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.

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

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

  2. 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

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

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

  5. 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

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

  7. 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!!!

  8. 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

  9. 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

  10. 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 .

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

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

  13. 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

  14. 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.

  15. Boooooo! "Top notch logician," is a horrid qualifier. I would argue that allowing a 98,0,1,0,1 split is illogical.

    Look at it this way… Logically, A offers 2 of them a gold piece each. A is then made to walk the plank. B, as a "perfect logician," would realize that an offer of 1 gold piece would end with him recieving nothing, and being forced to walk the plank.

    That, and allowing the guy who proposed the split to count for 20% of the vote is assinine.

    These, "riddles," feel more like knock-knock jokes when the answers end up being something like "you forgot to count the captains vote," or, "when we say perfect logician, we mean "imagine they were all robots. As such, they are incapable of percieving subtext."

  16. This riddle is based on Nash equilibrium … the same equilibrium theory Russell Crowe devised in " A beautiful mind "

  17. Divide the coins among the pirates, 20 coins for each, they Will go to the nearest bar to celebrate and spend it all,
    I chose to be the bar owner.

  18. This is pure mathematical logic. If the real world even if everyone was logical mathematicians, this would still never happen.

  19. Plan e
    Mine: 100 percent
    the other people who got eaten by sharks: Dead 😀
    Its a good day to be a pie rate
    (it keeps auto correction im lazy to fix it sooo)

  20. What i know about pirates is that the captain doesn't need the other's permition to do what he wants he could offer them all 1 gold and keep the rest LMAO

  21. I'm just gonna point out that if Amaro offers Elizabeth one gold coin, she'll just make him walk the plank, since she'll receive it later from Pirate C

  22. Many possible answers for the given condition, for example, Amaro might give 1 coin to Bart and another to Daniel, while keeping the rest (98). Lol read rules again.

  23. What if Amaro says that Elizabeth and Daniel have to walk the plank. E and D will vote nay ,and B and C will say yar plus amaro's vote are 3 yars against 2 nays. Then E and D walk the plank.
    Now only Amaro, Bart and Charlotte are in the ship. So, Amaro says that charlotte will recieve one coin and he keeps 99 coins. With that he can keep more gold.

  24. But isn't there a flaw?

    You also said if the pirates knew that regardless of their vote they'd end up with the same amount of gold they'd vote to make the proposer walk the pank just for fun?

    So Eliza would vote no for Amaro just for fun, vote no for Bart to ensure the hat goes to Charlotte and then vote yes for Charlotte. This way she got to see 2 people walk the plank and ended up with atleast 1 coin!

    Tl;Dr Amaro is kinda screwed!

  25. Well I would Like to enkrece the chances so I would ofer to all pirates 10 coins and keeping 50 for myself wich would make me look good infront of my pirate friends

  26. Yeah this riddle was completely redundant once he said they are all logical thinkers. The only solution to this would be 20 each if they truly are logical thinkers.

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