Catan Resource Probability Calculator
Why 6 and 8 Are the Board's Prime Real Estate
Every Catan tile is labeled with a number from 2 to 12 (excluding 7, since rolling a 7 triggers the robber instead of production), and those numbers are not equally likely on two six-sided dice. Tiles marked 6 and 8 sit one step below the impossible-to-land-on 7, giving them the highest production odds of any number on the board — which is exactly why settlements next to them are contested early in the game.
The Formula
P(at least one hit across multiple numbers) = 1 − Π(1 − P(number_i))
The second formula accounts for the fact that a settlement often touches two or three different numbered tiles — the chance of producing on a given turn is the chance that at least one of them hits, not any single tile alone.
Production Odds by Tile Number
| Number | Combinations (out of 36) | Probability per roll |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
A settlement touching both a 6-tile and an 8-tile has a combined 25.85% chance of producing on any given roll — noticeably better than either tile alone, since it counts as a hit if either number comes up.
Where This Gets Used
- Initial settlement placement — the single most consequential decision in a Catan game, made almost entirely on these production odds.
- Evaluating trade offers — weighing whether a resource you're short on is actually being produced often enough to justify a bad trade.
- Robber targeting — understanding which opponent tiles produce most often helps prioritize where to place the robber.
How to Use This Calculator
- Enter one or more tile numbers, comma-separated (2–12, excluding 7) — for example, "6, 8" for a settlement touching both.
- Select Calculate to see each tile's individual probability and the combined chance of producing at least one resource per roll.
Related Calculations
Check the underlying 2d6 distribution with the Dice Probability Calculator, or work out a fair trade with the Resource Trade Ratio Calculator.