It would be better to ask what kind of mutations and “random with respect to what”? End of the day, nothing is truly random, there are always factors which influence it and that is why we see patterns even in “random” events.
As far as i understand, the claim in evolution is that heritable mutations are random with respect to environmental stimuli/fitness… i.e a lack of fitness/environmental stress should not effect mutation rates if they are truly random.
Shapiro/Noble/Lynn Margulis/Jablonka etc have been arguing thta mutations are not random with respect to firness/environment.
Edit: For your example, the question would be whether roulette is actually random with respect to the winnings of the house.