I flip a coin $n$ times, at each toss I count how many heads and how many tails have come out so far.
An example with $n=4$ might be:
Heads Tails 1 0 1 1 (here I count 1 tie so far) 2 1 2 2 (and here I count a total of 2 ties)
In this run, I get 2 ties total.
Now my question is, assuming I flip the coin an even number of times, what is the expected value for the amount of ties total after $n$ coin tosses, in terms of $n$?