A new article by Jan Vrbik called "Betting Two Patterns against Each Other" was recently posted in The Mathematica Journal, which contains some ideas for exploring probability that other faculty may be interested in replicating in their classroom. Here is the abstract:
We present a technique for computing the probability that a specific pattern of successes and failures is generated randomly before another such pattern, thus winning the corresponding game. The program we build for this purpose finds the mean and standard deviation of the number of trials needed to complete one round of such a game. It can be used to maximize the probability of winning a game by choosing the best possible pattern and also by adjusting the probability of a success. Finally, we verify our theoretical results by a Monte Carlo simulation.
You can download the CDF of the article here:
http://www.mathematica-journal.com/data ... tterns.cdf