### Deconstructing 2d6

Check this out. Just take a look. Come on.

2d6 | d66 |
---|---|

2 |
11 |

3 |
21, 12 |

4 |
31, 22, 13 |

5 |
41, 32, 23, 14 |

6 |
51, 42, 33, 24, 15 |

7 |
61, 52, 43, 34, 25, 16 |

8 |
62, 53, 44, 35, 26 |

9 |
63, 54, 45, 36 |

10 |
64, 55, 46 |

11 |
65, 56 |

12 |
66 |

Do you see it?

You can map the individual dice of a 2d6 roll onto a d66 table [1]. In other words, or for people who aren’t very familiar with d66, we know mathematically which permutations of the two dice will result in which total sums. One plus one is always two, and three plus four is always seven. This means that we can treat the set of possible permutations for each sum as its own table.

This is most useful for sums which are most frequent. Obviously, you can’t use it for sums of 2 and 12 since they both only have one possible dice permutation (11 and 66 in the d66 format). However, sums of 5 and 9 each have four permutations, sums of 6 and 8 each have five permutations, and a sum of 7 has six permutations. Isn’t that handy!

The 7-sum is perhaps the most interesting; this is not just because it has six permutations, but because all numbers from 1-6 are used across the whole set. You can just pick one die as your ‘favorite’ and treat that die as the d6 roll when you roll a 7. For example, let’s say you have a white and a black die and your ‘favorite’ is the black one. When you roll a one and a six, you get a sum of 7; since you rolled a six on the black die, you also know to look at the entry for that index on your d6 table.

There are other tricks you can use. For example, odd sums always have an even number of permutations. This means that you can pick a favorite die again, and look at whether it is even or odd to make a binary decision. The even-numbered rolls always have the possibility of a double roll; for example, if you were looking at 10-sum, there is a one-third chance of rolling a 55.

That’s all. Maybe some of y’all will find this useful for something! The nice thing about it is that it’s not anything systematic, but it’s just a strategy you can use to quickly add some granularity to your typical 2d6 roll. I thought of this idea while reading Nick LS Whelan’s updated post about encounter tables [2], and realized that 7-sum would be a handy shortcut for a d6 table of recurring characters.

[1] d66 is analogous to d100 but with six-sided dice instead of ten-sided ones. You roll two dice and treat each one as a digit, rather than adding them up.

[2] Whelan, Nick L.S. 2022-07-22. "Structuring Encounter Tables, Amended & Restated", *Papers & Pencils*.

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