Plunder that booty Five buccaneers have obtained 100 doubloons and have to divide up the loot. The buccaneers are all extremely intelligent, treacherous and selfish (especially the captain).
The captain always proposes a distribution of the loot. All buccaneers vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no buccaneer would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all buccaneers will turn against him and make him walk the plank. The buccaneers start over again with the next senior buccaneer as captain.
What is the maximum number of doubloons the captain can keep without risking his life?
20 comments
My guess would be 33 doubloons. If the captain agrees to split the pot three ways with two other pirates, then they have no reason to revolt, as they would get treated equally. The other two pirates would not have a majority and get screwed with one doubloons between the two of them, but not enough force to revolt.
I don't believe in the haphazard use of economic theory though, so its hard for me to take any hypothetical like this seriously. Are pirates even rational actors? | | |
| I'm going 60- he gets 2 guys to vote to get their fair share, and screw the other two. | | |
| My inital, incomplete guess is 48, but I'm going to think about it some more. | | |
| Hey, Alex, have you heard this one before? | | |
| On actual pirate ships the booty was almost always divided in equal share to all members. That being said, my guess is also 48. | | |
Life-maximizing captain will concentrate the division on two pirates. He will not give any to the next-in-line, who will want a premium to forego his chance at being captain.
The two pirates who are chosen to get loot will vote aye if the risk of getting more by voting no is equal to or less than the amount they receive. They know that they cannot expect to get more than half the money (50) since the captain would need to have two pirates vote aye. Since they have a 1-in-3 chance of getting nothing on the next go-around, that means they will vote aye if they get 2/3 x 50=30. So the captain can give two of the pirates 30 each and keep 40 for himself. | | |
| Damn, I hate math. 2/3*50 = 33.3, round up to 34. 34+34=68. 100-68=32. So he can keep 32. But since the captain now gets less than the regular pirates, does that screw up the incentive for the next-in-line to be captain? Urgh... | | |
| No, it doesn't, I've decided. 32 is the equilibrium point- if the captain keeps any more, the next-in-line has an incentive to vote against him, even if he is given a share of the booty. 32, final answer. | | |
Vinny emailed me the correct answer (different from what he posted above.)
It's fun when you get it, so I won't spoil it for you just yet. | | |
| It's a trick question, right? Like, only the captain has Keira Knightley's phone number, so he can keep as much as he likes and still not to have to worry about being killed? | | |
What is the maximum number of doubloons the captain can keep without risking his life?
There will always be a risk to the captain's life if he takes some, since the crew may decide to mutiny just to get a bigger share. The only way the captain could not risk his life is to take 0. | | |
| no, it's 100, because it's no risk to his life if he kills every other buccaneer. I don't care who you are, you get hit with a sack full of a hundred doubloons, you're not getting up. | | |
| I would like to know the answer. I don't know how to think about this question. | | |
| I like Dustin's answer, but I think Goodladd makes a lot of sense too. | | |
| Don't give up! Consider an easier problem: What if there were only 2 pirates, what would happen? What if there were 3 pirates? Keep going for X pirates and Y gold. | | |
Here's the solution:
Name the pirates A, B, C, D and E. Pirate A is the captain, B is next in line, C is 3rd in line, etc.
Suppose that only D and E were alive. D could keep all 100 coins because all by himself, he has 50% support required to avoid a mutiny. E gets nothing.
If C, D and E were alive, captain C would need to get one other pirate's support. So as not to get killed, he has to offer one of the other pirates a better deal than what he would get after a mutiny. Since E gets nothing if there's a mutiny, C can offer E 1 coin and keep 99 coins. D gets nothing.
If B, C, D and E are alive, captain B need only convince 1 pirate. In the 3-pirate scenario, D got nothing, so he's willing to accept 1 coin cause it's better than nothing. So B keeps 99, D gets 1, and C and E get nothing.
Now we get to the 5-pirate scenario. A has to convince two pirates not to mutiny. In the 4-pirate scenario, C and E got nothing, so A can offer them each 1 coin, and keep 98 to himself.
So the answer is 98. | | |
Bryan, your supposed "answer" shows a shocking lack of knowledge about piracy. In no way could the captain keep 98 dubloons and avoid a knife in the back in the future. To me, that counts as "risking your life".
I urge you to stay on land, where you might still be safe... | | |
The below is the solution another website gave...
Answer: 98
The captain says he will take 98 coins, and will give one coin to the third most senior pirate and another coin to the most junior pirate. He then explains his decision in a manner like this...
If there were 2 pirates, pirate 2 being the most senior, he would just vote for himself and that would be 50% of the vote, so he's obviously going to keep all the money for himself.
If there were 3 pirates, pirate 3 has to convince at least one other person to join in his plan. Pirate 3 would take 99 gold coins and give 1 coin to pirate 1. Pirate 1 knows if he does not vote for pirate 3, then he gets nothing, so obviously is going to vote for this plan.
If there were 4 pirates, pirate 4 would give 1 coin to pirate 2, and pirate 2 knows if he does not vote for pirate 4, then he gets nothing, so obviously is going to vote for this plan.
As there are 5 pirates, pirates 1 & 3 had obviously better vote for the captain, or they face choosing nothing or risking death.
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This is late, but:
The captain here relies to much on his crew's intelligence! True pirates would never vote for only one coin!
That also means that their intelligence is their weakness. If they were dumb, they'd get more money. Think about it :D | | |
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