Settlers Calculator

A strategic tool for analyzing placement odds in Settlers of Catan.

Probability Calculator

Enter the number chits adjacent to your settlements and cities to calculate the expected resource probability. Use numbers only, separated by commas (e.g., 4,9,10).

Player 1

Player 2

Player 3

Player 4

Dice Roll Probability Analysis

Probability distribution of rolling two six-sided dice. The ‘dots’ represent the number of chances out of 36 for a roll to occur.

Dice Roll	Combinations	Probability (x/36)	Dots on Chit
2	1+1	1/36 (~2.8%)	1
3	1+2, 2+1	2/36 (~5.6%)	2
4	1+3, 3+1, 2+2	3/36 (~8.3%)	3
5	1+4, 4+1, 2+3, 3+2	4/36 (~11.1%)	4
6	1+5, 5+1, 2+4, 4+2, 3+3	5/36 (~13.9%)	5
7	1+6, 6+1, 2+5, 5+2, 3+4, 4+3	6/36 (~16.7%)	Robber
8	2+6, 6+2, 3+5, 5+3, 4+4	5/36 (~13.9%)	5
9	3+6, 6+3, 4+5, 5+4	4/36 (~11.1%)	4
10	4+6, 6+4, 5+5	3/36 (~8.3%)	3
11	5+6, 6+5	2/36 (~5.6%)	2
12	6+6	1/36 (~2.8%)	1

About The Settlers Calculator

What is a settlers calculator?

A settlers calculator is an essential tool for players of the board game Settlers of Catan. Its primary purpose is to quantify the probability of earning resources from different positions on the game board. By inputting the number chits corresponding to the hex tiles your settlements and cities are adjacent to, this calculator provides a clear “probability score.” This score helps players make informed strategic decisions, especially during the crucial initial placement phase, by comparing the statistical likelihood of different spots yielding valuable resources over the course of a game.

The Settlers Calculator Formula and Explanation

The calculation is not based on a complex formula, but rather on the fundamental probabilities of rolling two six-sided dice. In Catan, the “dots” on each number chit represent the number of combinations that can produce that roll, out of 36 total possibilities. Our settlers calculator uses this to create a score.

Player Score = ∑(Dots on Settlement Numbers) + ∑(2 * Dots on City Numbers)

Essentially, we sum the “dot value” for each number a player has a settlement on. Since cities produce double the resources, we multiply the dot value of their numbers by two. A higher score indicates a higher statistical probability of receiving resources throughout the game. For more details on probability, check out our guide on statistical analysis.

Probability Variables

Variable	Meaning	Unit	Typical Range
Dice Roll	The sum of two six-sided dice.	Unitless	2-12
Dots	The number of combinations out of 36 that result in the dice roll.	Chances	1-5 (for non-7 rolls)
Score	A player’s total dot count, representing resource potential.	Points	0 – 50+

Practical Examples

Example 1: Balanced Placement

• Inputs: Player A chooses a starting spot touching hexes with numbers 5, 9, and 10. Their second settlement is on 6, 8, and 3.
• Calculation:
  • Spot 1 Dots: 4 (for 5) + 4 (for 9) + 3 (for 10) = 11
  • Spot 2 Dots: 5 (for 6) + 5 (for 8) + 2 (for 3) = 12
• Result: Player A’s total probability score is 23. This is a very strong starting position with a high chance of receiving resources frequently.

Example 2: City Upgrade

• Inputs: Player B has a settlement on 4, 8, and 11. Their score is 3 (for 4) + 5 (for 8) + 2 (for 11) = 10 dots. They upgrade this settlement to a city.
• Calculation: The score for each adjacent hex is now doubled. The new score is (2 * 3) + (2 * 5) + (2 * 2) = 6 + 10 + 4 = 20 dots.
• Result: By building a city, Player B has doubled their resource potential for this location, making it a powerful engine for their economy. Learn more about economic strategy in our detailed guide.

How to Use This Settlers Calculator

1. Locate Player Sections: Find the four player sections at the top of the calculator.
2. Enter Settlement Numbers: In the ‘Settlement Numbers’ field for a player, type the numbers of the hexes their settlements touch. Separate each number with a comma.
3. Enter City Numbers: If a player has cities, enter the adjacent numbers in the ‘City Numbers’ field, also separated by commas.
4. Calculate: Click the ‘Calculate’ button.
5. Interpret Results: The calculator will display the total probability score (in ‘dots’) for each player. The player with the highest score has the highest statistical chance of gaining resources. This analysis can be a key part of your winning tactics.

Key Factors That Affect Placement Strategy

• Number Diversity: Covering a wide range of different numbers (e.g., 4, 5, 8, 10) is often safer than doubling or tripling up on one good number (e.g., 8, 8, 8), which can be prone to unlucky streaks.
• Resource Diversity: Having access to all five resources (Wood, Brick, Sheep, Wheat, Ore) is crucial for balanced growth. A high probability score on only one or two resource types can be a weakness.
• Port Access: Placing on a port can make a lower-probability number more valuable if it gives you a favorable trade ratio for a resource you produce in abundance.
• The ‘7’ and the Robber: High-probability numbers (6 and 8) are the most frequent targets for the Robber. This risk must be balanced with their high reward.
• Expansion Lanes: Your initial placements should provide clear paths for you to build new roads and settlements. Don’t get boxed in!
• Development Card Strategy: If you plan to pursue a “Largest Army” or “Victory Point” card strategy, having strong access to Ore, Wheat, and Sheep becomes a higher priority. A good beginners guide can explain this further.

Frequently Asked Questions

Q: What is a “dot” in Catan?
A: A “dot” is a visual representation of an outcome’s probability. Each dot represents one chance out of 36 for a specific number to be rolled. For example, ‘8’ has 5 dots, so it has a 5/36 chance of being rolled.

Q: Does a higher score from this settlers calculator guarantee a win?
A: No. Catan involves luck, strategy, negotiation, and managing the Robber. A higher probability score gives you a statistical advantage, but it does not guarantee victory.

Q: Why isn’t ‘7’ included in the calculation?
A: Rolling a ‘7’ activates the Robber and does not produce resources, so it is not included in the resource probability score.

Q: Should I always place on the 6s and 8s?
A: While statistically the best numbers, they are also prime targets for the Robber and are often highly contested. A balanced strategy involving 5s, 9s, 4s, and 10s is often more resilient.

Q: How do I account for ports?
A: This calculator focuses on pure resource probability. To factor in ports, you must apply your own strategic judgment. If you have a 3-Sheep starting spot and are on a 2:1 sheep port, that spot is significantly more valuable than the raw numbers suggest.

Q: What do the input fields mean?
A: ‘Settlement Numbers’ are for hexes adjacent to your settlements (1 resource). ‘City Numbers’ are for hexes adjacent to your cities (2 resources).

Q: Can I input the same number twice for one settlement?
A: No, a settlement or city sits at a vertex of up to three unique hexes. You should only input the numbers of the hexes it touches.

Q: How does the chart help my strategy?
A: The chart provides a quick visual reference of which numbers are most likely to be rolled. This reinforces the value of placing settlements on numbers like 6 and 8, and the lower value of 2 and 12. Considering this is an important part of any advanced strategy.