The

is the usual measure of the distance between a
list of experimental results and the list of their expectations. In
a first part, our paper exemplifies this protocol with the simulation
of unfair die throwing (and everything works as in textbooks). In
a second part, the same protocol is applied to fair die throwing...
and almost everything is proven to go wrong. In a third part, this
striking behavior is related to the nature of the set of all possible

, which is quite continuous for a random unfair die,
and coarse discrete for a fair die.