“The cards are dealt.” «Les cartes sont distribuées.»
I realize that's “the way it is” in all extant academic mathematical literature in the French language, but the idiom of playing cards being laid down on the table as “law” -- in any way, shape, or form or manner of speaking -- is so offensive to me as to completely rule out any polite discourse on the subject.
«Une distribution» is a perfectly valid and decent French word.
«La distribution normale» would be a fine way to describe in French what is called “the normal distribution” in English. The mathematical language of the dealing of a deck of cards ought not to be conflated with that of legislation, civil suits, or crime and punishment under any circumstances.