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URL:  https://boards.fool.com/i-guess-i-figure-if-im-3-and-1-offers-me-1-i-16641356.aspx

Subject:  Re: The Pirate Puzzle Date:  2/5/2002  2:07 PM
Author:  jrr7 Number:  146 of 297

I guess I figure if I'm #3, and #1 offers me 1, I would probably turn it down if I have even a 100:1 chance of getting that 993 if it comes to me. Same way down the line until we get to #7. So it seems like #7 should get a lot of dough.
But it's not about "chance" or "probability" or "luck" at all. Each pirate is perfectly rational and acts so as to maximize his own payout. And all the pirates know that the other pirates are rational, too.

If you turn down an offer that gives you gold, the next player knows you are not acting rationally, and so won't bother to give you any the next time either.

I'm also having trouble with the judgment calls. If #9 is up and gives #10 all the gold, does #9 live? Why? Is there some assumption that given pareto-equal outcomes, a person will live rather than die? Because if the risk of having to deal with #10's whims is eliminated, I think it changes the answer.
This information is not available to us or the pirates, so we must reason without it. Suffice it to say that #9 will never get the chance to put forth his plan, because the pirates are rational. We're really just considering "What's the case if we started out with only 2 pirates in the boat" and then slowly increasing the number of pirates.

A pirate will never willingly put himself in a situation where his life or death is determined by someone else's whim. Whim or no whim does not change the answer.
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