How to set Alphas per Face ID using Random Texture node

Here is the render for context:

Here is my question:

I have a material with three bitmaps/colors plugged into a Random Texture generator that is randomly assigning values 1-3 to each face on the applied object. (Via the Random Per Island node > the color ramp node)

What I need now is for the three IDs to be split into separate AOV outputs so each of the three have a separate alpha, which should look something like this:

Which is what the top AOV output is showing, unfortunately the two lower AOV outputs look like this:

Where does you map the random number (usuall in the intervall [0,1]) to 1-3 ??

Anyway: in the first you are “diverting” the random value with the ramp into two halfs in the last you are “picking” only a tiny little percent at the top/bottom of the range.

So to split the [0,1] into three you should use should use 1/3 amd 2/3 threshold like so (without AOV just for presentation; the “spheres” do have an island per face )