Last year, I received a paper from Prof. Henk Tijms of the Vrije University Amsterdam on using stochastic dynamic programming to analyze some simple dice games (pdf version available). A few years ago, I tried to do something similar with an analysis of a game I called Flip, but which is more commonly known as “Close the Box” (the paper appeared in INFORMS Transactions on Education). Both Tijms’ work and mine spend a fair amount of time discussing how well certain easy heuristics do relative to optimal decision making in simple games. Ideally, heuristics would get good, but not optimal solutions: that would make the game challenging as players tried to come up with better and better heuristics. For “Close the Box”, while the optimal decision was quite subtle, some simple heuristics got pretty close (perhaps too close to discern the difference). These games make good classroom demonstrations and even better mini-projects for summer schools and the like. Tijms’ paper was written for a journal aimed at students.
Tijms has also done the field a great service by making his software for applied probability available, which are good tools for education. Check it out at his web page.