Archipelago
How it works
Archipelago is a 2-player game. Here's how to play:
We start with some dots in a row.
The players take turns taking dots.
Each turn, you can either take one dot or you can take two dots that are next to each other.
Whoever takes the last dot (or dots) wins!
Can you beat an expert at this game?
In this activity, students start by playing the game against each other. Next, they play against a computer that has been programmed to be an expert.
First, they play against the computer with only 3 dots. When they’re confident they can beat the computer every time with 3 dots, they move on to play against the computer with 4 dots, and they keep going from there.
Why we like this activity
- It’s fun! Students enjoy playing the game and figuring out the strategy.
- It helps students develop algorithmic and game-theoretic reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies to win the game.
- Making observations / looking for patterns / making and testing predictions / understanding and explaining when trying to develop a more powerful strategy.
- It has a low floor and a high ceiling: It's easy for students to get started playing the game, but beating an expert is challenging, especially as the number of dots increases!