The Mathematics of Game Shows

My mother loves watching Wheel of Fortune while my father is a Jeopardy lover.  Both play the game from the comfort of their chairs hoping they beat the contestant with the correct answer.  I figure its good for their brains because it exercises the brains and keeps them active.  When I watch, I think of the odds each player has of winning the game.

I'd love to teach a statistics class focused on the odds of winning various television games, especially the more popular ones. Most every game on television is based on the statistics of spinning the right space or choosing the right letter or number, or space.  All game shows are based on probability.

If you've ever seen Let's Make a Deal, you know they have one activity in which a person has a choice of selecting one door for a prize.  If they get the goat, it's over.  So the person chooses a door and the MC shows the goat  behind one of the other doors, indicating that one of the two left has the prize.  The person is then given the choice of keeping the door they chose or switch to the other one.  Most people stay with their choice because they feel they have a 50% chance of being right but mathematics indicates, it is better to switch because it increases your odds of winning.

I found a paper that sprinkles game show probabilities with information on regular probability. Its actually notes from a class but I like the way the author discusses various games throughout the paper.  The first two shows he discusses are Deal or No Deal, and the Price is Right with a short summary of each game.

As he introduces probability beginning with the basics such as sample space, followed by  expectations, counting, poker, inference, competition, backwards induction, and special topics, he sprinkles bits about various game shows and how certain parts apply to the topic.

For instance, when he introduces sample spaces, he discusses the squeeze play in the Price is Right.  In this game, you remove one digit, usually the first or last, to find the correct price.  He shows how the sample space applies to this particular situation.

As the author discusses various topics, he continues to apply probability to each situation which makes it more interesting because its not usual examples.  Back to the Price is Right and its 10 chances game.  The small prize has a two digit price but the contestant is given three digits,  the medium prize has a three digit price but given four digits and the big prize is made up of five digit price with no extra digits.  The object is to guess the correct price to win as many prizes as possible.

The author analyzes the probability of getting all the prizes and how to figure out the most likely prices based on mathematics.  The cool thing is that every example he sites, he's included a video clip so you can actually watch the activity he's talking about.

This 146 page paper is actually class notes form a class taught on The Mathematics of Game Shows from 2018.  I had a blast reading it but I plan to go back and read it in more detail.  Let me know what you think, I'd love to hear.  Have a great day.