Calculating Dice Roll Averages for xDyKHz
Olivia Zamora 
In the game of Dungeons and Dragons, often there are situations where you have to roll a certain amount of dice and only keep the highest few values. In roll notation, this is expressed as xDyKHz where x is the amount of dice rolled, y is the amount of sides on the die and z is how many of the highest dice are you keeping.
As an example, 3D6KH2 would have you roll three 6-sided dice and only keep the two highest rolled values.
I'm wondering if there is a general and easily computable way of finding the average roll for any xDyKHz values.
I have so far noted that for rolling 2 dice and only keeping the highest, the equation is $\frac{x}{2}\sum_{i=1}^y i\frac{2i-1}{y^2}$ but that is about all the progress I've made myself
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