You are the leader of 999 other pirates (making 1000 in total). You recently captured 1000 gold pieces and now need to divide the spoils between all your fellow pirates.
If a majority of the pirates agree with your scheme, then the gold will be distributed in that manner. If, however, majority disagree, then they will rebel and throw you overboard, leaving the next leader in line to propose a better plan which again will be voted upon. The leader will get the tie breaking vote.
You, like the rest of the pirates, are greedy and want the most for yourself. Your fellow pirates are all equally smart and will only vote for a scheme if they believe that is the most they will get. They will vote against you if they believe the next leader would propose a plan in their favour.
How much gold will you get to keep and how will you distribute the gold to the rest of your fellow pirates? Can you mathematically prove your solution is optimal?
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