The Pirate Game: How to Keep 98 Coins and Survive the Vote
The Pirate Game: How to Keep 98 Coins and Survive the Vote
Five pirates find 100 gold coins. The captain proposes a split. Everyone gets a vote. Somehow, the captain can keep 98 coins and still get the plan accepted.
The trick is to ask what each voter expects after rejecting the proposal.
The ship's rules
Call the pirates A, B, C, D, and E, from most senior to least senior. A proposes first.
- Coins are indivisible, and the proposal must distribute all 100.
- Every remaining pirate votes, including the proposer. At least half must vote yes; a tied vote passes.
- Rejection sends the proposer overboard. The next pirate proposes a fresh split of the same coins.
- Pirates prefer survival first, then more coins. If survival and coins are equal either way, they prefer rejecting the proposer.
- Everyone reasons perfectly and knows that everyone else does too.
Those assumptions define the classic version presented in Waterloo's game-theory lesson . They are the rules of a puzzle, not a prediction about an actual crew.
Take the captain's chair
Start with an equal split, then try to keep more. Change the crew's offers and put the proposal to a vote. The captain automatically keeps the remainder. Reveal the solution when you want to inspect the reasoning.
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Work backward from the last pirate
With only E left, E keeps everything. With D and E, D's own vote is enough: D keeps 100 and E receives zero.
That makes E cheap to persuade in the preceding round. C offers E one coin, which beats the zero E would get under D. Continue that reasoning:
| Pirates remaining | Optimal split in seniority order |
|---|---|
| E | 100 |
| D, E | 100, 0 |
| C, D, E | 99, 0, 1 |
| B, C, D, E | 99, 0, 1, 0 |
| A, B, C, D, E | 98, 0, 1, 0, 1 |
This is the backward-induction solution also developed in the University of Houston's game-theory slides .
A wins with votes from A, C, and E. C and E each prefer one coin now to zero under B. D rejects: one coin from A would merely match D's next-round payoff, and equal payoffs favor rejection.
Change one rule, change the bargain
Switch the experiment to strict majority, where tied votes fail. Its calculation now produces a different five-pirate proposal: 97, 0, 1, 2, 0. This follows from the alternate rules in the model; it is not the classic table above.
The distinction begins with two pirates: the captain can no longer approve a proposal alone. Work forward again and every earlier bargaining position shifts.
This is a useful companion to deductive reasoning : make the assumptions explicit, solve the final decision, and reason backward. There are no coin tosses in this experiment. The uncertainty is in our intuition about incentives.