Can you solve the pirate riddle? - Alex Gendler

• Category: Video
• Date: 2026-01-08
• Rating: 5/5
• Link: YouTube - Can you solve the pirate riddle?

The Video

About

It’s a resting day on the pirate ship. The five pirates: Amaro, Bart, Charlotte, Daniel, and Elizabeth have found a treasure chest with 100 gold coins. They must decide how to partition them.

Pirates are ranked by seniority: Amaro is #1, Bart is #2, Charlotte is #3, Daniel is #4, and Elizabeth is the most junior, #5.

The rules of pirate democracy are as follows: the most senior pirate proposes a distribution. Then, everyone, including the proposer, votes. If at least 50% of the pirates agree, the gold is distributed as proposed. If not, the proposer is thrown overboard, and the process starts again with the next most senior pirate.

Pirates are perfectly rational, but they also have a hierarchy of goals:

1. Stay alive.
2. Maximize their own gold.
3. If all else is equal, they prefer to see others thrown overboard.

Can you figure out what Amaro should propose?

The Solution

To solve this, we work backward from the most junior pirates:

1. Two Pirates (Daniel, Elizabeth): Daniel needs only 50% of the vote. He votes for himself and wins. He takes all 100 coins, and Elizabeth gets 0.
2. Three Pirates (Charlotte, Daniel, Elizabeth): Charlotte needs one other vote. She knows Elizabeth will get 0 if it goes to Daniel's turn, so she offers Elizabeth 1 coin. Elizabeth accepts. Distribution: 99, 0, 1.
3. Four Pirates (Bart, Charlotte, Daniel, Elizabeth): Bart needs one other vote. He knows Daniel gets 0 in Charlotte's plan, so he offers Daniel 1 coin. Daniel accepts. Distribution: 99, 0, 1, 0.
4. Five Pirates (Amaro, Bart, Charlotte, Daniel, Elizabeth): Amaro needs two other votes besides his own. He knows Charlotte and Elizabeth both get 0 in Bart's plan. By offering them each 1 coin, they are better off and will vote with him.

Final Proposal:

• Amaro: 98 coins
• Bart: 0 coins
• Charlotte: 1 coin
• Daniel: 0 coins
• Elizabeth: 1 coin