The Pirate Problem – Famous Game Theory Puzzle

How would 5 selfish pirates divide up 500 pieces of gold?
A video on one of the most famous problems from Game Theory, showing that if you know how to abuse the rules of a system you can always do much better than you think.
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63 Comments

  1. yay! A feeling of accomplishment AND a sense of self worth? Yes!

  2. I love how his accent just acts like the problem of murderous pirates on your ship forming a mutiny against you isn't important nor dangerous at all :D.

  3. I would be a selfish pirate and disagree even if I'm just getting one. Then kill everyone else.

  4. I thought the problem was only non captain pirates get to vote and I ended up with 496 0 0 2 2 for the gold distributions.

  5. This is flawed. It would be accurate if one of the conditions was that the pirates may only consider one step ahead. If the pirates go by logic on any future outcomes, the 4th pirate would never accept unless he got all the gold, since when it gets down to 2 pirates, as you explained, he will get all the gold. So, he can just play the waiting game. Thus, at least, working backwards, the step with 4 pirates is based on flawed logic, and so must the one with 5 be. If the pirates prefer present gain over future possibility, which is more likely, none of the pirates would accept just one piece of gold. . .

  6. To much talking i could not understand

  7. For those new to these kinds of puzzles, here's something to be aware of. If a puzzle says, "everyone is perfectly logical," then that means these people are emotionless computers. Just give up on any human element or human error in puzzles with that line. These are soulless beep-boops with pirate costumes thrown on them.
    Because the puzzle stated: "they care about money first, but if that is not a factor then they will like to see someone killed," that means 1 gold vs 0 gold is totally enough to gain their vote. Normal people will get pissed that you're ripping everyone off, but these pirates aren't people, they are emotionless computers. So they will take the 1 gold, because the rules said they would.

  8. Why the hell are you talking like that? It's an effort to understand you dude..

  9. I got (497, 0, 1, 0, 2) BUT I misread the rules — I thought the voting only occurs with the non-captain pirates.

    If anyone is interested, in this version of the game I get 497 as the answer by the following:

    Let's refer to the sums of gold as for each of the respective five pirates as (a, b, c, d, e), where a + b + c + d + e = 500. Or put an X there if that pirate is dead. Pirate a is the first captain, e would be the last. You can think of "a=X" as "pirate a gets -1 gold: i.e. even worse than 0".

    By backwards induction:

    (1) One pirate left: he gets all the 500 gold
    —- i.e. X, X, X, X, 500

    (2) Two pirates left: the captain gets nothing, the other pirate gets 500
    — X, X, X, 0, 500 (Because if the captain offers less than 500 to e, then e will vote No; the captain d gets nothing!)

    (3) Three pirates left: Captain keeps his share as long as not both the other two say No…

    — the next pirate d votes wants to avoid the (2) case because d always gets nothing from it. So he votes Yes for 1 gold coin

    — so in three: the captain offers X, X, 499, 1, 0

    (4): Captain b knows that the first mate c stands to get 499 from killing him, so either offers 500 to the first mate, or bribes the others to vote Yes.. He can bribe the last two pirates with 2, 1

    — so in (4): X, 497, 0, 2, 1

    (5) Since the next game would result in X, 497, 0, 2, 1, the captain needs at least two people to vote Yes, getting more than they would:

    497, 0, 1, 0, 2

  10. Why were there 500 gold coins on a near by cruise ship?

  11. It's 497, if the captain doesn't vote. It wasn't clear in the video, if the captain voted or not.

  12. question in a perfectly logical world i wouldnt pirate 5 know he can get more gold out of pirate 3 in exchange for threataning him and saying he will vote against the distribution? since game theory takes psycology into account too?

  13. Not enjoyable due to accent and terrible speed. Earlier videos were nicer.

  14. Please do more videos! I found these both very interesting and humorous, not something much people can pull off. Also, the topics you cover are really cool.
    EDIT: I am coming back to this years later, and do not intend to come off as someone mindlessly asking for more stuff. What I actually mean to say is that I appreciated your content in its time, and it has helped me to become who I am, as I discovered some of your videos when I was younger (I am a teenager at the time of writing this), and they helped shape my interests in learning and comedy. Regardless, thank you for the things that you made and I hope you are doing well.

  15. If pirate 4 distributes the gold, then no matter what they cannot be murdered this way. So, they can keep all the gold to themselves and will wants want to DISAGREE. Pirate 5 knows this and will AGREE to anything he can get.

    If pirate 3 distributes the gold, then he knows that pirate 4 will DISAGREE no matter what and pirate 5 will AGREE if he gains something. Pirate 3 just has to offer him 1 coin which is better than what pirate 5 can get otherwise. So, pirate 3 can gain 499 coins this way will always want to disagree with the previous pirates.

    If pirate 2 distributes the gold, then he knows that pirates 3 and 4 will want to disagree no matter and needs pirate 5 to agree. Because pirate 5 cannot gain any coin by himself, he'll want to accept any offer even just one coin. Pirate just has to offer pirate 5 one coin and pirate 2 can keep the 499 coins. Because of this pirate 2 will want to disagree with pirate 1.

    Now, pirate 2 will always want to disagree because he stands to gain the most right away. Similarly, pirate 4 can gain all of the coins by always disagreeing. Pirate 5 cannot gain anything himself so he'll accept any offer, even just one coin.

    All pirate 1 needs to do is convince pirate 3 to accept his offer. Pirate 3 knows that if he doesn't accept pirates 1's offer, then he won't get any coins if pirate 2 distributes them. He will take anything he can get, even 1 coin.

    My answer: 498 coins by giving 1 to pirate 3 and 1 to pirate 5.

  16. You didn't make it clear whether or not the person who is distributing the gold gets to vote. This should be clarified, because you could set up the problem where the leader doesn't get to vote and it'll change the problem.

  17. No pirate in this group would be ok with just 1 gold piece game theory will get you dead.

  18. explain me how can u buy the votes by only 1 coin

  19. How about telling pirate 1 to that he would get 50% if he killed the 2nd one and tell the 2nd one to kill the 3rd etc etc. Then kill the last pirate by yourself and get 500? Then make a big promise to new pirate recruits to get 50% and then always end up getting all the gold + earing a title of a (rich) massmurderer? :/

  20. Yeah this is bs. No one would be okay with 1 coin just because it isn’t 0.
    I think 298 is my optimistic answer. Give two pirates more than they’d get if it was split evenly. And keep the most while screwing over only 2/5 people.

  21. That is the wrong answer. The question posed is that only the crew gets to vote — the question says that "after you divide the treasure among your crew, if a majority of them disagree . . . ." Thus, the captain does not get to vote. But the explanation assumes that the captain is voting, and thus leads to the wrong answer. The right answer is: 497 for for the captain, one gold to pirate 3 and 2 golds to either pirate 4 or 5.

    Reasoning: if there were just pirates 4 and 5, then 5 would vote no every time (even if 5 got all the gold) since that leads to 4 dying and 5 getting 500 gold.

    If there were pirates 3, 4 and 5, then 3 keeps all 500, since 4 will vote yes (to avoid dying). The vote is tied with 4 voting yes and 5 voting no.

    If there were pirates 2, 3, 4 and 5, then 2 would keep 498 and buy the votes of 4 and 5 by giving them 1 each. 3 gets nothing. Since 4 and 5 get more than they would in the prior scenario, they vote yes. Vote is 2-1 in favor.

    So pirate 1 can keep 497, and buy the vote of 3 for 1 gold, and buy the vote of either 4 or 5 by giving them two gold. The vote is tied with 3 and either 4 or 5 voting in favor.

  22. …? If i were a pirate, or frankly anybody I wouldn't settle for 1 piece of gold. I'd disagree. You can't give ONE GOLD TO SOMEONE TO GAIN YOUR VOTE

  23. This problem just shows that game theory is extremely divorced from human reality. No Pirate in history took this approach in actuality they distributed the loot almost equally with a little bit more for skilled workers and the captain to ensure a maximum in group cohesion.

  24. Can you explain the Nash Equlibrium for this problem

  25. All I have to say is that I would love to see you as CEO of a company. Wouldn’t last long. This is a perfect case of something being logical on paper with zero practical import.

    Let me explain. You say there are no alliances prior to the distribution of gold right. You never said anything about alliances forming because the pirates were all getting shafted. You did not say, thankfully for you, that no future alliances couldn’t be made. The four pirates could have all made the argument that they were involved in the raid and every person deserves more than either 1 or 0 coins. I could have said, let’s kill the brighter and we all get 125 a piece. That is better than the 1 and certainly better than the zero.

    Since they are voting, we are obviously dealing with political science whether they are pirates or not and the Lockean social contract would certainly apply here. Ultimately, what would Most likely happen is that if the head pirate tried to do that BS, he would be killed whether by vote or not. Remember, they just murdered a Norwegian cruise liner. The head pirate also would have seen other scenarios play out unless this was their
    Maiden marauding voyage and they have never seen a pirate captain get killed for this same behavior.

    I guess all people whether pirate or not are nothing more than the mathematical tropes we put them in. This was utter tosh!

  26. Changed so each has an unknown arbitrary minimum to choose gold over seeing death, if 4 and 5, no change. 3, 4, 5, 3 gives all to 5, since 4 stands to get all, meaning nay no matter what as he'd witness 3 dying. 2, 3, 4, 5, 2 knows 4 gets nothing if 2 loses, so gives it all to 4 to tie. 1, 2, 3, 4, 5, 1 knows 3 and 5 get nothing if they lose, 2 gets to see murder, and 4 recieves profit, 1 splits it 50-50 between 3 and 5, hoping they both say Yarr, as if either doesn't, he loses even with the best solution, since if either wants over half, that cuts into the other's half, and, choosing randomly from 1% to 100% of the coins, 50% chance at least one wants over half, 25% both do making it be unwinnable, so the best bet is even split and hope both Yarr.

  27. If I was the captain I would give myself 104 gold and give the other pirates 99 gold. For 2 reasons 1: so I survive. and 2: keep most of the gold

  28. I managed to solve it for 1, 2, 3 pirates but somehow didnt see the pattern with 4th and it broke for me

  29. “Let me give you a problem. You’re on a ship.”
    Yes, one of the biggest hardships of our generation.

    Also before watching the answer, I believe what you have to do is start from the end.
    If the last 2 pirates remain, #4 will request all gold for himself and #5 can’t stop that. Because #5 is scared of that happening, he will agree to whatever #3 decides. #3 plans to request all but one gold coin for himself, giving that last one to #5. But #2 stands in his way, and if #2 allows #4 to get one coin and keeps the rest, the 2 agreements will overpower the 2 disagreements. So you must take advantage of this, by offering 1 coin to #3 and #5, and keep the remainder of coins. #2 and #4 will disagree, but #3 and #5 will agree because they know the other options are worse for them.

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    game theory -"The Game Theorists" -"The Film Theorists" -"The Food Theorists" -"MatPat" -"GTLive"

  31. I heard this problem before but they just asked the question, they didn't explained well the rules, so I never though that they would kill each other as well. Thanks for that

  32. How is this actually the correct solution, given the constraint that pirates would vote to throw over board if the outcome would be the same? In this example starting with only three pirates C would take 499 and offer Pirate E 1 coin. So in the iteration of 4 pirates B would have to offer pirate E 2 coins and take 498 himself to tie the vote, as Pirate E knows that he will get 1 coin in the previous example by throwing pirate B off. So what we end up with is a solution of A=496, B=0, C=1. D=0 and E=3. I don't quite see where I've made an error, as the wiki page seems to have the same solution.

    Edit: my apologies, the solution in this video is correct. You can get away with this A=498, B= 0, C=1, D=0, E=1, due to the fact that in the iteration with 4 pirates, B=499, C=0 D=1 !, E=0, which makes the outcomes swap between iterations and hence doesnt keep increasing priate E's gold for number of pirates in this equation.

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