The 2 in Catan
1 of the 36 ways two dice can land make 2, so you see one about every 36.0 rolls — 2.8 times in 100. Among the ten production numbers that makes it the 2nd least productive number of 10 — tied with the 12, which is rolled exactly as often.
Why the pips are the odds
The dots on a number token are not decoration and they are not a rating someone assigned. They are a count: 1 pip because there is exactly 1 way for two dice to make 2. Read the pips and you have read the probability.
- 1 + 1
Ways to roll each sum with two dice. 7 is the peak, which is why it moves the robber instead of producing anything.
What a settlement here is worth
A settlement on a single 2 hex earns 0.028 cards per roll — 2.8 over 100 rolls, and double that for a city. Against the weakest numbers on the board that is 1× the production, which is the entire reason placement matters more than almost any later decision.
One caveat worth keeping: this is one hex in isolation. A real spot touches up to three, and if two of them share a number they fire together — one correlated event, not two independent ones. The resource odds calculator handles that properly for a board you actually build.