Sums 3–18
All sixteen possible sums when rolling three dice, from 3 to 18. Each has a traditional interpretation and an exact probability.
Table of Sums
| Sum | Interpretation | Combinations out of 216 | Probability |
|---|---|---|---|
| 3 | Unexpected luck | 1 | 0,46 % |
| 4 | Disappointment | 3 | 1,4 % |
| 5 | Help from a stranger | 6 | 2,8 % |
| 6 | Loss and gain | 10 | 4,6 % |
| 7 | Gossip, other people’s words | 15 | 6,9 % |
| 8 | Unjust reproach | 21 | 9,7 % |
| 9 | Agreement, marriage | 25 | 11,6 % |
| 10 | Addition, growth | 27 | 12,5 % |
| 11 | Parting | 27 | 12,5 % |
| 12 | A letter, news | 25 | 11,6 % |
| 13 | Tristitia | 21 | 9,7 % |
| 14 | A new friend | 15 | 6,9 % |
| 15 | Caution in your affairs | 10 | 4,6 % |
| 16 | A lucky journey | 6 | 2,8 % |
| 17 | Change of plans | 3 | 1,4 % |
| 18 | Complete success | 1 | 0,46 % |
How to Read a Sum
Interpretation first, probability second. Probability is useful not for mysticism but for keeping a clear head: you will see a sum of 10 or 11 in every fourth roll, so “addition” and “parting” will be the answers you get most often.
If you need a yes-or-no answer, 3, 9, 10, 14, 16 and 18 count as favorable; 4, 7, 8, 11, 13 and 15 as unfavorable. The sums 5, 6, 12 and 17 are neutral and describe outside intervention.
Why the Sums Are Unevenly Distributed
A sum of 3 comes from only one combination, 1-1-1. A sum of 10 comes from twenty-seven different combinations: 1-3-6, 2-4-4, 3-3-4 and so on, with all their permutations.
That is why the closer a sum is to the middle, the more often it comes up. The peak falls on 10 and 11 — 27 combinations each out of 216. Gamblers of the 17th century knew this property too, and it is what led to the birth of probability theory.