The Catan Probability Cheat Sheet (Bookmark This)
A single-page reference for Catan probability — number frequencies, pip values, expected production. Bookmark and consult mid-game.
By Henrik Mølmer · Editor & Founder, Cartographer's Almanac
6 min read ·
TL;DR
The complete Catan probability reference: number probabilities (6/8 = 13.9%, 7 = 16.7%, 2/12 = 2.8%), pip values (1–5), expected production over 36 turns, dev-card draw odds (Knight 56%, VP 20%, others 8% each), and the math behind the Robber. Bookmark for mid-game reference.
This is the single-page Catan probability reference. Bookmark it. Consult mid-game when you're trying to decide whether a trade is worth it, whether to buy that dev card, or whether the Robber is statistically due. Every number is from official rulebook math; nothing house-ruled.
Number-roll probabilities
| Number | Pips | Probability per roll | Expected rolls per 36 turns |
|---|---|---|---|
| 2 | 1 | 1/36 = 2.78% | 1 |
| 3 | 2 | 2/36 = 5.56% | 2 |
| 4 | 3 | 3/36 = 8.33% | 3 |
| 5 | 4 | 4/36 = 11.11% | 4 |
| 6 | 5 | 5/36 = 13.89% | 5 |
| 7 | 6 | 6/36 = 16.67% | 6 |
| 8 | 5 | 5/36 = 13.89% | 5 |
| 9 | 4 | 4/36 = 11.11% | 4 |
| 10 | 3 | 3/36 = 8.33% | 3 |
| 11 | 2 | 2/36 = 5.56% | 2 |
| 12 | 1 | 1/36 = 2.78% | 1 |
Pip values for placement
The "pip count" under each number is the visual shortcut for probability:
- 5 pips: 6, 8 (red numbers — most likely to roll)
- 4 pips: 5, 9
- 3 pips: 4, 10
- 2 pips: 3, 11
- 1 pip: 2, 12
For opening placement, sum the pips of all three adjacent hexes at each candidate corner. Aim for 14+. Top-quartile openings hit 16+.
The 7 (Robber statistics)
- The 7 rolls 1 in 6 (16.67%).
- Expected rolls per 36 turns: 6.
- Discard threshold: more than 7 cards in hand → discard half (rounded down).
- Two consecutive 7s: probability 2.78% (1 in 36). The "Robber stays for 6 turns" pattern is statistically rare but feels common because of memorability bias.
Development card draw odds
| Card | Count | Probability per draw |
|---|---|---|
| Knight | 14 | 56% |
| Victory Point | 5 | 20% |
| Year of Plenty | 2 | 8% |
| Road Building | 2 | 8% |
| Monopoly | 2 | 8% |
Note: probabilities shift as cards are drawn from the deck. Track buys mentally — after 10 buys, the deck composition is much more weighted toward utility cards. (See our dev card guide.)
Expected resource production
For a 6 or 8 hex (the strongest non-red numbers don't exist — these are the strongest):
- 13.89% × 36 turns = ~5 productions per 36 turns.
- So a single red-number hex produces ~5 cards over 36 dice rolls.
For a 5 or 9 hex: ~4 productions per 36 turns.
For a 2 or 12: ~1 production per 36 turns.
Bank trade economics
- Default bank rate: 4:1 (4 of one resource for 1 of any other).
- 3:1 generic port: 3:1 (any resource).
- 2:1 specific port: 2:1 (only the matching resource).
Breakeven for a 2:1 port: you need to use it 4+ times across the game to outweigh the placement opportunity cost. (See port strategy.)
Robber positioning expected value
If your Robber move denies an opponent's 5-pip hex, you're denying them an expected ~5 cards over the rest of the game (assuming Robber stays 4–6 turns). That's a substantial swing — usually larger than the +1 random card you steal.
Conclusion: blocking the leader's best hex is almost always higher EV than stealing.
Largest Army threshold
Largest Army awards +2 VPs to the first player with 3+ Knights played. The dev deck has 14 Knights total. With 4 players, expected per-player Knight allocation is ~3.5, so the race is competitive.
Longest Road threshold
Longest Road awards +2 VPs at 5+ contiguous road segments. Cost: 5 wood + 5 brick = 10 resources for the bonus alone. (See Longest Road strategy.)
5–6 player Catan adjustments
The expanded number distribution adds one of each token (2 through 12, except 7). The pip math per-hex is identical; the total board pip count rises proportionally. (See 5–6 player strategy.)
For more on placement decisions using these probabilities, see opening placements and balanced board math.
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