A number of memorable tasks have been revealed through collegial exchanges with underlying philosophical, theoretical, and potentially nefarious motivations. Such was the origin of the probability problem, and the various differences of opinion, presented herein. This article recounts how, together, we explored and disputed the probabilities…

The "Borel" board game consists of a series of experiments involving dice rolls, coin flips, or drawing colored balls from bags. Before each experiment is conducted, each player bets for or bets against a statement regarding the random outcome. We suggest that the collection of "Borel" experiments be used as a resource to…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

The Price is Right Bidder's Row and games provide many opportunities for mathematical connections. The Price is Right website has videos or pictures for students to see how each game is played (http://www.priceisright.com/games/). This article will describe the mathematics of probability and statistics that is integrated in the famous television…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

In this paper, the dice game "Unders and Overs" is described and presented as an active learning exercise to introduce basic probability concepts. The implementation of the exercise is outlined and the resulting presentation of various probability concepts are described.

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

We walk through a module intended for undergraduates in mathematics, with the focus of finding the best strategies for competing in the Showcase Showdown on the game show "The Price Is Right." Students should have completed one semester of calculus, as well as some probability. We also give numerous suggestions for further questions that…

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3,...., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7. 8,..., 70 occur equally often. We investigate such relabelings for "pq"-sided dice, where "p" and "q" are distinct primes, and show that these relabelings usually…

We describe how the use of a games environment combined with technology supports upper primary children in engaging with a concept traditionally considered too advanced for the primary classes: "The Law of Large Numbers."

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

This article shows a generalization of Galileo's "passe-dix" game. The game was born following one of Galileo's [G. Galileo, "Sopra le Scoperte dei Dadi" (Galileo, Opere, Firenze, Barbera, Vol. 8). Translated by E.H. Thorne, 1898, pp. 591-594] explanations on a paradox that occurred in the experiment of tossing three fair "six-sided" dice.…

Mutual support societies for problem gamblers have existed in Sweden for 20 years. They have helped more people with gambling problems than any other institution inside or outside the Swedish health care system. This paper outlines the background of these societies and describes the meetings of one of them. Data come from interviews with members…