# The pirates

Meneer Dries
Posers and Puzzles 07 Mar '07 18:31
1. 07 Mar '07 18:31
One that I think is quite hard, but I like the riddle a lot.

Five pirates have robbed another ship and have stolen 100 golden coins. Now there's an argument on how to divide those coins. But they've managed to think of a system to divide it all. The eldest pirate can suggest a way and then everyone votes (including the eldest) and if the vote is against, the pirate gets killed and the next one in line can suggest something.
If you are that eldest pirate what would you suggest, assuming that all of the pirates think logically and want the biggest amount of cash they can muster?
2. 07 Mar '07 18:34
Suppose there are 4 pirates left and the vote goes 2 for and 2 against. Does the suggestion pass? Or does it matter?
3. 07 Mar '07 18:381 edit
Ah, game theory! Given that the pirates are perfectly logical, I would suggest the optimum solution thus:
A - 98
B - 0
C - 1
D - 0
E - 1

Edit: where A is the eldest.
4. 07 Mar '07 19:05
If we assume that ties result in the proposal being accepted, we should be able to build this up from simpler cases:

1 pirate: he takes all the gold
2 pirates: the older one takes all the gold
3 pirates: the youngest one gets no gold if the oldest one is killed, so the oldest one offers him 1 gold for his vote and takes 99 for himself
4 pirates: the oldest needs one vote to get a tie, so he offers the second-youngest (who doesn't get anything if the oldest is killed) 1 gold for his vote and takes 99 for himself.
5 pirates: If the oldest is killed, the youngest and third youngest get no gold, so the oldest offers them each 1 gold for their votes and a 3-2 majority, taking 98 gold for himself.

So as itisi said, in descending order of age the gold goes 98-0-1-0-1
5. 07 Mar '07 20:01
wow, you really are fast in solving this riddle. I had some more trouble finding this one but congratulations. I indeed forgot to tell that a draw is a win too.

another one quickly then.
You got 8 balls of which one weighs more than the others. You only have an old set of scales, you know, the balancing type. You only get to weigh twice. How do you find the heavier ball?
This one is simpler
6. 07 Mar '07 20:03
Originally posted by itisi
Ah, game theory!

what do you mean by "game theory"?
7. 07 Mar '07 22:05
[i]You got 8 balls of which one weighs more than the others. You only have an old set of scales, you know, the balancing type. You only get to weigh twice. How do you find the heavier ball?
This one is simpler[/b]
You have to put three balls on one side and three on another. If scales are equal, you just have to check the remaining two. If one scale is lighter you take the three, put one away, and two on the scales. If they are of the same weight,it is the third. If not you'll see it on the weight.
8. XanthosNZ
Cancerous Bus Crash
07 Mar '07 22:21
Meener, look at the thread titled Small Change, it contains discussion of the balls problem.
And game theory:
Game theory is often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. The essential feature, however, is that it provides a formal modelling approach to social situations in which decision makers interact with other minds. Game theory extends the simpler optimization approach developed in neoclassical economics.
(wikipedia)
9. 08 Mar '07 11:11
The odd thing with the pirate game is that there is no single correct answer, because social standards may differ from one group to the next. It is closely related to the Ultimatum Game, which has 3 parties, two of which have a decision to make.

The first is the one giving the money. The second is told by the first the amount of the money, told the rules, and gets to make one offer to the third on how the money will be divided between them. The third (who also knows the rules) may either accept the offer, and the money is split as arranged, or reject the offer, and no money changes hands at all.

Now you would think that the third would accept any offer as being better than nothing and would get the minimum, but this is where the social (and replay) aspect comes in. Offer too little, and the other person will consider it worth the loss to deny the person setting the terms anything as well. Supposedly the other person knows this, and as such will attempt to make a fairer division. Now where this mark gets set depends on culture and individuals involved.

In the case of this pirate game, it would be foolhardy to think you could get away with taking 98%, and thus your life would be forfeit. The other pirates could logically reason that if they vote down the greedy proposal, the next pirate is more likely to be more generous, in addition to the fact that the average share is now greater.

Ask yourself, as pirate #2, you are now the eldest living pirate. The more junior pirates have declined one minimal offer, would your make another of the same, or would you try to set the compensation a little higher, lest ye befall the same fate?

(For another example of the game theory paradoxes, consider the Prisoner's dilemma, in which regardless of how your partner acts, you're better off spilling the beans, and yet you both do best overall when you both keep silent..)