Five Pirates Are Stranded on an Island...

Pre-College Topics High School Life
1

<p>And find a treasure chest with 100 pieces of gold inside of it. The pirates need to come up with a plan to split the gold and the plan must be approved by MORE THAN 50% of the group. Should the plan be rejected, the corresponding pirate will not get any gold AND forfeit his life. For instance, if the 1st pirate’s plan is rejected, then he dies and doesn’t get any gold. If a pirate is killed, then the next pirate gets to come up with a plan, until the last pirate remaining.</p>

<p>Assume that you are the 1st pirate to come up with a plan. How would you split the gold so that you get the MOST gold possible?</p>

<p>Note: You CANNOT kill any other pirates or use any trickery to obtain the gold. The gold must be split while all 5 pirates are conscious. Also, THIS IS NOT HOMEWORK.</p>

<p>EDIT: Oh, and tell me if there are any conditions that are unclear. I’ll try to clarify them as long as they don’t require giving hints.</p>

2

<p>I split it three ways, me, pirate 1and pirate 2. When we vote, pirates 4 and 5 obviously object, but 3/5 is more than 50%. We walk away w/ 1/3 rather than 1/5, and hopefully the other pirates don’t kill me. :P</p>

3

<p>Since they are stranded you promise to build them a new boat if they let you have the majority of the gold and don’t kill you.</p>

4

<p>^But if you can build a boat, they can build a boat. You don’t necessarily have skills that they don’t.</p>

<p>The problem with qdawg’s plan is that we don’t know the order of the voting, or the style of voting. Is it a survey, or is it just “all who agree say aye”?</p>

<p>The safest way is to split it evenly, because it gets you the most while also assuring you your life. No one can complain if everyone’s getting the same amount, right?</p>

5

<p>^ Yeah, they can. Why would they settle for 1/5th each if they can kill you and get 1/4th each?</p>

6

<p>Alright, let’s look at this starting from the end</p>

<p>only 2 pirates left. Pirate 4 (as in the 4th in line to come up with a plan) comes up with a plan, pirate 5 always votes against it so he can kill pirate 4 and take all the money.</p>

<p>3 pirates left. Pirate 4 will approve any plan pirate 3 comes up with, because 4 doesn’t want to die. But 5 will reject any plan. Without more than 50% approval, 3 dies no matter what.</p>

<p>4 pirates left. Pirates 3 and 4 will approve any plan pirate 2 comes up with, as if the plan isn’t approved 3 and 4 both die. Pirate 2 can abuse this like crazy and give 100 gold to himself and 0 to the others (as getting 0 gold is better than dying).</p>

<p>5 pirates left. Pirate 2 will vote against no matter what. Pirates 3, 4, and 5 will vote for the plan as long as they get more than 0 gold. Thus pirate 5 can give 97 gold to himself, and 1 each to 3,4, and 5.</p>

<p>edit: I’m working under the assumption that the plan maker doesn’t vote. The solution is slightly modified if he does, but the strategy of attack is similar.</p>

7

<p>^ But the question is how to get yourself the most money not pirate 5</p>

8

<p>I meant to say pirate 1 (who is me, correct?). I give myself 97 gold and 1 to each of 3,4,5 and I’ll get 3/4 of the votes.</p>

9

<p>I’m pretty sure you do vote. That’s what I was assuming</p>

10

<p>But either way why would pirate 5 go with anyone else’s plan</p>

11

<p>alright, so 2 pirates left: pirate 4 dies no matter what.</p>

<p>3 pirates: pirate 3 can take all the gold. Pirate 4 approves because 0 gold > death.</p>

<p>4 pirates: pirates 2 buys the votes of 4 and 5 with 1 gold apiece, and takes 98 for himself.</p>

<p>5 pirates: I can buy 3’s vote for 1 gold and then either 4 or 5’s vote for 2 gold, and take 97 for myself.</p>

12

<p>Pirate 5 will approve plans in which he gets >0 gold because if it gets down to 3 pirates pirate 5 isn’t getting anything.</p>

13

<p>But pirate 2 can get them to vote against pirate 1 promising them more gold than pirate 1 is willing to offer.</p>

14

<p>are you a humanities person?</p>

15

<p>The thing is in real life what would happen would be the three or four pirates who were the closest friends would make sure that when they were figuring out the order to put the pirates they didn’t like as first two planners kill them and then divide it as they wish. </p>

<p>What I would do in this situation would be to join up with a couple of them then choose the weakest one and give all of the gold to him then in the middle of the night we’d make away with it like pirates on our badass new pirate ship we built.</p>

16

<p>humanities people crack me up</p>

17

<p>^ Yeah I want to be a philosophy major</p>

18

<p>Backsolved this. I’m assuming that everyone is rational, each pirate wants the maximum he can get (and that he understands how things will go if the next scenario were to play out), and no one wants to die.</p>

<p>Myself: 97 coins
Pirate 2: 0
Pirate 3: 1
Pirate 4: 0
Pirate 5: 2</p>

<p>Pirates 3, 5, and myself would vote because: </p>

<p>Scenario 1
Assuming there are only two pirates left, pirate 4 would offer 100 coins to pirate 5 (a 0-100 split). Otherwise, pirate 5 votes against him, he doesn’t get his >50% vote, and pirate 4 dies.</p>

<p>Scenario 2
Assuming there are only three pirates left, pirate 3 proposes a 99-1-0 split. Pirate 4 would agree to this because if he doesn’t, scenario 1 occurs and he gets nothing. Pirate 5 would have voted against him no matter what, because he wants scenario 1 to occur.</p>

<p>Scenario 3
Assuming there are only four pirates left, pirate 2 proposes a 97-0-2-1 split. Pirate 3 would vote against him, but pirates 4 and 5 would agree because this is already more than what they would’ve gotten if scenario 2 occurred (if they killed pirate 2, pirate 3 would get 99 coins, pirate 4 gets only 1 coin as opposed to the current 2 coins, and pirate 5 gets nothing as opposed to the current 1 coin).</p>

<p>Scenario 4 - You as Pirate 1 are still alive
All five pirates are alive. I suggest a 97-0-1-0-2 split. Pirate 5 votes for me because the alternative is getting only 1 coin in scenario 3. Pirate 3 votes for me because he would’ve gotten 0 coins in scenario 3.</p>

<p>The scenarios don’t mirror the chronological events of how things would go. You start with scenario 4 occurring, and if for some reason pirate 1 is killed, scenario 3 occurs, and so on.</p>

19

<p>wouldn’t you obviously just split it equally?</p>

20

<p>25% split > 20% split. Pirate 1 would be killed to split it among fewer people. If everyone up to pirate 4 suggested to split, pirate 5 refuses in the final scenario and gets 100 coins for himself.</p>