# Egg Russian Roulette – A Cracking Probability Lesson

On Friday morning I was sitting at home having coffee before I left for school, still dissatisfied with my most recent lesson with my usually receptive Year 8 class. I had them first block that morning and felt like I really needed to reconnect them with not only the concept of dependent probability but also to the purpose it serves beyond being able to tell the likelihood of something happening. On Monday, I had an awesome introduction lesson with them in which I used a classic activity I’ve used with many of my classes in the past: Egg Roulette – Jimmy Fallon vs. Bradley Cooper. This is a truly mathematically rich 6.5 minutes that really highlights how, despite factual information about the likelihood of an event happening, we still are fooled by our own gut feeling about what “should” happen. If you haven’t seen this episode, both contestants pick up only cooked eggs for the first 6 rounds. In this task, I also introduce the structure of tree diagrams and, on Wednesday, I used another episode (where Ryan Reynolds is the guest) with an exit card to check procedural understanding and fluency. After two episodes in consecutive lessons, I was wary that the students could start becoming somewhat tired of the egg roulette routine and I decided not to use it at all in Thursday’s lesson. I went for a complete change of tune and lost them. Friday morning was my opportunity to bring them back.

In my mind, I kept returning to Egg Roulette and just couldn’t stay away from a few key elements it brings to a lesson:

• students can easily follow the probability of cooked/raw eggs
• The proportion of cooked/raw eggs continually changes as the game goes on
• There’s opportunities to guess the result each round
• It’s hilarious

I decided to change it up, but still use Egg Roulette. I decided to start a different episode at a point of the video where one player already had egg on their face and the other was just about to crack one on their’s. This gave them some information, but not everything right up front. Students essentially had to analyse the 30 second snippet to justify what happened before that point. It was awesome.

## Act 1

Play the video from 4:44 and stop it at about 5:13:

Record everything you notice, everything.

What is the story so far? Record a possible round by round summary. Write the probability for each round.

## Act 2

Students begin to sort through their notes on what they noticed. To try to figure out what happened in previous rounds, students have to determine what is information that will help them figure out what happened before the 4:44 mark and what were just general observations.

As a class, we recorded what students were willing to share on the board:

When someone else mentioned that “there are 5 eggs left”, Jack withdrew his comment that “Jimmy cannot win but he can draw”.

Some questions we went through were:

• What’s fact? What do we know for certain? How do we know?
• Imagine you’re a detective arriving on a crime scene. What information will help you figure out what led to this situation?
• Who started the game? How do you know?
• How many raw eggs are left? How do you know?
• When would’ve the first raw egg been cracked? How do you know? *I didn’t ask this question, but had it up my sleeve in case students were really struggling*

This all led into: what is the most probable story so far?

Give a possible round by round summary of the most likely result each instance.

### Act 3

Unveiling the most likely scenario. (Students came up with this themselves):

“C” = Cooked or Hard-boiled, “R” = Raw, “A” = Anna Kendrick, “J” = Jimmy Fallon

Key talking points were:

• Discussion about Round 5: When the odds are even, how do we know what result it should be?
• The key realisation that each of Anna’s rounds before Round 7 had to be cooked eggs.

The solution – play video from start. As the game continues past 4:44, ask for hand votes on cooked/raw.

This lesson, although it was a last minute decision to run the way I did, was the result of a lot of reflecting and thinking about how to make the learning meaningful for my students. It gave the students who were away during the week to “catch up” and, for those who were still not grappling the probability aspect of the game, gave them a second bite of the cherry. For everyone else, I really hoped it consolidated their understanding about dependent probability.