386 Frequently Asked Questions In Quantitative Finance
loot for themselves but they are also democratic and
want to make the allocation of gold as fair as possible.
But how?
They each pick a number, from one to 10, out of a hat.
Each person in turn starting with number one, decides
how to divvy up the loot among the pirates in the boat.
They then vote. If the majority of pirates approve of the
allocation then the loot is divided accordingly, other-
wise that particular pirate is thrown overboard into the
shark-infested sea. In the latter case, the next pirate in
line gets his chance at divvying up the loot. The same
rules apply, and either the division of the filthy lucre
gets the majority vote or the unfortunate soul ends up
in Davy Jones’s locker.
Question, how should the first pirate share out the
spoils so as to both guarantee his survival and get a
decent piece of the action?
Solution
This is obviously one of those questions where you
have to work backwards, inductively, to the solution for
10 pirates. Along the way we’ll see how it works for an
arbitrary number of pirates.
Let’s start with two pirates, with 1000 doubloons to
share. Pirate 2 gets to allocate the gold. Unless he gives
it all to Pirate 1 the vote will be 50:50 and insufficient to
save him. Splash! We are assuming here that an equal
split of votes isn’t quite enough to count as a majority.
So he gives Pirate 1 the entire hoard, and prays that he
lives. (Of course, Pirate 1 could say hard luck and dump
Pirate 2 overboard and still keep the money.)
Now on to the three-pirate case. In making his alloca-
tion Pirate 3 must consider what would happen if he
loses the vote and there are just two pirates left. In
