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.
Comments
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.
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.