If you would like to visually play with a Markov chain model my non-profit research org built a Markov plugin for, CODAP, our data analysis tool:

https://codap.concord.org/app/static/dg/en/cert/index.html?d...

If you select drawing mode from the first screen shown and then click the "T" icon you can type some text and it will generate a state diagram for you that you can then "play" and examine the output sequences. If you have states that have multiple exit routes you can click on that state and adjust the probabilities of each option.