Activity icon - Double or Nothing.png
 
 

Double or Nothing

How it works

In the game Double or Nothing, we have 3 cards:

  • One with a plus on both sides
  • One with a minus on both sides
  • One with a plus on one side and a minus on the other side

We put the 3 cards in a bag, and then we draw one at random. If the side facing up has a plus, we get +1 point. If the side facing up has a minus, we get –1 point.

For example, imagine we draw a card from the bag and the side facing up has a plus. We have +1 points for the round so far. Now we have a choice to make: We can either put the card back in the bag without looking at the other side, or we can flip the card over and get the points on the other side before putting the card back in the bag.

  • If we put the card back in the bag, then we get +1 point total for this round.
  • If we flip the card over, then:
  • If the other side has a plus, we get another +1 point, so we get +2 points total for this round.
  • But if the back has a minus, we get –1 point, which cancels out the +1 point from the front, and we get 0 points for this round.

What should your strategy be if you want to maximize your score?

In this activity, students start by playing Double or Nothing. They then investigate the chances of getting a plus or a minus when they flip the card over, and discover some surprising results. Students use these results to inform their strategy for playing Double or Nothing, and then explore why the chances come out the way they do. Students can also explore what happens when the distribution of cards in the bag changes!

Double or Nothing intro handout

Playing the Odds handout

Why we like this activity

  • It’s fun! Students enjoy playing the game and figuring out the strategy.
  • It helps students develop probabilistic and statistical reasoning.
  • It requires students to engage in mathematical habits of mind:
  • Making observations / making and testing predictions when investigating the odds.
  • Finding and using strategies based on the odds to maximize your score.
  • It has a low floor and a high ceiling: It's easy for students to get started playing the game, but finding an optimal strategy is more challenging, and there’s lots to explore about the relationship between the distribution of cards in the bag and the probabilities!