pass to Charlotte,
他清楚丹尼尔不会想要让夏洛蒂做船长，
so he would offer Daniel one coin for his support with nothing for Charlotte or Eliza.
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.
现在我们再回到一开始的场景，五名海盗都在场。
Having considered all the other scenarios, Amaro knows that if he goes overboard,
考虑到了所有的情况后，阿马罗知道，如果他的提议被否决，
the decision comes down to Bart, which would be bad news for Charlotte and Eliza.
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。
So he offers them one coin each, keeping 98 for himself.
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。
Bart and Daniel vote nay,
巴特和丹尼尔会投票反对，
but Charlotte and Eliza grudgingly vote yarr knowing that the alternative would be worse for them.
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.
海盗游戏包含了博弈论中一些有趣的概念。
One is the concept of common knowledge where each person is aware of what the others know
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，
and uses this to predict their reasoning.
并以此进行推断。
And the final distribution is an example of a Nash equilibrium
海盗们最后形成的分配称为纳什均衡，
where each player knows every other players' strategy and chooses theirs accordingly.
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,
虽然这样做的结果对每个人来说都比相互合作更差，
no individual player can benefit by changing their strategy.
但没有参与者会通过改变策略而获益。
So it looks like Amaro gets to keep most of the gold,
似乎阿马罗可以保留大部分金币，
and the other pirates might need to find better ways to use those impressive logic skills, like revising this absurd pirate code.
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。