Bloodthirsty Pirates
Arr!! After discovering a buried treasure chest and hauling it on board, the five pirates of the Crying Skull open it to reveal 1000 gold coins. After the initial shock of gleaming metal wears off, the pirates quickly enter a fierce debate over how to divide up the money. The problem is that Captain Avery outranks first-mate Blackbeard, who outranks Cook, who outranks Drake, who outranks Edward.
They ultimately decide on a viciously democratic method of deciding how many coins each pirate gets:
1) The highest ranking pirate alive proposes a treasure distribution method.
2) Then all the pirates on board the ship (including the highest ranking pirate) vote Aye or Fuck No!
3) If a majority votes Aye, then the gold is divided according to the suggested system.
4) Otherwise, the highest ranking pirate is unceremoniously cast overboard (where he is immediately eaten by sharks), and the remaining pirates go back to step one.
Each pirate's proposal must be a simple non-random partitioning of the money among all remaining pirates. No breaking coins in half or melting them! For the purposes of argument, each pirate will not resist (successfully) being thrown overboard, and each pirate knows this. There are no tricks involved in the solution here.
Each pirate has the following priority of values:
1) Self-presevation.
2) Greed.
3) Bloodthirsty.
In other words, when each pirate is deciding which way to vote, they first try to vote in such a way that will maximize their chances of staying alive. If they will stay alive no matter which way they vote, they will vote to try to get the most number of coins possible. If their vote will not change this outcome either, they will vote for killing as many crewmates as possible. The pirates use the same set of priorites when coming up with thier proposals.
If a pirate needs to make a choice that the above value system is not clear on, they will flip a coin to help them decide.
Each pirate is infinitely logical and each one understands the motives of his fellow pirates and that each of his shipmates is also infinitely logical.
Which pirates die? How are coins divvyed up? Which pirate would you want to be? Try to figure this one out, the answer is cool.
HINT: Need a hint? If it gets down to two pirates, what happens? Work backwards.
LAST HINT: If there are two pirates left, it doesn't matter what Drake proposes, Edward will always vote No! which will result in the death of Drake and Edward's appropriation of the entire contents of the chest. Even if Drake proposes to give all the coins to Edward, he will vote No! since the pirates are bloodthirsty. Remember, since there is not a majority, the proposal is dismissed in the case of a tie. It is not defined above how Drake will vote, and indeed it doesn't matter.
Drake Aye Dead
Edward No! $1000
What if there are three pirates left? Remeber that each pirate knows what will hapeen if it gets down to two pirates. Try to work back up to five pirates before looking at the solution below.
Ok here's the solution. Let's say there are three pirates left. In order to stay alive, Cook must get a majority vote. He already has his own vote, so he only needs one more. In order to get another vote he must give Drake or Edward a better offer than what they get after Cook dies. Cook can't offer Edward a better deal, who will always vote No! so that he can watch Cook and then Drake die and eventually take all the money. Fortuantely, since Drake doesn't want to die, he will always vote Aye no matter what Cook's proposal is. So Cook's proposal is guaranteed to win. So how many coins should Cook give to Drake and Edward? Should he be nice? Since he is guaranteed to live, Cook falls back on his greed and takes all the money for himself. Since nothing is better than death, Drake will still vote for the proposal.
Cook Aye $1000
Drake Aye $0
Edward No! $0
If there are four pirates, Blackbeard must convince two of the three other pirates so he can get a 3-1 majority vote and stay alive. He cannot offer Cook a better deal who will always vote No!, so he msut offer Drake and Edward a better deal than the three-pirate scenario. To do this, he need only give them one coin each.
Blackbeard Aye $998
Cook No! $0
Drake Aye $1
Edward Aye $1
So at the very start of the whole process, for reasons that should be clear by now, Captain Avery will offer Cook $1, and either Drake or Edward (he flips a coin - let's say it comes out Drake) $2.
Avery Aye $997
Blackbeard No! $0
Cook Aye $1
Drake Aye $2
Edward No! $0
So Avery makes out like a scallywag! Unfortunately, no one dies. Here are some variants you can try that I came up with, feel free to post your solutions in the comments section, I'll post the solutions in a few weeks.
1) What if there are 1000 coins and six pirates? Seven pirates? Eight? Nine? If you are the lowest ranking pirate on the ship, how many total pirates would you want there to be on board (besides one or two)?
2) What happens if there's five pirates and only two $1 coins in the treasure chest?
3) Let's say that there are six pirates and only three coins, and two of the coins are worth $2 each. What's the highest denomination that the third coin could be if the first proposal is accepted?
4) Let's say that, in each pirate's proposal, he may decide to give each pirate a certain number of coins (as before) or propose that certain other pirates get thrown overboard as part of the proposal. What's the maximum number of pirates you can have on board if there is only one coin in the chest, and you want the first proposal to be approved?
Good luck!
They ultimately decide on a viciously democratic method of deciding how many coins each pirate gets:
1) The highest ranking pirate alive proposes a treasure distribution method.
2) Then all the pirates on board the ship (including the highest ranking pirate) vote Aye or Fuck No!
3) If a majority votes Aye, then the gold is divided according to the suggested system.
4) Otherwise, the highest ranking pirate is unceremoniously cast overboard (where he is immediately eaten by sharks), and the remaining pirates go back to step one.
Each pirate's proposal must be a simple non-random partitioning of the money among all remaining pirates. No breaking coins in half or melting them! For the purposes of argument, each pirate will not resist (successfully) being thrown overboard, and each pirate knows this. There are no tricks involved in the solution here.
Each pirate has the following priority of values:
1) Self-presevation.
2) Greed.
3) Bloodthirsty.
In other words, when each pirate is deciding which way to vote, they first try to vote in such a way that will maximize their chances of staying alive. If they will stay alive no matter which way they vote, they will vote to try to get the most number of coins possible. If their vote will not change this outcome either, they will vote for killing as many crewmates as possible. The pirates use the same set of priorites when coming up with thier proposals.
If a pirate needs to make a choice that the above value system is not clear on, they will flip a coin to help them decide.
Each pirate is infinitely logical and each one understands the motives of his fellow pirates and that each of his shipmates is also infinitely logical.
Which pirates die? How are coins divvyed up? Which pirate would you want to be? Try to figure this one out, the answer is cool.
HINT: Need a hint? If it gets down to two pirates, what happens? Work backwards.
LAST HINT: If there are two pirates left, it doesn't matter what Drake proposes, Edward will always vote No! which will result in the death of Drake and Edward's appropriation of the entire contents of the chest. Even if Drake proposes to give all the coins to Edward, he will vote No! since the pirates are bloodthirsty. Remember, since there is not a majority, the proposal is dismissed in the case of a tie. It is not defined above how Drake will vote, and indeed it doesn't matter.
Drake Aye Dead
Edward No! $1000
What if there are three pirates left? Remeber that each pirate knows what will hapeen if it gets down to two pirates. Try to work back up to five pirates before looking at the solution below.
Ok here's the solution. Let's say there are three pirates left. In order to stay alive, Cook must get a majority vote. He already has his own vote, so he only needs one more. In order to get another vote he must give Drake or Edward a better offer than what they get after Cook dies. Cook can't offer Edward a better deal, who will always vote No! so that he can watch Cook and then Drake die and eventually take all the money. Fortuantely, since Drake doesn't want to die, he will always vote Aye no matter what Cook's proposal is. So Cook's proposal is guaranteed to win. So how many coins should Cook give to Drake and Edward? Should he be nice? Since he is guaranteed to live, Cook falls back on his greed and takes all the money for himself. Since nothing is better than death, Drake will still vote for the proposal.
Cook Aye $1000
Drake Aye $0
Edward No! $0
If there are four pirates, Blackbeard must convince two of the three other pirates so he can get a 3-1 majority vote and stay alive. He cannot offer Cook a better deal who will always vote No!, so he msut offer Drake and Edward a better deal than the three-pirate scenario. To do this, he need only give them one coin each.
Blackbeard Aye $998
Cook No! $0
Drake Aye $1
Edward Aye $1
So at the very start of the whole process, for reasons that should be clear by now, Captain Avery will offer Cook $1, and either Drake or Edward (he flips a coin - let's say it comes out Drake) $2.
Avery Aye $997
Blackbeard No! $0
Cook Aye $1
Drake Aye $2
Edward No! $0
So Avery makes out like a scallywag! Unfortunately, no one dies. Here are some variants you can try that I came up with, feel free to post your solutions in the comments section, I'll post the solutions in a few weeks.
1) What if there are 1000 coins and six pirates? Seven pirates? Eight? Nine? If you are the lowest ranking pirate on the ship, how many total pirates would you want there to be on board (besides one or two)?
2) What happens if there's five pirates and only two $1 coins in the treasure chest?
3) Let's say that there are six pirates and only three coins, and two of the coins are worth $2 each. What's the highest denomination that the third coin could be if the first proposal is accepted?
4) Let's say that, in each pirate's proposal, he may decide to give each pirate a certain number of coins (as before) or propose that certain other pirates get thrown overboard as part of the proposal. What's the maximum number of pirates you can have on board if there is only one coin in the chest, and you want the first proposal to be approved?
Good luck!
posted by flowbeus at 6:00 PM
5 Comments:
I think that your solution is somewhat flawed because it feels naive. If the 2nd law of pirates is greed, it hardly makes sense to settle for 1 coin. Also, the puzzle doesn't take into account the fighting prowess of the various pirates. If a pirates proposal is rejected by the others, then he is thrown overboard or killed, but he might kill or mortally wound one of the others in the ensuing melee. It is probably reasonable to assume that the Captain is one of the better fighters in the crew (since he has survived to make Captain) and that he is better armed according to his rank -- so he could probably take out another pirate with him if they attempt mutiny. The first law of pirates (according to you) is self-preservation, so they might hesitate in killing another knowing that they could be wounded or killed trying (even if they are guaranteed to ultimately succeed given greater numbers). A smart and infinitely logical pirate Captain would distribute the coins more rationally -- he would give just enough to satisfy the greed and stem the blood-thirst of his crew, otherwise he would always have mutiny on his hands. The infinitely logical Captain would have a better solution, I think, otherwise he would never have lived long enough in the pirating business to become a Captain. I don't think any pirate worth his sea-salt would settle for 1 or 2 coins, as it could barely pay for a jug of rum or a night with a wench.
I have already said that the pirates have agreed to the mechanics of the voting system and do not resist being thrown overboard.
Any analysis of what is essentially a hypotheitcal abstraction in the context of the real world only has amusement value.
I invite you to not change the subject and try to determine the answers to the four questions.
I'll post the names of anyone who can figure out the answers to any of the four additional problems.
Not to be nit-picky, but you said that the pirates "would not resist (successfully)" which to me implies that they may resist, only ultimately fail. But I'll concede the point.
However, seeing that the logical abstraction takes place in a hypothetical reality, I don't see my comments as "changing the subject" nor do I think that hypothesizing on their philosophical dilemmas or possible state of mind and personal motivations is somehow out of bounds.
What's wrong with the Captain proposing the following distribution?
A - 500 (Captain Avery)
B - 250 (First Mate)
C - 125
D - 75
E - 50
He would keep all of his crew, and they would be more pleased than with 1 or 2 coins each. Morale would be increased, perhaps keeping the crew stable and together long enough for another conquest -- thus maximizing all their chances at more coins in the future. And with 5 pirates working together, they also maximize their chances of self-perservation in a raid, and satisfying their blood-thirst by slaughtering merchants and sailors.
So, I maintain my objections.
I guess there's nothing wrong with your objections, but you shouldn't assume the pirates have motivations (the desire to increase morale, the desire to not get injured) outside what was already stated.
These are not real pirates.
Hi flowbeus
I never realised that so many different types of blog would show up if I did a search on something like how to cook lobster. I'm still not sure how well Bloodthirsty Pirates fits into that category, but I've enjoyed visiting :0) Adios Amigo.
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