A variety of video games use uniformly distributed numbers to decide the outcome of an event, such as a "50% chance to hit" almost always means to check if a random floating point number from 0-1 is greater than 0.5. Many games will layer a few of these uniform percentages on top of each other, for instance a D&D hit roll is a uniformly distributed number from 1-20, except that 1 and 20 have special outcomes. To my mind it seems like things like critical hits are added by designers to try and emulate the fact that in reality hitting/missing or winning/losing is not actually a binary outcome.
In many cases the real life amount of "damage" done by an attack would likely be closer to a gaussian/bell curve distribution, which many results in the middle but the occasional very exciting outlier and smooth curve connecting them. Dice games like Settlers of Catan emulate gaussian distributions by adding together multiple independent rolls, but I feel like I've almost never seen this mechanic in video games.
It seems like games like Civilization (Sid Meier talked extensively at GDC about player perception not matching the actual math used in the game) would benefit from results that matched how things work in the real world. Have any video games used a gaussian or otherwise non-uniform distribution of random numbers in interesting ways?