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海盗谜题

Can you solve the pirate riddle? - Alex Gendler

对海盗来说 今天是个好日子
It’s a good day to be a pirate.
Amaro和他的4个同伴Bart Charlotte
Amaro and his four mateys, Bart, Charlotte,
Daniel和Eliza找到了财宝:
Daniel, and Eliza have struck gold:
一个装有100金币的箱子
a chest with 100 coins.
但是现在 他们必须根据海盗法典进行分赃
But now, they must divvy up the booty according to the pirate code.
作为船长 Amaro要提出分配金币的方案
As captain, Amaro gets to proposehow to distribute the coins.
然后每个海盗 包括Amaro自己
Then, each pirate, including Amaro himself,
要投票决定支持与否
gets to vote either yarr or nay.
如果投票通过 或打成平局
If the vote passes, or if there’s a tie,
那么金币按照计划分配
the coins are divided according to plan.
但是如果大部分否决
But if the majority votes nay,
Amaro就必须走跳板
Amaro must walk the plank
并且Bart成为船长
and Bart becomes captain.
然后Bart要提出一个新的分配方案
Then, Bart gets to propose a new distribution
剩下的所有海盗再次投票
and all remaining pirates vote again.
如果他的计划被否决 那么他也要走跳板
If his plan is rejected,he walks the plank, too,
Chartlotte取代他的位置
and Charlotte takes his place.
这样的过程以此类推
This process repeats,
船长的帽子传给Daniel然后是Eliza
with the captain’s hat moving to Daniel and then Eliza
直到其中一个方案被采纳或是只剩下一个海盗
until either a proposal is accepted or there’s only one pirate left.
当然 每个海盗都想活着
Naturally, each pirate wants to stay alive
也想尽可能得到更多的金子
while getting as much gold as possible.
但是身为海盗 他们互不信任
But being pirates,none of them trust each other,
所以他们不能事先合作
so they can’t collaborate in advance.
身为嗜血的海盗
And being blood-thirsty pirates,
如果有人认为他们能通过其它分配方式
if anyone thinks they’ll end up with the same amount
获得相同数量的金子时
of gold either way,
他们会闹着玩地投票让船长走跳板
they’ll vote to make the captain walk the plank just for fun.
最后 每个海盗都有卓越的逻辑推理能力
Finally, each pirate is excellentat logical deduction
并且知道其他人也是如此
and knows that the others are, too.
那Amaro应该怎么分配才能保证自己活下去?
What distribution should Amaropropose to make sure he lives?
如果想自己解决这个问题 请在这里暂停
Pause here if you want to figureit out for yourself!
答案揭晓倒计时3
Answer in: 3
2
Answer in: 2
1
Answer in: 1
如果我们跟随直觉
If we follow our intuition,
那么看起来Amaro应该试着以大量的金子
it seems like Amaro should try to bribe the other pirates
贿赂其他海盗
with most of the gold
来增加他的计划被采纳的可能性
to increase the chances of his plan being accepted.
但是结果是 他可以做得更好
But it turns out he can do much better than that.
为什么?
Why?
正如我们说的 海盗们都知道对方是逻辑高手
Like we said, the pirates all know each other to be top-notch logicians.
所以当每个人投票时
So when each votes,
他们所思考的不只是当前的提案
they won’t just be thinking about the current proposal,
而且还有接下来所有可能的结果
but about all possible outcomesdown the line.
因为排名次序事先知道
And because the rank order is knownin advance,
每个人可以准确预测出
each can accurately predict how the
其他人在任何情况下的投票
others would vote in any situation
然后相对应地调整他们自己的投票
and adjust their own votes accordingly.
因为Eliza排最后 她需要考虑的结果是最多的
Because Eliza’s last, she has the mostoutcomes to consider,
所以我们从她的思考过程开始入手
so let’s start by followingher thought process.
她会从最后可能的情况开始反推
She’d reason this out by working backwards
来缕清头绪
from the last possible scenario
也就是只剩下她和Daniel的时候
with only her and Daniel remaining.
Daniel很显然会打算拿走所有的金子
Daniel would obviously proposeto keep all the gold
而Eliza的一票不足以推翻他
and Eliza’s one vote would not beenough to override him,
所以Eliza会不惜任何代价阻止这种情况发生
so Eliza wants to avoid this situationat all costs.
现在我们来看这之前的决定点
Now we move to the previous decision point
也就是剩下三个海盗 由Charlotte提出方案
with three pirates leftand Charlotte making the proposal.
每个人都知道如果她被多票否决 决定权就到了Daniel手上
Everyone knows that if she’s outvoted,the decision moves to Daniel,
那么他将得到所有的金子而Eliza什么都得不到
who will then get all the goldwhile Eliza gets nothing.
所以为了得到Eliza的投票
So to secure Eliza’s vote,
Charlotte只需给她比零多一点的报酬:一个金币
Charlotte only needs to offer her slightly more than nothing, one coin.
就可以保证得到她的支持
Since this ensures her support,
Charlotte不需要给Daniel任何金子
Charlotte doesn’t need to offer Daniel anything at all.
那如果是4个海盗呢?
What if there are four pirates?
作为船长 Bart还需要一票支持
As captain, Bart would still only need one other vote
来通过他的计划
for his plan to pass.
他知道Daniel不想让
He knows that Daniel wouldn’t
决定权到Charlotte的手里
want the decision to pass to Charlotte,
所以他会给Daniel提供一个金币让他支持自己
so he would offer Daniel one coinfor his support
这样就不用给Charlotte和Eliza分配任何金子
with nothing for Charlotte or Eliza.
现在我们回到最初 即有5个海盗投票的情况
Now we’re back at the initial vote with all five pirates standing.
思考了所有其它的情况后
Having considered all the other scenarios,
Amaro知道如果自己跳船
Amaro knows that if he goes overboard,
决定权落到Bart手里
the decision comes down to Bart,
这对于Charlotte和Eliza来说是不妙的
which would be bad news for Charlotte and Eliza.
所以他给他们每人一个金币 剩下的98给自己
So he offers them one coin each,keeping 98 for himself.
Bart和Daniel反对
Bart and Daniel vote nay,
但是Charlotte和Eliza勉强地支持
but Charlotte and Eliza grudgingly vote yarr
因为他们知道其它方案对他们更不利
knowing that the alternativewould be worse for them.
海盗游戏涉及到了一些来自游戏理论的有趣概念
The pirate game involves some interestingconcepts from game theory.
一个是共有知识的概念
One is the concept of common knowledge
也就是每个人都知道其他人知道什么
where each person is aware of whatthe others know
并且利用它来预测他们的推理
and uses this to predict their reasoning.
最终的分配方案是纳什均衡的一个例子
And the final distribution is an exampleof a Nash equilibrium
即每个玩家都知道其他玩家的策略
where each player knows every otherplayers’ strategy
并相应地选择他们自己的策略
and chooses theirs accordingly.
即使它相比合作会给每个人带来更差的结果
Even though it may lead to a worseoutcome for everyone
但没有个体玩家可以通过改变他们的策略而获利
than cooperating would, no individual player can benefit by changing their strategy.
所以看起来
So it looks
Amaro会得到最多金子
like Amaro gets to keep most of the gold,
其他海盗可能需要把他们出色的逻辑能力
and the other pirates might needto find better ways
运用到更好的地方
to use those impressive logic skills,
比如修订这个荒唐的海盗法典
like revising this absurd pirate code.

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通过逻辑 解决看上去不太可能发生的事情

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视频来源

https://www.youtube.com/watch?v=Mc6VA7Q1vXQ

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