Come on down! Are you a fan of games shows such as The Price is Right, Who Wants to be a Millionaire, Let's Make a Deal, Jeopardy, Deal or No Deal, Wheel of Fortune, and more? Contestants on these shows are asked to make decisions which could win or cost them a lot of money, and mathematics can be used to figure out the best strategies. This course will explore these game shows while explaining the mathematics behind good decision-making.
Specific subjects to be covered include: probability and expected value; conditional probability and Bayesian inference; and classical game theory. The course will also have a heavy modeling component: some games are too complicated to analyze completely, but can be analyzed if you make some simplifying assumptions.
This class will teach real mathematics in a fun context. (Beware: "fun" does not mean easy.)
Instructor : Frank Thorne, LeConte 317O, thorne [at] math.sc.edu.
Office Hours: Monday 3:45-4:45, Tuesday and Friday 9:00-10:00. I am also frequently (but not always) available immediately after class.
Learning outcomes:
"Education is what survives when what has been learned has been forgotten." -- B.F. Skinner
Successful students will:
(Previous versions available upon request.)
Meeting schedule : TTh, 2:50-4:05, Honors Residence Hall B111.
There will also be a special presentation on Friday, October 21, in Sloan 112, at 4:00, by Bill Butterworth of DePaul University, who was previously a mathematical consultant for The Price Is Right.
Attendance is expected unless you have a prior excuse. If you would like to go to dinner with the speaker, please let me know in advance.
Grading :
You will be graded both on correctness and on quality of exposition. The standard is that someone who doesn't know the answer should be able to easily follow your work. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.
You are guaranteed at least the following grades: A for 88%, B+ for 83%, B for 76%, C+ for 70%, C for 64%, and D for 50%.
% of grade | |
Homework: | 30% |
Weekly Feedback: | 10% |
Participation: | 10% |
Term Project: | 20% |
In-class midterm: | 10% |
Final exam: | 20% |
Homework : Homework will be assigned and graded up to weekly. You are welcome to work with others but you are responsible for your own written solutions. You are always welcome, and strongly encouraged, to come to office hours or stick around after class, show me your written up solutions to homework problems, and ask whether they are correct.
Weekly Feedback : I have never taught a course like this before. As far as I know, nobody else has, ever. I have to create all my course materials from scratch.
You are responsible for helping me do a good job. Every week (by Friday at 5:00 pm), an e-mail is due reflecting on the lectures, course notes, and/or homework assignment. What are you struggling with? What do you enjoy, and what is boring? Is there anything in the lecture notes which you don't think is adequately explained?
Being brief is okay, but you're expected to say something more substantial than "Good job, no comments!" Weeks without lectures on both Tuesday and Thursday are exempt, and in addition you may skip at most two weeks. This is not only for my benefit, but also very much for yours. Reflecting on your own learning will help you cement your study habits and assist with retention of the material for years to come.
Participation : Active participation in the course is also very important. The most obvious (and most highly recommended) way to fulfill this requirement is to actively participate in class discussions and ask questions during class. You may also fulfill this requirement by periodically coming to office hours to ask questions, by e-mailing me with your questions, or by being particularly thorough in your weekly feedback.
Term Project : You are also responsible for a term project. Generally, this will involve analyzing a game (or a part of a game), writing a short paper on it, and making a 10-15 minute presentation to the class. You are welcome to work with others if you like.
I recommend (but do not require) that you use software called LaTeX for writing up your term project. Here are some resources and some Windows downloads. If you use a Mac, this is the software which I use and which you can download.
Here is a sample of how your term project might be formatted if you use LaTeX, together with a description of how to get started using LaTeX. This is the .tex file which was used to produce this document, and here is the same file renamed .txt, so that a web browser will open it immediately.
You can also download the TeX file for the course notes above -- if you see something in the notes you want to imitate, you can see how I did it.
Exam schedule :
Requirements: There are no formal prerequisites for the class, although the more mathematical background you have (especially in topics like probability, statistics, or discrete math) the better.
You don't need to have taken calculus. That said, you should feel your background is easily sufficient to take Honors Calculus I (Math 141H) if you have not done so already (or taken AP Calculus). If that sounds difficult, this course will be too.
Calculators are permitted but not required, including on the exams. A four-function calculator is more than adequate; graphing functionality won't be useful. Programming functionality is not permitted on the homework or exams. If you bring a programmable calculator to the exams, you are bound by the Honor Code not to use this functionality.
Access to the internet is required. Many of the course videos will refer to clips from game shows which are on Youtube. You must be able to watch these (with sound). Try the links below and make sure you can see and hear everything.
Make-up policy :
If you have a legitimate conflict with any of the exams it is your responsibility to inform me at least a week before the exam. Otherwise, makeups will only be given in case of emergency.
Accommodations :
Please contact the Office of Student Disability Services if you have any sort of disability which requires any sort of accommodations. I am always happy to follow their recommendations; it is your responsibility to inform me at least a week before the exam.
This will be updated with much more detail as the course progresses.
Such computations are at the root of most of what we will do.
Expectation. The expected value of a game is the average amount of money you expect to win, with each possibility weighted by its probability. You're playing Who Wants to Be a Millionaire. Quit or keep going? Do you press your luck?
We will also look at limitations to what the mathematics says about human behavior. Would you rather have $900,000, or a one-in-ten chance at $10,000,000?
You actually can't answer this without making additional assumptions. We will discuss Bayes' theorem and Bayesian inference and watch old episodes of Let's Make a Deal. We will of course discuss the Monty Hall Problem, which actually did not appear on the show.
Multi-player Strategy. Special considerations are required if you are competing with other players -- especially if you all play simultaneously.
Here is a round of Final Jeopardy. Perhaps an English class would be most helpful here, but the math question here is: how much should you wager?
Modeling. Try and figure out the optimal strategy for Switcheroo. I dare you. (The rabbit hole runs very deep.) You are going to have to make some simplfiying assumptions if you want to get started at all. Which are useful to make?
Student Presentations and Conclusion.