Are the wizard keys always on the first floor?

I've found them once on a save that I discontinued, but I haven't found them on the few characters I made afterwards. Are they guaranteed to be on the first floor or is it random?

Edit: Just found them again. I must have just had a stroke of bad luck.

 

They are on every floor. For as long as you don't pick them up, they are supposed to spawn from time to time.

 

It's a challenge not to find one of those.

 

Are they really that easy to find? If so why not just have players start with one?