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 -> 1A 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.
Opening placement strategy
The first two settlements in Catan shape the entire game. A few principles follow directly from the probability math:
Target 9+ pips at your first settlement. Corners touching three producing hexes average about 9–10 pips for solid players. Anything below 7 pips means you will struggle to keep up in production unless you own a port.
Avoid duplicate numbers. A corner on 5-ore, 5-lumber, and 8-wheat gives you two 5s and one 8. If someone plays the robber on your 5 hex, you lose income from two spots at once. Spread across different numbers where you can.
Balance resources, not just pips. A 6-ore, 8-ore, 9-ore corner is strong on pips but gives you only ore — you will need to rely entirely on trading and ports. Ideally a starting settlement touches at least two different resource types.
Account for the robber. 7 is the most likely single roll (six ways out of 36). A hex that shares a number with the desert space at game start is one fewer productive hex to worry about. When placing second, if a strong 6 or 8 hex is uncontested, that is often the priority pick.
Cities versus settlements
Once a settlement upgrades to a city, each hex hit produces two cards instead of one, exactly doubling the expected yield from that corner. Running the tool on your city corners is useful for deciding where to upgrade first — the corner with the highest total pips gets the most value from the 2× multiplier.