Overview
This game-theory gem shows how backward induction — reasoning from the last possible outcome to the first decision — lets the top pirate keep almost everything.
How to solve The Pirates' Gold
- Solve the smallest case first: with two pirates, the senior keeps all 100.
- Step up one pirate at a time; each proposer buys the cheapest votes — those who'd get nothing otherwise.
- With five pirates, the captain bribes two of them with one coin each and keeps 98.
The key insight
Each pirate compares the current offer to what they'd get if the proposal fails. Knowing every downstream outcome, the proposer offers each ally exactly one coin more than their fallback — usually zero.
Variations & echoes
- Backward induction solves chess endgames, auctions, and bargaining alike.
- Changing the voting threshold or adding pirates shifts the split in surprising jumps.
Frequently asked questions
Why would a pirate accept just one coin?
Because the alternative — if this proposal is rejected — leaves them with zero. One coin beats nothing.