My name is Abby Sine. I am a senior mathematics major attending West Virginia University in a program called WVUteach to certify as a secondary mathematics teacher. I develop this Webquest to help my geometry students learn a little bit about expected value since they are designing their own casino games in a unit on probability.
Introduction
As part of the request from Kassem O. at the Wheeling Island Casino, your design team must calculate the "financial outlook" of your designed casino games. But how do casinos know they will make money? If they are going to make money, how much should they expect to earn? You will answer these questions and more in the following Webquest, where you and your team will visit different websites and videos to learn about the mathematical concepts casinos use to make sure they won't be giving away free money.
Task
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The goal for this activity is to define expected value and relate it to the way casinos not only earn money, but can predict how much money they will make. Your task is to work with your game design team to 1) Understand and be able to apply the expected value formula, 2) Interpret the sign of the expect value in a game scenario, and 3) Be able to develop your own house edge so your casino game will be supported and featured by the Wheeling Island Casino.
As you move through the webquest, make sure to keep your own Google Document with solutions that you can submit (individually) to Google Classroom.
Process
Step 1: Start with this video to see a simple example of expected value.
Question 1: Define "expected value" in your own terms. Think back to what those terms mean in our everyday language.
Question 2: What would the interpretation of the expected value be if our Expected Value=4?
Step 2: Visit https://towardsdatascience.com/what-is-expected-value-4815bdbd84de and then watch:
Question 3: Why is the + or - sign when important when we are interpreting expected value?
Question 4: Based on the second video, do you think the casino wants its players to have a positive or negative expected value? Justify your answer.
Step 3: Go to https://math.info/Misc/House_Edge/ and read the introduction and Example #1.
Question 5: Where have we seen the values 2/38 = 1/19 before?
Question 6: Show the relation ship between -5.29% and -2/38.
Question 7: Why is the house edge positive when the expected value is negative?
Step 4: Visit https://www.888casino.com/blog/expected-value and look at the table of house edges.
Question 8: Look at the different levels of house edges. Do you see anything in common? Why do you think most casino games have a similar house edge?
Evaluation
Be sure to submit your answers to the eight questions in a Google Document on Google Classroom.
Conclusion
Congratulations design team! Now that you know a little bit about expected value and how casinos know they will make money, you can begin to define a house edge for your casino games!