  This paper looks into the gain or loss from rolling a fair die multiple times
and choosing the highest or lowest number as the outcome over rolling the die
just once. Specifically, this paper gives a general formula for the expected
value of choosing the highest or lowest value of any number of die rolls and
sides. It also shows how, for a fixed number of rolls, the ratio between this
expected value and the number of sides converges as the number of sides
increases asymptotically. The converging behavior of this ratio helps formulate
the aforementioned gain or loss.
