> I agree with most of your comment, but this part is misleading: >> This means that every state is recurrent, i.e. will happen if you wait long enough. > It

> I agree with most of your comment, but this part is misleading: >> This means that every state is recurrent, i.e. will happen if you wait long enough. > It doesn't mean that the expected frequency of every state in the chain is equal. Moreover, the frequencies are very different. I do not find it misleading; I do not see how you equate "if you wait long enough it will happen" with "every state is equally likely" or "the average waiting time to get to any state is the same" (which may or may not be equal depending on your where you consider your starting point).