Ever get a problem in your head that you obsess over for days, or even weeks (or longer)? This is the one I’ve been working on for a while.
At some point, I started to wonder about dice rolling. Specifically, I wondered about the difference between rolling a single 12-sided die and two 6-sided dice. How do the two compare? Obviously, with a 12-sided die (which I will refer to as d12, in grand D&D tradition) every number on the die has an equal chance of being rolled (8.33%), ignoring variations in dice shape, weight, texture, etc.
But what about when you use a pair of six-sided die (d6)? Like a d12 (or any properly made dice) each number has the same chance of being rolled (16.67%). But when using them in a game, you add them up. How does that affect your odds of getting certain numbers?