How to Gamble if You Must

Paul Zeitz took the lead on this activity for the 2012 Circle on the Road festival.

AUDIENCE: Middle and High School?

Topics will cover non-transitive dice, gambler’s ruin, Kruskal count, Sicherman dice, St. Petersburg paradox



I’m not quite sure of the facilities, time window, audience, etc., but I envision—at least right now—many possible self-contained or connected activities at various levels. The main types of activities are:

1) Creating and analyzing “sucker bets” (why casinos work so well for casino owners)
2) Creating and analyzing magic tricks
3) Learning about probability “paradoxes”
4) (if feasible) an introduction to Sage, an open-source, free computing platform that anyone in the world can run on any computer using a web browser.

The mathematical themes are:
1) random walks
2) expected value
3) conditional probability

We should probably talk on skype soon about how to proceed. I am attaching the handout that I used with teachers this week. We didn’t do all the problems, of course.

I think all the activities sound good. I really like the non-transitive dice, since that can be done at different levels, and can be played in groups too. The St Petersburg paradox could be very lively (if a computer is available) with some fun expected value problems to prepare for it. I saw the Kruskal count done with cards, and it is a very surprising trick, and might be a great one to finish with. I’m not sure how much you can go into explanations, maybe like the explanation in the AMS feature column here?

What do you usually do? Would you include some other magic tricks before that?

I haven’t seen Sicherman dice before, but it seems really cool. I have a math circle on Wednesday with a group of middle and high school students, and would be happy to try some of these activities.

Best regards,