The five pirates
have found another 500 gold coins and wonder how to split them up. This time they say that unless a majority
(more than 1/2) say yes to a plan, the one that proposed that plan will get killed and they will move on to the next plan. The order of plan making starts with 5, then 4, 3, 2, 1.
The pirates will try above all else to stay alive, even if it means accepting no coins. If they will stay alive either way, they would like the most coins possible. Also, the pirates have been on board the ship for a while and are getting tired with each other, so if faced with the decision to reject a plan or keep it, they will reject it if nothing else matters more to them.
What should Pirate 5's offer be?
Just pirate 1: everything to himself.
Pirates 1 and 2: 2 proposes to give all to pirate 1. Anything else and pirate 1 will vote no since he can get more if he is alone.
Pirates 1 through 3: 3 proposes 499 for himself, 1 for pirate 2 and nothing for pirate 1. Pirate 2 will vote for the plan, since if pirate 3's plan is rejected he will end up with nothing.
Pirates 1 through 4: 4 proposes 497 for himself, 2 for pirate 2 and 1 for pirate 1. 1 and 2 will vote yes since the each get more than if pirate 3 was in charge.
All 5 pirates: 5 proposes 497 for himself, nothing for pirate 4, 1 for pirate 3, nothing for pirate 2 and 2 for pirate 1. Pirates 3 and 1 vote yes since it is more than either will if pirate 4 was in charge.