Greedy Sadistic Pirates

PS: Other places around the internet where a version of this puzzle has been discussed:

  1. https://en.wikipedia.org/wiki/Pirate_game
  2. https://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-the-pirate-booty/
  3. https://waitbutwhy.com/2016/06/pirate-booty-puzzle.html
  4. https://www.thebigquestions.com/2015/09/10/are-you-smarter-than-google-part-three/ (points out the multiple equilibria problem, where everyone can vote against their own interest because everyone else is and so no one’s vote matters; the concept of trembling-hand perfect equilibrium fixes that)