How to Win Catan — the numbers
Catan opening placement is a math problem with an exact answer. Two dice are summed every turn, so each number has a known probability — and 6 and 8 are gold at 13.89% each. Score every spot by counting its "pips," and the best opening corner falls out of the arithmetic. Here's the full breakdown.
Number probabilities — the exact 2d6 odds
Every number token's probability is exactly its pip count over 36. This is the whole game in one chart — the closer a number is to 7, the more often it pays out:
6 and 8 are the best numbers in the game at 13.89% (5 pips) each — they sit one step from 7, the most common roll. 2 and 12 are the worst at 2.78%. Fight for corners touching a 6 or an 8.
Number priority tiers
Grouped by pip value — your placement shopping list, best to worst:
| Tier | Numbers | Pips | Per roll |
|---|---|---|---|
| Gold | 6 & 8 | 5 | 13.89% |
| Strong | 5 & 9 | 4 | 11.11% |
| Good | 4 & 10 | 3 | 8.33% |
| Weak | 3 & 11 | 2 | 5.56% |
| Avoid | 2 & 12 | 1 | 2.78% |
2 and 12 are the weakest numbers — just 1 pip (2.8%) each. A hex on a 2 or 12 barely ever pays out; never let a 2/12 hex be your reason for a placement.
The "count the pips" method
A settlement sits on a corner touching up to three hexes and earns a resource each time any of those hexes' numbers is rolled. Because every number's probability equals its pip count over 36, a spot's long-run resource rate is simply the SUM of the pip values of its neighbouring hexes. Add the pips, pick the highest — that is the exact, math-correct way to rank opening spots.
| Example corner | Hexes (number, pips) | Pip total | Any-hex per roll |
|---|---|---|---|
| Premium corner (6, 8, 5) | 6(5) + 8(5) + 5(4) | 14 | 38.9% |
| Strong corner (8, 9, 4) | 8(5) + 9(4) + 4(3) | 12 | 33.3% |
| Average corner (10, 5, 3) | 10(3) + 5(4) + 3(2) | 9 | 25.0% |
| Coastal 2-hex (6, 9) | 6(5) + 9(4) | 9 | 25.0% |
| Weak corner (12, 3, 11) | 12(1) + 3(2) + 11(2) | 5 | 13.9% |
"Pip total" = sum of the adjacent hexes' pips (the spot's resource rate). A premium 3-hex corner tops out around 14 pips; a 6+8 pair alone is 10 pips (27.8% chance of a payout per roll).
Score every opening corner by adding the pip values of its hexes (6/8=5, 5/9=4, 4/10=3, 3/11=2, 2/12=1). The highest pip total is the mathematically best spot, full stop.
Beyond pips: diversity, ports & the snake draft
The dice math picks the richest spot, but winning openings also balance two established principles:
Resource diversity
Pips aren't everything: you also want a spread of the five resources (brick, wood, sheep, wheat, ore) so you can actually build. A settlement needs wood+brick; a city needs ore+wheat; development cards need ore+sheep+wheat. A high-pip spot on only two resources can starve you, so balance raw pip count against resource coverage.
2:1 ports
Generic 3:1 and resource-specific 2:1 ports turn a surplus into flexibility. A 2:1 port is strong only when paired with a high-pip hex of that exact resource — e.g. a 2:1 ore port next to an 8-ore hex — so you reliably generate the surplus the port discounts.
The snake-draft plan: The opening uses a snake draft: in a 4-player game the order is 1-2-3-4 then 4-3-2-1, so player 1 picks first and last-but-one while player 4 gets back-to-back picks at the turn. Take the highest pip-total spot available on your first settlement; on your second, prioritise the resources and numbers your first spot is missing (diversity), and grab a 2:1 port only if it matches a high-pip hex.
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How we got these numbers
The dice math here is exact, not simulated: we enumerate all 36 ordered rolls of two dice to get each number's probability, which equals its pip count over 36 (2 and 12 = 1/36; 6 and 8 = 5/36 = 13.89%; 7 = 6/36 but 7 is the robber, not a token). That distribution validates exactly against the printed token pips. The 'count the pips' spot-scoring method follows directly from this math — a corner's resource rate is the sum of its hexes' pips. The placement heuristics (6 & 8 are gold, 2 & 12 are weak, resource diversity, 2:1-port logic and the snake-draft opening) are long-established, widely-documented Catan strategy, presented as such alongside the exact math. A guide to opening value — the robber, trades and opponents still shape every game.
Validation: the 2d6 distribution computes exactly to the known token pip values (6 & 8 =
5/36 = 13.89% each; 2 & 12 = 1/36; the eleven probabilities sum to 1). The
dice math is computed; the placement heuristics are established Catan strategy, labelled as such. Source code
lives in our sims/ folder (catan_sim.py). See also the full Catan entry.
Common questions
What are the best numbers in Catan?
6 and 8 — they each come up 13.89% of the time (5 pips out of 36), the highest of any number token (7 is more common but it's the robber, not a resource number). After those, 5 and 9 (11.11%), then 4 and 10. The worst are 2 and 12 at just 2.78% each.
How do you count pips to pick a settlement spot?
Every number's probability equals its 'pip' count over 36 (6/8 = 5 pips, 5/9 = 4, 4/10 = 3, 3/11 = 2, 2/12 = 1). A settlement corner touches up to three hexes, so its long-run resource rate is just the sum of the adjacent hexes' pips. Add the pips on each open corner and take the highest — that's the exact, math-correct way to rank opening spots.
What's the best opening strategy in Catan?
Use the snake-draft order to grab the highest pip-total corner you can on your first settlement, then use your second pick to fill in the resources and numbers you're missing (diversity beats stacking one resource). Prioritise corners touching a 6 or an 8, keep a spread across the five resources, and only take a 2:1 port if it sits next to a high-pip hex of that exact resource.