# Understanding Markov Chain by Comparing “First Order Sequence Model” and “Second Order Sequence Model”

Apr 27, 2023

First, let’s assuming we have a book, count follow sentences in a book:

- Check whether the battery
**ran**down please. - Check whether the program
**ran**please.

Totally, they appeared for 100 times; the first line appeared for 40 times and second for 60 times.

Our goal here is to **predict next word after word “ran”.**

- First Order Sequence: only look at “ran” , so next word could be “down” (.4 probability) and “please”(.6 probability).

- Second Order Sequence: look at two words, “ran down” + “please” (1 probability) and “program ran” + “please” (1 probability). Comparing with above .4 and .6, the predicting rate is improved.