There are 5 rational pirates (in strict order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them. The pirate world’s rules of distribution say that the most senior pirate first proposes a plan of distribution. The pirates, including the proposer, then vote on whether to accept this distribution. If the majority accepts the plan, the coins are disbursed and the game ends. In case of a tie vote, the proposer has the casting vote. If the majority rejects the plan, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. The process repeats until a plan is accepted or if there is one pirate left.[1] Pirates base their decisions on four factors. First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins each receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.[2] And finally, the pirates do not trust each other, and will neither make nor honor any promises between pirates apart from a proposed distribution plan that gives a whole number of gold coins to each pirate.

It might be expected intuitively that Pirate A will have to offer the other pirates with most of the gold to increase the chances of his plan being accepted. However, this is quite far from the theoretical result. When each of the pirates votes they won’t just be thinking about the current proposal, but all other outcomes down the line. Also because the order of seniority is known in advance, each of them can accurately predict how the others might vote in any scenario. This is apparent if we work backwards. The last possible scenario would have all the pirates except D and E thrown overboard. Since D is senior to E, he has the casting vote. So D would obviously propose to keep 100 for himself and 0 for E, and so this is the allocation. If there are three left (C, D and E) C knows that D will offer E 0 in the next round; therefore, C has to offer E 1 coin in this round to win E’s vote, and get C’s allocation through. Therefore, when only three are left the allocation is C:99, D:0, E:1. If B, C, D and E remain, B considers being thrown overboard when deciding. To avoid being thrown overboard, B can simply offer 1 to D. Because B has the casting vote, the support only by D is sufficient. Thus B proposes B:99, C:0, D:1, E:0. One might consider proposing B:99, C:0, D:0, E:1, as E knows it won’t be possible to get more coins, if any, if E throws B overboard. But, as each pirate is eager to throw the others overboard, E would prefer to kill B, to get the same amount of gold from C. Assuming A knows all these things, A can count on C and E’s support for the following allocation, which is the final solution: A: 98 coins B: 0 coins C: 1 coin D: 0 coins E: 1 coin[2] Also, A:98, B:0, C:0, D:1, E:1 or other variants are not good enough, as D would rather throw A overboard to get the same amount of gold from B.