5 pirates discover 100 gold coins.
Their protocol for dividing the loot is as follows.
The most senior pirate proposes an allocation (how much each pirate should get). All the pirates vote. If at least half agree to the allocation, then that is the allocation.
Otherwise, the senior pirate is executed and the process is repeated with the remaining 4 pirates (the second-most-senior pirate proposes an allocation, etc.), then, if necessary, with the remaining 3 pirates, and so on. If it gets down to the least senior pirate, she gets it all.
Assuming that each pirate has the following priorities, what will the most senior pirate propose?
priorities, in order of importance:
1) stay alive
2) get as much gold as possible
3) kill as many other pirates as possible