Five pirates are to divide 1000 coins from a pillaged ship. They decide to divide it like this: the strongest pirate suggests a division, and then all pirates (including the one who suggested) vote on it. If majority accepts, then the division is done. Otherwise, the strongest pirate is killed, and the second strongest pirate makes a suggestion. They vote on it as well, with the same procedure. Note that in case of a tie the suggestion is accepted.
Assume the pirates are very smart and their priorities are (1) living (2) getting money (3) killing other pirates. Furthermore assume that the pirates are highly inteligent and they will always make the optimum choice, and they know that the others are intelligent, and they know that they know, ad infinitum.
What should the strongest pirate suggest to maximize his gains?