# Probability Games

In Nathan Kaplan's general education course EMR 14, "Fat Chance," students play games to connect the probability concepts learned in lecture to some fun activities that the students are familiar with. On some broader level, the goal is to see that probability is at work in lots of situations outside of the somewhat artificial classroom setting.

These activities requires dice and playing cards. For full instructions, see the four attachments below. Before the games, the students are supposed to be up to date on the homework which involved computing probabilities. With a larger section, the instructor breaks them into groups; in a smaller section he has them all in one larger group.

Professor Kaplan wrote a few worksheets focused on games involving dice and cards (see attached). For example, there is a popular game called Liar's Dice where several players each have several dice. In each round a player rolls his own dice and does not show them to anyone else. Players then make bids involving the number of dice that come up with a given denomination. For example, with 5 players each with three dice, an opening bid might be "I believe there are four sixes among these 15 dice". The next player in the circle must decide whether to make a higher bid or to 'challenge'. The class plays a few rounds and then answers some questions about the probabilities inherent in the game. The other worksheets are for the card game War, the dice rolling in the game Risk, the dice game Cee-Lo, and rolling a 20-sided die.

After playing the games, students try to figure out questions on the worksheets individually or in small groups and then discuss them as a class. The questions range in difficulty so that there are some that are too complex to answer in the time allotted.

Professor Kaplan says this allows the students to play a few rounds and get familiar with the game before starting to ask probability questions. Part of the point is to let them develop intuition through experience.

Our ABLConnect Curriculum Specialist notes: Instructors might consider including a model of the games before sending students off to do them.

 liars_dice.docx 112 KB risk_management.docx 86 KB three_dice_cee_lo.docx 110 KB the_art_of_war.docx 84 KB