I’ve finally had a bit of time to finish up the code for the Rock-Paper-Scissors bot discussed in the previous posts; I’ve put the code in a GitHub repository here. Feel free to file issues if you would like it to be a bit more user friendly.
The bot which uses the Fourier transform on move probabilities to search for profitable patterns is named `diaconis`, after Persi Diaconis. It’s currently working just fine, but is a bit slow computationally. On startup, it generates all possible move patterns that it will investigate during the course of each game, as well as some character tables. After each play, it tests some of these patterns, and tries to determine if their predictive power is better than any of the patterns seen thus far. If so, it begins using that pattern to choose move probabilities.
This works fine as a proof-of-concept of the basic ideas. Additional improvements could be had by doing some code optimization to speed things up a bit, and keeping a list of good patterns and allowing a bit more dexterity in switching between the patterns used for prediction.
As the strike drags on, I’ve had some time to actually do some maths. In particular, I’m preparing to run a weekly seminar on using representation theory for certain statistical problems. The plan is to work from some old lecture notes by Persi Diaconis entitled ‘Group Representations in Probability and Statistics.’ These deal with, for example, how long one should apply a random shuffling process before the thing which is being shuffled is well-mixed. Particular examples include the question of how many times one should shuffle a deck of cards, and how long one should let a random walk on Z_n run before we can be reasonably sure that every point has been reached. There are numerous real-world applications of the results, and it uses a lot of first-rate representation theory along the way!