thermodynamics - Why doesn't the entropy increase when two similar gases mix with each other?

Entropy increases when two substances mix with each other.

For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$

But, the entropy doesn't increase when the two gases mixing are same.

This is pointed by Daniel V Schroeder:

It's important to note that this result applies only if the two gases are different like helium and argon. If you start with the same gas on both sides, the entropy doesn't increase at all when you remove the partition.

Now, why is this so? Both the gases, though the same, increase their individual entropies when they expand, don't they?

So, why did Schroeder say there is no entropy of mixing? What actually happens such that there is no change in entropy when the gases are the same?