Let us imagine five self-interested, rational and bloodthirsty pirates. They have recently found a treasure of 100 gold coins. Now the captain, being the most well-respected, has to propose how to split the treasure among themselves. After he makes his proposal all pirates vote to accept it. If majority of pirates vote yes, then the treasure is split as proposed. But if not, then the captain is executed and new captain is appointed. This new captain will make a new proposal. Having in mind that succession order is known to all pirates devise a strategy for the initial captain. He should retain as much treasure as possible, but stay alive.
Note that if votes are tied, the tie is broken according to captains vote. So we can hint you to start solving the problem backwards. Let us assume that only two pirates are left. In such case captain (P4) could keep all the treasure to himself as votes would equally split (1 on 1). So try to imagine how the previous captain (P3) could have used this information in order to retain his life? What about P2? Original captain? You can try your solution using applet below.