You could think of it this way: If R is the ratio of (combinations that total N on two dice) to (combinations that don’t total N on two dice), then the chance of (rolling N on two dice) is R/(R+1). For example, there are 2 ways to roll a 3 (1 and 2, and 2 and 1) and 34 ways to not roll a 3. The probability of rolling a 3 is thus (2/34)/(1+2/34)=2/36.
From Reddit:
You could think of it this way: If R is the ratio of (combinations that total N on two dice) to (combinations that don’t total N on two dice), then the chance of (rolling N on two dice) is R/(R+1). For example, there are 2 ways to roll a 3 (1 and 2, and 2 and 1) and 34 ways to not roll a 3. The probability of rolling a 3 is thus (2/34)/(1+2/34)=2/36.