GAME & ENTERTAINMENT – BOARD GAME & TABLETOP CALCULATOR
Catan Settlement Value
A precise tool.
What is the Catan Settlement Value & How does it work?
In Catan, each settlement is placed at the intersection of up to three hexes, each producing a specific resource when its numbered token is rolled.
The probability of rolling a particular number with two six‑sided dice follows a well‑known distribution: 2 and 12 appear 1/36 of the time, 3 and 11 appear 2/36, 4 and 10 appear 3/36, 5 and 9 appear 4/36, and 6 and 8 appear 5/36. The number 7 triggers the robber and yields no resources.
E = \sum_{i=1}^{3} p_{n_i}
p_{n_i} = probability of rolling number n_i (e.g., 5/36 for 6 or 8)
By summing the probabilities of the three adjacent numbers, we obtain the settlement’s expected resource income per turn, which helps players evaluate the strategic value of placement.
Parameters
Result
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Frequently Asked Questions
How do I calculate the probability of rolling a specific number in Catan?
The probability of rolling a specific number with two six-sided dice follows a distribution: 2 and 12 have a probability of 1/36, 3 and 11 have 2/36, 4 and 10 have 3/36, 5 and 9 have 4/36, and 6 and 8 have 5/36.
What is the impact of the robber on resource generation in Catan?
The number 7 triggers the robber, which prevents resources from being collected from any hexes until moved. This makes it crucial to consider when placing settlements.
How do I determine the value of a settlement in Catan?
Calculate the expected resource value by summing the probabilities of each adjacent hex’s number rolled, excluding 7.
Can you explain how dice roll probabilities affect settlement placement in Catan?
Settlements should be placed on intersections with high-probability numbers to maximize resource collection. Avoid placing near a 7 to prevent the robber from blocking resources.
What is the formula for calculating the expected value of a settlement in Catan?
E = sum_{i=1}^{3} p_{n_i}p_{n_i}, where p_{n_i} is the probability of rolling the number on one of the three adjacent hexes.
How does the robber affect the strategy for placing settlements in Catan?
The robber’s presence necessitates strategic placement to avoid high-probability numbers, ensuring a steady resource flow even when the robber is active.
What are the key factors to consider when using this calculator for Catan?
Consider the dice roll probabilities of adjacent hexes and the presence of the robber. Place settlements on intersections with high-probability numbers, avoiding areas prone to robbery.
Results are for informational purposes only and do not constitute professional advice.