Catan Resource Roll Probability
Two-dice roll probabilities (2–12) for Catan resource production.
Overview
The Catan Resource Roll Probability tool shows the chance of each possible two-dice total (2 through 12) coming up on a turn in Settlers of Catan, alongside the standard "dot" notation used on Catan number tokens. Because each turn rolls two six-sided dice, the totals are not uniform — 7 is the most common result and 2 or 12 are the rarest.
This is the canonical reference for evaluating settlement placements. A spot touching a 6 and an 8 is dramatically more productive than one touching a 2 and a 12, and the dot pips printed on each tile encode exactly that relative frequency. Use the tool to settle disputes, to plan opening builds, or to quickly compute the combined output of three tiles touching one corner.
How it works
Two fair six-sided dice produce 36 equally likely ordered outcomes. Counting the ordered pairs that sum to each total gives: 2 -> 1, 3 -> 2, 4 -> 3, 5 -> 4, 6 -> 5, 7 -> 6, 8 -> 5, 9 -> 4, 10 -> 3, 11 -> 2, 12 -> 1. Dividing by 36 gives probabilities ranging from 1/36 (about 2.78 percent) for 2 or 12 up to 6/36 (about 16.67 percent) for 7.
The dot notation on Catan tokens visualises this by printing one pip per ordered pair: a 6 or 8 token shows five dots, a 5 or 9 shows four, and so on. Because 7 triggers the robber rather than resource production, no tile receives a 7 token — but its 16.67 percent probability still matters for hand-size limits and robber blocks.
Examples
- A corner touching tiles numbered 6, 8, and 9 produces resources on 5+5+4 = 14 of every 36 rolls on average, or about 38.9 percent per turn.
- A corner touching 2, 11, and 12 produces on only 1+2+1 = 4 of every 36 rolls, or 11.1 percent — one-third the output of the strong corner above.
- A single 5-token tile produces 4/36 of the time, so over 36 turns it averages 4 cards.
- A 7 is rolled on roughly one in six turns, meaning the robber moves and discards trigger fairly often.
FAQ
Why is 7 the most common roll?
There are six ordered pairs that sum to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), more than any other total.
Are 6 and 8 the best numbers?
Yes — they tie at 5/36 each, the highest probability for any number that produces resources.
Do dice have memory between turns?
No. Each turn is independent. Streaks of repeated numbers are normal in finite samples.
Why does my game seem to roll 7s constantly?
Variance. In a 20-turn run, rolling four or more 7s is common even though the expected count is about 3.3.
Are these probabilities the same with the cities-and-knights expansion?
The base resource dice are unchanged. The red die in the expansion is separate and tracks event symbols.