The Pirate Problem - Famous Game Theory Puzzle
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- čas přidán 29. 06. 2016
- 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.
Also subscribe for more videos. - Věda a technologie
Nice explanation! I was surprised and happy to see a quote from Myerson's game theory book.
EckoChamb3r , So you telling me that the game theory is basically promoting bribery ? :/ , Buying other gamers votes, I think they need to change some famous games rules , like in football , they need to allow teams to sell their "we-are-going-to-lose-anyways" matches !! Don't you agree? .. because some pirates are going to lose the full treasure anyways, unless they took 1 coin each, it's better than nothing! if they disagree :/
I'm going back to MindYourDecisions channel, it's too much effort to understand you with that ridiculous accent
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.
So whats the use for human interaction? Its just a puzzle and a dangerous one at that because it opens the gateway for animosity among the crew.
Go watch Anticitizenx’s “The langauge of logic.” He explains this common misunderstanding about logic.
"Look at me, I'm the pirate now"
Hi man. I agree with some of the other comments: your style is awesome.
Minor feedback: I missunderstood something at the beginning of the video. I thought that after the captain proposed the distribution, only the 4 crew members would vote. I didn't realise that the "proposer" gets one of the votes too.
So I ended up solving a different problem than the one you meant to pose.
Very well explained. You captured every detail of the problem before asking the solver to solve it. I wonder if, rather than giving the final answer right away, you should have started working toward it. That might allow a baffled solver to realize what was happening, pause the video, and solve the rest of it himself.
if acting irrational can give you more than just 1 coin, wouldn't it be rational to vote in unprdictable ways just to get the chance to get more than 1 coin?
let's say the pirates are super greedy and don't know what each other is thinking because of their greedyness. no matter that the first pirate proposes, the other 4 could collectively vote no (except the one who would get 500 coins if that was part of the proposal) to raise their chance to get more.
this process would repeat, and then pirate 4 would get 500 and pirate 5 would get 0.
Dennis Haupt yes. This is pretty much what happens in reality.
People behave in ways that are, from a certain perspective, irrational. But because they usually make their "irrationality" clear in advance, and because they are *precommited* to following through, they force other people to behave differently. And the net result of this "irrationality" often makes them better off.
I got frustrated because I didn't know how much gold the lesser pirates needed to be satisfied and stopped at 480-10-0-10-0 because I thought that was already absurd and I was probably just missing information
Pheobe Owusu actually, I think the way to figure out how much would satisfy a pirate is to look at the outcome. Say the two only get 1, if they don't like this then they vote him off and now there are four pirates. Now captain #2 can only give captain #4 gold (only 1) if he wants the outcome of him having the most gold as possible. Captain #4 is unsatisfied and votes him off, leaving us with three captains. Now captain #3 has to split it. If he wants the best outcome for himself, then he would have to give only 1 gold to either captain #2 or captain #1. Let's say he gave #2 the gold (only 1) and he is unsatisfied. Both 2 and 1 vote against him and he loses. Now there are only two, and captain #2 keeps all the gold since there is no one else to vote against him (except for #1, but a deadlock would occur and he can't win since in order to do so, he would need a majority). Thus, only captain 2 gets gold, and if the original 2 pirates who got the gold when captain #5 was still around complain, they end up losing even more, cause a "Better something then nothing" situation. They probably didn't like the fact that they got 1 gold, but if they fight against it, then they lose that one gold. I'm sorry if this explanation is too long or confusing.
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.
How the hell have you only got
DumbButt Seconded
The thought of trying to take almost all the gold literally never came to my mind
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
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.
Great vid :)
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
it's quite interesting how the solution appears to mimic increases in binary. though i'm pretty sure no pirate would be content with 1/500 gold. you know, considering they're pirates.
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.
I love the animations, your voice and your "passion" for riddles. And I love that I got to be your 111th sub :)
"These are the most valuable prizes" YEAH!!!
Do more videos like this!
Not the mat pat one 😂👌
yay! A feeling of accomplishment AND a sense of self worth? Yes!
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.
“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.
This is also a ted ed riddle
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
How 'democracy' really works
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.
Can you explain the Nash Equlibrium for this problem
It's 497, if the captain doesn't vote. It wasn't clear in the video, if the captain voted or not.
It was clear because he should an answer of all five pirates voting.
Hugo I did the same thing giving 1 to pirate 2 and 2 to 4
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.
I managed to solve it for 1, 2, 3 pirates but somehow didnt see the pattern with 4th and it broke for me
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.
Why were there 500 gold coins on a near by cruise ship?
You. I like you.
explain me how can u buy the votes by only 1 coin
...? 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
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? :/
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?
Ted ed stole it😞
MATPAT!!!!
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.
Really Enjoyed!! Lets go out?
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.
OMG I actually got it right!!!!
Why can't you give gold to Pirate 4 and Pirate 5? Why is it 3?
Where r u ??????
?
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. . .
The solution is not flawed. Is it possible for pirate 4 to be killed? No, because if pirates 1-3 are killed, then pirate 4 would need to be disagree with his own distribution but that won't happen. Thus, pirate 4 will want all the gold to himself. Pirate 5 knows if pirates 1-3 are killed, then he will get nothing and cannot do anything about it. Pirate 5 does not want this to happen so he'll accept ANY offer, even just one coin.
If pirate 3 distributes the coins, then he knows that pirate 4 will always disagree and he needs pirate 5 to agree. If he offers pirate 5 nothing, then whether pirate 5 agrees or disagrees he'll end up with nothing. According to the rules when a choice doesn't matter, the pirates will always disagree. So to get pirate 5 to agree, pirate 3 just has to offer 1 coin because that is better than what pirate 5 could ever get otherwise.
If pirate 2 distributes the coins, then he knows pirates 3 and 4 will disagree but they only need one other pirate to agree. Again, pirate 2 just has to offer pirate 5 one coin. That way there is not be a majority of disagrees. Thus, pirate 2 will always want to disagree.
Pirate 1 just needs two pirates to agree. Pirate 2 will disagree because if pirate 1 is killed, then pirate 2 can keep 499 coins. Pirate 4 will want to disagree because they can keep all the coins if pirates 1-3 are killed. Pirate 5 will agree if offered one coin. Now pirate 3 knows he'll gain nothing if pirate 2 is the distributor and won't be able to kill pirate 2. Because of that he'll accept pirate 1's offer of anything but not nothing. Pirate 1 has to offer pirate 3 something because otherwise he choice makes no difference and thus the choice defaults to disagree.
Thus, pirate 1 offers one coin each to pirates 3 and 5. Since pirates 2 and 4 will want to disagree regardless, pirate 1 can give them nothing. Thus, pirate 1 keeps 498 coins!
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.
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!
Are you speaking English?
It is now legal to legally change your birth-name. Just so you know.
TED ed copied this riddle
But that's just a theory.... 😂
A GAAAAME THEORY
To much talking i could not understand
Too fast :D
subscribe!
com bk pls
Why the hell are you talking like that? It's an effort to understand you dude..
JUST SPEAK SLOWLY MAN...
think faster
Copy & paste
Your voicing is annoying I can't want watch