Adventure

Monty the Goblin

Rolling 1–3 with a d6

How would you generate a random number in the range 1–3 uniformly using a d6?

There are at least three ways which seem natural to me:

     d6   ⌈d6/2⌉   d6%3+1  d6%3 replace 0 w/ 3
    ----  ------  ------  -------------------
      1      1       2             1    
      2      1       3             2
      3      2       1             3
      4      2       2             1
      5      3       3             2
      6      3       1             3

Most people, I imagine, would divide by two and round up.

Rounding strikes me as a trait of a poorly designed game. I prefer to use modular arithmetic.

There is the problem that the modulus operator returns a number in the range 0–2, at least when we are computing a number modulo 3. We can add 1 to the result, but I prefer to use 3 in place of 0. After all 0 and 3 are the same modulo 3.

Blink Elf