The Pirate Gold Problem

The problem
5 pirates · 100 gold · senior proposes split12345≥½ votes (with tie-break) ⇒ proposal passeselse senior is thrown overboard

Five pirates, ranked 1 through 5 (1 is most senior), have looted 100 gold coins. Rules:

  • The most senior pirate proposes a distribution.
  • All pirates (including the proposer) vote yes or no.
  • If at least half agree (the proposer breaks ties), the proposal passes.
  • Otherwise, the proposer is thrown overboard, and the next most senior repeats.

Every pirate is perfectly rational and greedy. Each prefers more gold, prefers staying alive, and — all else equal — enjoys throwing crewmates overboard.

What does pirate 1 propose?

Tempting (but wrong)
intuition: split evenly12022032042052020, 20, 20, 20, 20 ✗

The common guesses:

  • "Split evenly: 20-20-20-20-20." Surely the senior has to bribe people to keep his head.
  • "Maybe 40 for himself, 15 for each of three others." A generous-but-skewed split.

Both miss that pirate 1 has total information about every future round, and can engineer a vote majority with minimal coins. The actual split is far more extractive.