The Pirate Game
Five pirates must divide 100 gold coins. The most senior proposes, majority rules, and losers walk the plank. The shocking result: the first pirate claims 98 coins—and survives!
The Rules of Pirate Democracy
Five perfectly rational pirates (A, B, C, D, E in order of seniority) have found a treasure of 100 gold coins. They must divide the loot according to ancient pirate code:
- The most senior pirate proposes a distribution of the coins
- All pirates vote (including the proposer)
- If at least 50% approve, the coins are distributed as proposed
- If majority rejects, the proposer is thrown overboard (dies!), and the next pirate proposes
- Pirates are bloodthirsty: if indifferent between outcomes, they vote to kill
Pirate priorities (in order):
- Stay alive
- Maximize gold
- Kill other pirates (if it doesn't affect 1 or 2)
Backward Induction Walkthrough
Step 1 of 4Click "Next Step" to see how backward induction solves this puzzle. We start at the END and work backwards!
| Scenario | A | B | C | D | E |
|---|
The Shocking Logic
🏴☠️ The Key Insight
Each pirate can calculate what happens if the current proposal fails. A pirate who would get 0 coins in the next round will accept even 1 coin now—it's better than nothing!
Pirate A (the most senior) exploits this perfectly:
- A keeps 98 coins for himself
- C gets 1 coin (C would get 0 if B proposes, so 1 > 0)
- E gets 1 coin (E would get 0 if B proposes, so 1 > 0)
- B and D get nothing (they'd vote no anyway—B wants to propose, D gets 1 from B)
The vote: A (yes), C (yes), E (yes) = 3 votes = 60% approval. A survives with 98 coins!
Why This Feels Wrong
Your intuition probably screams that this is unfair. Surely the other pirates would band together to reject such a greedy proposal?
But they can't. Each pirate acts individually and rationally. C and E know that if they reject A's offer:
- A dies (satisfying their bloodthirst)
- B proposes (99 : 0 : 1 : 0)
- C gets 0, E gets 0
So C and E each face a choice: 1 coin now, or 0 coins later. Even though A's proposal is "unfair," accepting it is the rational choice.
What About More Pirates?
The pattern becomes even more extreme with more pirates:
| Pirates | First Pirate Gets | Distribution Pattern |
|---|---|---|
| 5 | 98 coins | 98, 0, 1, 0, 1 |
| 6 | 98 coins | 98, 0, 1, 0, 1, 0 |
| 7 | 97 coins | 97, 0, 1, 0, 1, 0, 1 |
| 200 | 1 coin | 1, 0, 1, 0, 1, 0, ... (99 others get 1) |
| 201+ | 0 coins | First pirate dies! Can't buy enough votes. |
With 200 pirates, the first pirate can barely survive by giving 1 coin each to 99 others. With 201 or more, even giving away all 100 coins isn't enough to buy a majority—the first pirate is doomed!
Real-World Applications
The Pirate Game illustrates principles that apply far beyond treasure division:
- Legislative bargaining: How majority coalitions form and why some members get more
- Corporate negotiations: Why first-mover advantage matters in deal-making
- International treaties: How to build minimum winning coalitions
- Auction theory: Understanding what the "pivotal" bidder needs to win
Origins
The Pirate Game was introduced by game theorist Steven J. Brams and is discussed in Ian Stewart's "Mathematical Recreations" column in Scientific American (May 1999). It's a variant of the "ultimatum game" and "dictator game" studied in behavioral economics.
The puzzle demonstrates backward induction, a fundamental technique for solving sequential games where players can observe all previous moves.