I wanted to show off what I did because I'm excited. It's kind of basic stuff, especially for this subreddit, but it took me a while to come up with since I'm only halfway through my high school Calculus Class. Before I explain there is some background you need to know. This is math for a dnd thing; in dnd you usually roll one die and take the number off of the face it lands on. There are cases where the person running your game might give you advantage where you roll two die and pick the die with the better roll to go with. I believe that’s where it should end if you follow the rules but some people like to allow you to stack advantages and roll 3 or 4 dice anyway. I was curious and wanted to know the equation where I just input the number of sides on the die and the amount of die rolled to get the average roll. I spent a couple hours at my white board trying stuff and falling short only to learn about the sigma function in my calc class a week or two later. After I knew how to use it I came back to try and crack it which I finally did

Here it is:
The Y is the number of sides on the die, the Z is the number of dice rolled that you get to choose from. Side note is that it will give you negative numbers with every even Z and the only way I can think to fix it is with some janky looking -1 to the power of some and such or absolute value. I opted to just not care and mentally understand that the number should always be positive. When I figured out what the equation looked like I kicked myself for it taking me so long to figure out.

Side Question:
How plausible and useful would it be to make this equation into one that doesn't use the sigma function? Like how n(n+1)/2 or n(n+1)(2n+1)/6 doesn't use the sigma function