[taterbase]

Awesome intro! I've used Markov Chain libraries before but never took the time to try and understand them. This makes a lot of sense.

Are there different or more efficient probability calculations that can be done other than the provided algorithm? It seems somewhat simple.

[tantalum]

Yes there are more complex probabilities that you can calculate. For example you can calculate the probability of reaching some state that is one or more transitions away given a starting state. You can find more info on some of other calculations you can do on Wikipedia.