Penney Ante
It explains a phenomenon of a coin tossing game called Penney Ante
..., it is not in general. There is no best pattern that beats all others. The best we can do is let our opponent go first and then choose the best possible option that beats his particular pattern. To do so we need to be able to define relations between each two patterns. And this is where the fun begins.
To run the project use PenneyAnte.nb
Open .nb files using Mathematica. You can also use CDF Player but in this case .nb files will not function interactively.
See wiki for a full project description.