How are Catan number probabilities calculated?

Two six-sided dice produce each number a fixed number of ways out of 36: 6 and 8 have five ways (the best), while 2 and 12 have only one. The probability of a number is its number of ways divided by 36.

What are pips and why do they matter?

Pips are the dots printed under each number token and equal the number of ways to roll it on 2d6. Adding the pips of the hexes a spot touches gives a quick strength score — more pips means more frequent production.

Rolling a 7 triggers the robber and produces no resources, so no hex ever carries a 7 token. The tool only offers the producing numbers 2 to 6 and 8 to 12.

How many hexes can a settlement touch?

A settlement or city sits on a corner where up to three hexes meet, so you can add one, two, or three hexes. Cities produce two cards per hit instead of one, doubling the expected yield.

What counts as a strong starting spot?

A strong opening corner usually totals 10 to 12 pips across its hexes, ideally including a 6 or 8 and a spread of resources. Weak corners total only 3 to 5 pips and produce rarely.

Catan Dice Roll Probability Analyzer

The Catan Dice Roll Probability Analyzer scores a settlement or city by how often its hexes produce. Tell it which numbers and resources the corner touches and it returns the total pip strength, the expected cards per roll, and a per-resource breakdown so you can pick the best opening placement.

How it works

Every resource hex carries a number token, and that number is rolled on two dice. The number of ways to roll each value on 2d6 is what drives production:

2 -> 1   3 -> 2   4 -> 3   5 -> 4   6 -> 5
8 -> 5   9 -> 4  10 -> 3  11 -> 2  12 -> 1

A 7 produces nothing — it moves the robber — so it never appears on a hex. The “pips” printed under each token are exactly this number of ways, which is why 6 and 8 (five pips) are the prize numbers and 2 and 12 (one pip) are the weakest.

A settlement sits where up to three hexes meet, so its strength is the sum of the pips across those hexes. Dividing the total pips by 36 gives the expected number of resource cards per dice roll; a city doubles that yield because it draws two cards per hit.

Tips and example

Place a settlement on a corner touching a 6-ore, a 9-grain, and a 5-wool hex and you collect 5 + 4 + 4 = 13 pips — a premium opening that produces roughly 13 / 36 ≈ 0.36 cards every roll, spread across three useful resources. Compare that to a corner of 3, 11, and 4 (only 8 pips) and the difference in long-term income is large. Aim for high pip totals, a 6 or 8 if you can get one, and a mix of resources you actually need for your strategy.