Imagine you’re a pirate on a ship with your captain, Amaro, and four other mates: Bart, Charlotte, Daniel, and Eliza. You’ve just found a treasure chest with 100 gold coins, and now you need to figure out how to split the loot. According to pirate rules, the captain, Amaro, gets to suggest how to divide the coins. Then, everyone, including Amaro, votes on his plan. If the majority agrees or if there’s a tie, the coins are split as proposed. But if most pirates disagree, Amaro loses his captaincy, and Bart gets a chance to propose a new plan. This continues with Charlotte, Daniel, and Eliza until a plan is accepted or only one pirate remains.
Each pirate wants to stay alive and get as much gold as possible. They don’t trust each other, so they can’t make deals beforehand. If a pirate thinks they’ll get the same amount of gold no matter what, they’ll vote against the captain just for fun. Also, each pirate is a master of logic and knows the others are too.
At first, it might seem like Amaro should offer most of the gold to the others to get their votes. But he can actually do better. Since all pirates are logical thinkers, they’ll consider all possible outcomes before voting.
Let’s start with Eliza, the last pirate in line. If it comes down to just her and Daniel, Daniel would propose to keep all the gold, and Eliza wouldn’t have enough votes to stop him. So, Eliza wants to avoid this situation.
Now, consider when there are three pirates left, and Charlotte is proposing. Everyone knows if Charlotte is outvoted, Daniel will get all the gold, leaving Eliza with nothing. To get Eliza’s vote, Charlotte only needs to offer her one coin. This way, Charlotte doesn’t need to give Daniel anything.
With four pirates, Bart needs just one other vote for his plan to pass. He knows Daniel wouldn’t want Charlotte to decide next, so Bart offers Daniel one coin, giving nothing to Charlotte or Eliza.
Back to the first vote with all five pirates. Amaro knows if he steps down, Bart’s plan would be bad for Charlotte and Eliza. So, Amaro offers Charlotte and Eliza one coin each, keeping 98 for himself. Bart and Daniel vote against it, but Charlotte and Eliza agree, knowing the alternative is worse for them.
This pirate riddle is a great example of game theory, which involves strategic decision-making. One concept here is common knowledge, where each pirate knows what the others know and uses this to predict their actions. The final distribution is a Nash equilibrium, where each pirate’s strategy is the best response to the others. Even if cooperation could lead to a better outcome, no pirate can benefit by changing their strategy alone.
In the end, Amaro keeps most of the gold, and the other pirates might need to find better ways to use their impressive logic skills in the future.
Imagine you’re one of the pirates. Form groups of five and role-play the scenario. Each student takes on the role of a pirate and proposes a plan to divide the gold. Discuss and vote on each proposal, considering the logic and strategy involved. This will help you understand the decision-making process and the importance of strategic thinking.
Using the pirate riddle as inspiration, create your own logic puzzle involving a group decision-making scenario. Swap riddles with classmates and try to solve each other’s puzzles. This activity will enhance your creativity and logical reasoning skills.
Research another example of game theory, such as the Prisoner’s Dilemma or the Tragedy of the Commons. Present your findings to the class, explaining how strategic decision-making is applied in your chosen example. This will deepen your understanding of game theory concepts.
Work in pairs to come up with different strategies for dividing the 100 gold coins among the pirates. Analyze each strategy to determine which pirate benefits the most and why. Share your findings with the class to see the variety of logical approaches.
Participate in a class-wide competition where you solve a series of logic puzzles, including variations of the pirate riddle. Compete to see who can solve the puzzles the fastest and with the most accuracy. This will sharpen your problem-solving skills and encourage friendly competition.
Here’s a sanitized version of the transcript:
—
It’s a good day to be a pirate. Amaro and his four mates, Bart, Charlotte, Daniel, and Eliza, have struck gold: a chest with 100 coins. But now, they must divide the treasure according to the pirate code. As captain, Amaro gets to propose how to distribute the coins. Then, each pirate, including Amaro himself, gets to vote either in favor or against the proposal. If the vote passes, or if there’s a tie, the coins are divided according to the plan. But if the majority votes against it, Amaro must step down, and Bart becomes captain. Then, Bart gets to propose a new distribution, and all remaining pirates vote again. If his plan is rejected, he steps down as well, and Charlotte takes his place. This process repeats, with the captain’s role moving to Daniel and then Eliza until either a proposal is accepted or there’s only one pirate left.
Naturally, each pirate wants to stay alive while getting as much gold as possible. However, since they don’t trust each other, they can’t collaborate in advance. Additionally, if anyone thinks they’ll end up with the same amount of gold either way, they’ll vote against the captain just for fun. Finally, each pirate is excellent at logical deduction and knows that the others are too.
What distribution should Amaro propose to ensure his survival?
If we follow our intuition, it seems like Amaro should try to offer the other pirates most of the gold to increase the chances of his plan being accepted. But it turns out he can do much better than that. Why? The pirates all know each other to be top-notch logicians. So when each votes, they won’t just be thinking about the current proposal, but about all possible outcomes down the line.
Because Eliza’s last, she has the most outcomes to consider, so let’s start by following her thought process. She would reason this out by working backwards from the last possible scenario with only her and Daniel remaining. Daniel would obviously propose to keep all the gold, and Eliza’s one vote would not be enough to override him, so Eliza wants to avoid this situation at all costs.
Now we move to the previous decision point with three pirates left and Charlotte making the proposal. Everyone knows that if she’s outvoted, the decision moves to Daniel, who will then get all the gold while Eliza gets nothing. So to secure Eliza’s vote, Charlotte only needs to offer her slightly more than nothing, one coin. Since this ensures her support, Charlotte doesn’t need to offer Daniel anything at all.
What if there are four pirates? As captain, Bart would still only need one other vote for his plan to pass. He knows that Daniel wouldn’t want the decision to pass to Charlotte, so he would offer Daniel one coin for his support, keeping nothing for Charlotte or Eliza.
Now we’re back at the initial vote with all five pirates present. Having considered all the other scenarios, Amaro knows that if he steps down, the decision comes down to Bart, which would be bad news for Charlotte and Eliza. So he offers them one coin each, keeping 98 for himself. Bart and Daniel vote against it, but Charlotte and Eliza grudgingly vote in favor, knowing that the alternative would be worse for them.
The pirate game involves some interesting concepts from game theory. One is the concept of common knowledge, where each person is aware of what the others know and uses this to predict their reasoning. The final distribution is an example of a Nash equilibrium, where each player knows every other player’s strategy and chooses theirs accordingly. Even though it may lead to a worse outcome for everyone than cooperating would, no individual player can benefit by changing their strategy.
So it looks like Amaro gets to keep most of the gold, and the other pirates might need to find better ways to use those impressive logic skills.
—
This version removes any inappropriate language and maintains the essence of the original content.
Pirate – A player in a game who tries to take advantage of others, often by breaking rules or acting selfishly. – In the game theory scenario, the pirate decided to keep all the treasure for himself, ignoring the needs of the other players.
Gold – A valuable resource or reward that players aim to acquire or maximize in a game. – The players used their strategies to collect as much gold as possible to win the game.
Vote – A method used by players to make a collective decision or choose between different options. – The team had to vote on the best strategy to defeat their opponents.
Plan – A detailed proposal or strategy designed to achieve a specific goal in a game. – The players spent time developing a plan to outsmart their competitors.
Logic – A systematic way of thinking that helps players make sound decisions based on reasoning. – Using logic, the player deduced the best move to ensure victory.
Outcome – The result or consequence of a player’s actions or decisions in a game. – The outcome of the game depended on the final move made by the team.
Strategy – A plan of action designed to achieve a long-term or overall aim in a game. – Developing a strong strategy was crucial for winning the chess match.
Decision – A choice made by a player that can affect the direction or result of a game. – The player’s decision to cooperate with others led to a shared victory.
Theory – A set of principles on which the practice of an activity is based, often used to predict outcomes in games. – Game theory helps players understand the best strategies to use in competitive situations.
Knowledge – Information and understanding that players use to make informed decisions in a game. – Having knowledge of the opponent’s tactics gave the player an advantage.
