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. Watches a riddle video
    makes no attempt at solving the riddle
    watches answer anyways
    still didnt understand what is going on

  2. The standard for booty distribution is actually 2 shares for captains, 2 shares for first mates (sometimes) and one for everybody else

  3. How about this idea? 28 for the Captain and 18 each for the crew. 100. Would that work best as a fair suitable solution? Or just 20 each? Or Captain proposes 25 each and kill off Eliza?

  4. I'd say 33% for Amaro, Bart and Charlotte, while Daniel and Elizabeth get nothing. Since it's 33% each (more than 20% each), Amaro odds of staying alive are pretty good. It's also unlikely that the vote will pass because Amaro, Bart and Charlotte will likely vote yarr, and Daniel and Elizabeth with likely vote narr, with a 3-2 split.

  5. Great riddle. One point though.
    While both Amaro and Bart need to bribe Eliza, if they are captains, Amaro doesn't necessarily need to bribe Charlotte. He can alternatively offer Daniel 1 coin.
    If Bart or Charlotte become captains, they're both interested in bribing Eliza, skipping Daniel. So Daniel is also in desperate need of gold, and will agree to anything from Amaro.
    So the more correct answer is IMHO Amaro can leave 98 to himslef and give 1 to Eliza and 1 to either Charlotte or Daniel.

  6. N ÷ P = Amount to given = N
    It does not even need to be 1 coin as you will end up in the same thing. And if the all knew they were going to say 99 coins. Then this would be the best out come because the other guys would know they get nothing.

  7. What if Elizabeth doesn't like Amaro, she would, after all, get the same amount from Charlotte, if Charlotte would be the captain. That's why I thought the answer was 2 coins for Elizabeth to ensure she wouldn't prefer Charlotte over Amaro.

  8. This riddle relies heavily on the blood thirsty factor. Additionally, I believe that this is like the paradox of the judge and the unexpected execution

  9. 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… :-/

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

  11. 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.

  12. 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

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

  14. 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

  15. 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

  16. 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?

  17. 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

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

  19. 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

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

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

  22. 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

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

  24. 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!!!

  25. 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

  26. 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

  27. 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 .

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

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

  30. 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

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