Odd One Wins
How it works
Odd One Wins is a 2-player game. Here's how to play:
- We start with an odd number of dots.
- The players take turns taking dots and putting them in their bank.
- Each turn, you can either take 1 dot or 2 dots.
- Whoever ends up with an odd number of dots in their bank 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. Their goal is ultimately to be able to beat an expert with any number of dots as long as they get to decide whether they go first or second.
Why we like this activity
- It’s fun! Students enjoy playing the game and trying to figure out how to beat an expert.
- It helps students develop algorithmic and game-theoretic reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies to beat an expert with a given number of dots.
- Making observations / comparing and contrasting / looking for patterns / making and testing predictions / finding and using strategies when trying to beat an expert with any number of dots.
- Understanding and explaining your strategy for beating an expert with any number of dots.
- It has a low floor and a high ceiling: It's easy for students to start playing the game by trial and error, but beating an expert is more challenging, especially as the number of dots increases!
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.