1 Wendy: How be we splittin' the treasure, cap'n?
1 Long Tom: The traditional pirate way, Wendy!
2 Long Tom: We be rankin' all crew, then I be makin' a sharin' proposal. The crew be votin' to be acceptin' or to mutiny, be killin' me, and be promotin' each pirate.
3 Wendy: Ye be relyin' on the crew bein' perfeckly logical, cap'n. {angry crew wielding weapons back her up}
4 Long Tom: <sigh> Equal shares?
4 Crew: Arrrrr!!!

This refers to a somewhat famous logic puzzle that goes something like this:

There are N pirates, ranked in some order (oldest to youngest, fiercest to least fierce, by crew seniority, whatever, so long as no two have the same rank). They acquire a treasure of G pieces of gold (or silver, or whatever). According to some strict rule that they all agree to follow, they split the treasure as follows:

The highest-ranked pirate proposes a split of the treasure, stating how many coins each pirate will get. Then the pirates all vote to accept or reject the proposal. If at least half the pirates accept, they all abide by the proposed split. But if a majority reject the proposal, they gang up to kill the highest ranked pirate. Everyone moves up a step in the rankings, and the process begins again with the newly appointed highest ranked pirate.

Each pirate is further characterised as being unequivocally greedy (i.e. each pirate will do whatever course of action guarantees a greater monetary reward for himself, with no regard for anyone else, but within the rules of the sharing agreement), bloodthirsty (i.e. given the choice between two otherwise equal outcomes, will prefer the one that allows him to kill someone), and - this is the really important one - flawlessly logical.

The question is, what split of the treasure should the senior pirate propose to ensure he is not killed?

Most formulations of the puzzle set the number of pirates N to 5, and the number of gold pieces G to 100. At this point, it would be useless for me to continue explaining the puzzle, or to describe its somewhat surprising solution, since it has been written up in some detail in many places:

• Wikipedia: Pirate game
• H2G2: The Pirate Game: A Logic Puzzle
• Everything2: Five Pirates Problem
• Google search for: "five pirates" problem

The solution is highly counter-intuitive, and often prompts responses of "that would never happen in a real situation with five real people". And indeed it wouldn't. For the simple reason that, although human greed and bloodthirstiness can be relied on, people are not flawlessly logical.

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2017-12-13 Rerun commentary: Continuing directly on from the original annotation above:

But we all know that fictional pirates are a all perfectly logical. After all, if you lived in a fictional world and were perfectly logical, what career option would you choose?

Exactly! There is no other sensible choice! Arrrrrr!!!!