I've never played a pen and paper RPG. I'm interested in them, but I've never really had an opportunity to play. In high school I was a huge nerd, and I hung around with other nerds, but for whatever reason none of us was into pen and paper games, and playing one just never really came up (in fact, my impression of D&D was that it was an old game that had been popular in the 80s, but which was out of fashion by the time the 90s rolled around).
BUT, I am fascinated by their mechanics, and I've been wondering recently why the norm for most of them (as far as I can tell) is to use twenty-sided dice. Is there a strong reason why the games don't use standard six sided dice? Like, why not give the chartacters lower stats (say, between 1 and 10 like in the original Fallouts) and resolve everything with 1d6?
Given my inexperience with actually playing the games, I feel like there might be some really obvious reason that I'm missing. Is there some problem with the odds, or the spread of possible outcomes? Or is it purely because leveling up a character means that their stats will get higher and thus require larger dice-roll scores to properly resolve stat checks or combat?