Can you solve the pirate riddle? – Alex Gendler


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.

100 thoughts on “Can you solve the pirate riddle? – Alex Gendler

  1. split it equally and everyone says yay?

  2. There is 0 logic to that. Logic tells us that at some point, you must get some sleep, and that's when the pirates that didn't get any gold would kill the other 3 and split the gold between them… :-/

  3. And here I was thinking I was clever splitting the money with 3/5 and screwing over the other 2 😕

  4. My answer.. The pirate crew keeps all the gold. Since im the captain, youll all be charged 20 coins for using my ship…

  5. It's a great example of why it's so difficult to apply game theory outside the business school classroom. Robots would act consistent to the solution; humans would not. The captain would be killed in the real world for his 98-0-1-0-1 plan, even if John Nash correctly argues that it wouldn't be rational to reject the plan.

  6. Couldnt amaro pick the two he liked least and say that they get nothing and him and the 2 others get 33 peices? That seems like it would definently work and he still gets a decent amount

  7. TedEd : can you solve this riddle?
    TedEd explaining the riddle : And everyone is an expert in logical thinking

  8. I was mislead. under the impression that no two pirates could have the same amount 🙁

  9. Lol, that last statement. I was thinking exactly that, this pirate law is awful and needs changed. 😀

  10. charlote says nay to the first 2 then yar when shes captain. she gives no coin to the 5th guy because if she dies, the 5 th guy also gets no coins. or lets say she does give the 5 th guy 1 coin and ends up with 99. why would she vote yay for 1 coin in the first place if she can get 100 or 99 after the first 2 are dead? or did i miss something

  11. if i have to give 2 coins to charlotte and eliza, can i choose any pirate?

  12. but why at 1:07 would Elisa throw Daniel down? she would say No and Daniel Yes, is a tie.
    Indeed in the final explanation, it says that it's bad for Elisa to be left alone with Daniel.

    Clearly, the riddle description tried to avoid/lie about this, in order for the person not to think of the scenario that they are 2 left, and just says "it would go on like that until Elisa is left" which is not true and will never happen

  13. Why couldn’t they just split the gold evenly like logical pirates.

  14. Bart and Daniel vote against Amaro cuz he got all the girls

  15. Bruh if I was Daniel I would just beat up everyone and get the gold

  16. i thought they should make chits and decide who gets how much money to keep!

  17. Why they became pirates , they are so intelligent they can get a decent job…

  18. Sorry but this cannot whittle down to one pirate, you'd get two and theyd get their own way so… What is the point in the rest of this?

  19. 2:33, he votes yarr for him self, he is the dumbest Pirate in History

  20. Wait a minute. In present day terms, those coins would only be worth one dollar.

  21. Well… in 100 gold and 5 per–i mean pirates they have 20 each i think…

  22. This kinda sounds like what the government does to the citizens. Give a little and keep all the rest So with that logic the government are pirates Rrrrrr

  23. i’m nice so i would keep 50 coins and give 25 to Charlotte and 25 to Eliza uwu

  24. Wow, I got really next to solve the riddle in only two minutes.I'm soo impressed with myself!!

  25. It cant get to one pirate left cause if there was two pirates it would be a tie which means the plan is used unless both voted no but why would the pirate that proposed the plan vote against it

  26. My solution: Armaro should just murder all the other pirates and take the gold. He lives and gets all the gold. The end.

  27. If they're that good at logistical deduction then why don't they just make a living off of that instead of being pirates?

  28. Why not do a 25-25-25-25-24 so it’s 4-1 easy

  29. Pirates A to D fell off the plank
    Eliza: Plan E
    Eliza: Nay
    Eliza: Walks off plank leaving the ship empty and no one gets the booty

  30. yall…just spilt it evenly why you gotta make this hard. 20 coins for each person.

  31. Does anybody notice that at the at there names the letters are the alphabet?

  32. Hmm the one who provides the plan can vote is the things that's stingy here or else answer would be better

  33. Hmmm I wonder if this will work irl

    Wait where did all my friends go?

  34. I remember Nash making a proposal to take the friends of the main girl and make everyone in the group happy as if they fought for the main girl, there would have been only 1 winner. Go watch a beautiful mind if you still havent. Just a masterpiece film made about a masterpiece genius!!!

  35. Başlık türkçe içi niye ingilizce anlamadım. Title is Turkish but video language is English.This is a inconsistency.And riddle is absurd. All of them give equal . Ok

  36. So like, i always come back to these riddles once in a while. and i skipped ahead a bit and it said

    “And his-“

    *skip*

    “Booty”

    and i died

  37. That if we assume that everyone is going act logically , but as complicated as humans are , we may never know what the other guy is actually thinking , so the most logical option would be to let the king decide what to do with the treasure , its better than letting things out of control and never know who is going to win .

  38. If they are expert in logical deduction then why make us do it? Let them solve their own problems for god's sake!

  39. At 3:50 , but C got two nays and only one yays so? Doesn't it kill him anyway

  40. PLOT TWIST, he took so long working it out that the ship sailed into a whirpool and sunk because he wasn't steering it.

  41. Actually i guess there is a mistake at 1:06
    Daniel cant go off the plank , if only him and eliza are left , whatever his plan is , even if eliza votes nay , there will be a tie which means daniel’s plan gets applied

  42. How girls Can satisfied with just one gold coin.. This mustnt be real..

  43. 1:07
    2:58
    You people simply can't change the rules according to whatever you want

  44. Charlotte and Eliza will vote to kill Amaro instead, 1 coin means nothing but insult irl

  45. I mean logically speaking, they would earn more if they invested it into a sailing business

  46. Sounds like the normal distribution of community wealth! The Bank takes nearly all…….

  47. i think amro should give 1 coin to charlotte and 2 coins to eliza to be sure that eliza will not choose the plan C for any reason.

Leave a Reply

Your email address will not be published. Required fields are marked *