Placeholder Image

Subtitles section Play video

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

It's a good day to be a pirate.

Subtitles and vocabulary

Click the word to look it up Click the word to find further inforamtion about it

B1 US TED-Ed eliza charlotte pirate daniel bart

【TED-Ed】Can you solve the pirate riddle? - Alex Gendler

  • 353 39
    Steven Wu posted on 2017/05/02
Video vocabulary

Keywords

individual

US /ˌɪndəˈvɪdʒuəl/

UK /ˌɪndɪˈvɪdʒuəl/

  • adjective
  • Made for use by one single person
  • Relating to, or characteristic of, a single person or thing.
  • Single; separate.
  • Having a striking or unusual character; original.
  • Made for or relating to a single person or thing.
  • Having a distinct manner different from others
  • Relating to, or characteristic of, a single person or thing.
  • Single; separate.
  • Having a striking personal quality or style.
  • noun
  • Single person, looked at separately from others
  • A particular person or thing distinguished from others of the same kind.
  • A person, especially one of specified character.
  • A person, especially one of a specified kind.
  • A single thing or item, especially when part of a set or group.
  • A single human being as distinct from a group.
  • A competition for single people.
scenario

US /səˈner.i.oʊ/

UK /sɪˈnɑː.ri.əʊ/

  • noun
  • An imagined sequence of events in a plan/project
process

US /ˈprɑsˌɛs, ˈproˌsɛs/

UK /prə'ses/

  • verb
  • To organize and use data in a computer
  • To deal with official forms in the way required
  • To prepare by treating something in a certain way
  • To adopt a set of actions that produce a result
  • To convert by putting something through a machine
  • noun
  • A series of actions or steps taken in order to achieve a particular end.
  • A summons or writ to appear in court or before a judicial officer.
  • A systematic series of actions directed to some end
  • Dealing with official forms in the way required
  • Set of changes that occur slowly and naturally
  • A series of actions or steps taken in order to achieve a particular end.
  • other
  • To perform a series of operations on (data) by a computer.
  • To deal with (something) according to a particular procedure.
  • Deal with (something) according to a set procedure.
  • To perform a series of mechanical or chemical operations on (something) in order to change or preserve it.
  • To perform a series of mechanical or chemical operations on (something) in order to change or preserve it.
  • Take (something) into the mind and understand it fully.
  • other
  • Deal with (something, especially unpleasant or difficult) psychologically in order to come to terms with it.
figure

US /ˈfɪɡjɚ/

UK /ˈfiɡə/

  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand or solve something.
  • To understand after thinking; work out
  • other
  • To consider, believe, or conclude.
  • To calculate or work out (a sum or amount).
  • noun
  • Your body shape
  • Numbers in a calculation
  • A diagram or illustrative drawing in a book or magazine.
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • A set pattern of movements in ice skating.
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • A person, especially one who is important or well-known.
  • A numerical amount or value expressed in numbers.
  • A statue or other representation of a person or animal.
  • An outline or shape, especially of a person or animal.
  • other
  • To conclude or expect; think.
situation

US /ˌsɪtʃuˈeʃən/

UK /ˌsɪtʃuˈeɪʃn/

  • noun
  • Place, position or area that something is in
  • An unexpected problem or difficulty
concept

US /ˈkɑnˌsɛpt/

UK /'kɒnsept/

  • noun
  • Abstract idea of something or how it works
  • A plan or intention; a conception.
  • An abstract idea; a general notion.
  • An understanding or grasp of something.
strategy

US /ˈstrætədʒi/

UK /'strætədʒɪ/

  • noun
  • Careful plan or method for achieving a goal
  • A plan of action designed to achieve a long-term or overall aim.
  • other
  • Branch of military dealing with command
majority

US /məˈdʒɔrɪti, -ˈdʒɑr-/

UK /mə'dʒɒrətɪ/

  • noun
  • Amount that is more than half of a group
  • The age at which a person is legally considered an adult.
  • The age at which a person is legally considered an adult.
  • The number by which votes cast for one candidate exceeds those for another.
  • The greater number; more than half of a total group or amount.
  • The excess of votes for one party or candidate over those for all others combined.
slightly

US /ˈslaɪtli/

UK /ˈslaɪtli/

  • adverb
  • Only a little
alternative

US /ɔlˈtɚnətɪv, æl-/

UK /ɔ:lˈtɜ:nətɪv/

  • adjective
  • A different choice
  • noun
  • Something different you can choose