Quick Answer: When rolling two d6 dice, there are 36 possible combinations. The sum of 7 can be made 6 different ways — more than any other sum — giving it a 16.67% probability. This creates a bell curve called a triangular distribution, where extreme values (2 and 12) are much less likely than middle values (6–8).
Why 36 Combinations?
Each die has 6 faces. When rolling two dice independently, the total number of unique combinations is 6×6 = 36. Each combination is equally likely (probability 1/36 ≈ 2.78%). The sum for each combination ranges from 2 (1+1) to 12 (6+6).
Full 2d6 Probability Table
| Sum | Ways to Roll It | Probability | Cumulative % |
|---|---|---|---|
| 2 | 1 | 2.78% | 2.78% |
| 3 | 2 | 5.56% | 8.33% |
| 4 | 3 | 8.33% | 16.67% |
| 5 | 4 | 11.11% | 27.78% |
| 6 | 5 | 13.89% | 41.67% |
| 7 | 6 | 16.67% | 58.33% |
| 8 | 5 | 13.89% | 72.22% |
| 9 | 4 | 11.11% | 83.33% |
| 10 | 3 | 8.33% | 91.67% |
| 11 | 2 | 5.56% | 97.22% |
| 12 | 1 | 2.78% | 100% |
Impact on Board Games
The 2d6 bell curve has profound effects on board games. In Monopoly, the most likely single movement is 7 spaces — making squares 7 ahead most frequently landed on from any position. In Settlers of Catan, resources on hexes numbered 6 and 8 are produced significantly more often than hexes numbered 2 or 12, which is a core element of Catan strategy.
Catan: Understanding Resource Probability
In Catan, each hex has a number (2-12). The probability dots under each number indicate production frequency. Number 7 has no hex (it triggers the Robber) but would have 6 dots if it did. Numbers 6 and 8 have 5 dots each — the maximum resource frequency. Numbers 2 and 12 have 1 dot — very rare. This is why initial settlement placement near 6 and 8 is competitively valuable.