Can you solve the pirate riddle? – Alex Gendler

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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 — and pirate code is notoriously complicated. Can you help come up with the distribution that Amaro should propose to make sure he lives to tell the tale? Alex Gendler shows how.

Lesson by Alex Gendler, animation by Artrake Studio.

420 Comments

  1. There could be a modification of the game when only remaining pirates vote (except one who proposed the distribution). Then the fourth pirate cannot allow the third one to be killed (because the last one will kill him and take 100%). So the third one may propose distribution 0-0-100-0-0. So the second may propose 0-98-0-1-1 to ensure a positive vote. And the first one may propose either 97-0-1-2-0 or 97-0-1-0-2 to ensure an even vote.

  2. Alternative ending: While Amaro is thinking, Royal Navy Pirate Hunters find them
    It's a bad day to be a pirate

  3. You’re pirates hang the code and hang the rules!

  4. Anyone else not even trying to solve the riddles they make

  5. Step 1: Prove that everyone except Amaro has green eyes
    Step 2: Make them walk the plank

  6. yes,they definetly had to be logicians,they definately couldve been educated at the middle of the ocean

  7. BUT as greedy pirates, Charlotte and Eliza decided last minute to refuse being given only 1 coin each and have Amaro keep the 98 coins-pile

  8. If you think about it logically, offering bloodthirsty Bart 99 coins wouldn’t solidify his vote

  9. "Your intellect is truly dizzying."
    "Wait til I get started!"

    "NEVER MESS WITH A SICILIAN WHEN DEATH IS ON THE LINE!!!"

  10. Game theory comes up with the dumbest answers. At bare minimum, if we reduce the crew to two, Daniel and Eliza won't feel like voting anymore and they'll just gut each other.

  11. The equilibrium is Nash for sure, but more refined than that and is called the subgame perfect equilibrium for Perfect Information Extensive Form Games.

  12. I thought it said the amounts wouldn't be equal
    2 of them get 1 coin

  13. Slight problem with the riddle. Given the pirates' bloodlust, the last pirate would need at least 2 coins in a set of 3(not including herself) or greater to agree, as if she gets one in such a case, she will overthrow the 4th…and still get one to secure the vote(as otherwise the second to last would take it all). ….
    WARNING….SPOILERS AHEAD(click read more)

    As such, the solution would be for the caption to take all the gold, save for a four pieces which would be divided such that he gives three to the last one, and one to the third one down(as the third one knows that should there be only 4 left, the last one can be bought with just 2 coins)….I may have to double check my response though.

  14. Can anyone recommend a good beginner book covering game theory and common knowledge?

  15. What if there are 10000 pirates?
    Amaro: Guess I’ll die.

  16. Yay not only I got this right but I had the exact same thought process as explained in the video.

  17. La respuesta no está bien, ya que tendria que darle 2 al último, porque 1 ya lo va a conseguir igualmente, no?

  18. so….. Bart and Daniel are both misogynists?

  19. I just thought each pirate would get 20 gold coins

  20. Shouldn’t you give them 50 50 to make sure they vote for the plan 100percent tho

  21. 20% each initially so they likely accept, then just steal the gold later.

  22. Actually all 5 are good logicians…
    So they could see that coming.
    In reality they should have gone with the equal splitting.
    And instead of killing a good logician teamate …. They should had been making plans to find the dead man's treasure……
    So the question is wrong if you consider its past… But if you consider it as present then the future is right…

  23. My idea was Amaro says that,” If you guys don’t give me all the gold I will get on the lifeboat and set the ship on fire!!!”

  24. Haven't looked at the solution yet. The Captain must propose that no one ever gets less than a fifth of the coins. If they accept this then the Captain lives and everyone gets a 5th of the coins. If they reject it then at least one of them will not get 1/5 or more no matter what because they have rejected everyone getting at least a fifth of the coins. Each person, afraid the others will cut them out and they will get less than a fifth, will vote in favor of the Captains proposal. The others can't divide the coins equally after they kill the Captain because they have already rejected the proposal that none of them get less than a fifth, which is the same as agreeing that at least one of them gets less than a fifth.

    Update after watching solution: The reason it doesn't work is that they all know that if they all reject the proposal, then the Captain is killed and gets nothing, increasing the likelihood of them getting more from the next proposal. Since whoever the Captain is, knows that he needs half or more total votes and he also knows that all of them know that they can get rid of him and get more, no Captain is going to offer less than an equal share to his own share to less voters than he needs. Thus Bart will not offer Daniel any less than an equal share. Upon witnessing Charlotte and Eliza voting nay and watching the Captain die, Bart is going to second guess what Daniel might do and choose not to risk insulting him with an offer of one coin. He'll offer him half, but knowing he could get more if he could get rid of Bart and Charlotte, and that Charlotte needs his vote to live, that she'll offer him half, he'll vote no. Bart walks the plank and Charlotte offers Daniel half. Knowing she didn't offer Eliza anything, and thus doesn't have her vote, Daniel again votes no to get rid of Charlotte. Then he offers Eliza nothing and wins the tie.

    Knowing that Charlotte and Eliza are going to vote no to send a message to Bart, and that Daniel is going to vote no on Bart's proposal so he can get rid of him then Charlotte and get it all, Captain Amaro isn't going to make any such offer. He's going to offer an equal share to all, but he can't do that because they'll vote no and still be able to divide the coins equally after the fact and thus each get more. He has to use their vote to add a permanent change to the conditions that will carry on after he's dead as a deterrent to them from voting nay. This conditional change must be such that the deal for any crew member is never going to get any better than the first offer. Thus my original answer.

    You might say that offering an equal amount is the same as offering a fifth, but offering an equal amount at that time- for that proposal – is different than saying no one ever gets less than a fifth. That carries the opposite of the condition on to the subsequent votes should they reject his proposal.

  25. I’d like to add you could also give E 30 gold coins D 25 C 20 B 15 and A 10…. So what if your the captain and get screwed on the loot. It’s your ship charge them for food and most of the gold ends up in your pocket anyways.

  26. I think the solution is wrong, hear me out: if they are all great logicians then this riddle cannot be solved. if we take the „solution“ from this video then B would adapt his strategy and give for example 2 coins to C. as C is a great logician she knows that B would make this strategy change and therefore say no to Plan A as she gets more in the new Plan B. this would continue like that for eternity with people adapting their own strategy. No?

  27. Well, there is one thing they can do. One of them can say nay. This means the captain, Amaro will be kicked off. The reason to disagree with him is that when Bart becomes captain votes will be equal. And Bart, not trying to get a tie, will propose more coins to Liza and Charlotte.

  28. 98, 0, 1, 0, 1
    if equal votes meant a loss, then he could propose 99, 0, 0, 1, 0 and get more

  29. This is faulty. C and E could easily just say to the captain, give us each 1/3 and we will vote with you, or you walk the plank lol.

  30. Does not work if Charlotte offers Eliza more than one coin…

  31. Based on the solution, wouldn’t it be better to keep 60 as the captain and distribute 10 equally to the crew?
    There’s aspects that aren’t considered in the solution:
    – what are the benefits of captain?
    – how often do they find treasure?
    – is the same scenario repeated each time they find treasure, and if so, what would motivate Bart and Daniel to ever continue working as part of the crew?

    Bart and Daniel would be extremely bitter with the solution, and the other two would equally be disgruntled with the distribution. The solution really only serves to trigger a mutiny.

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