Compare marginal production
An existing settlement on 6, 5 and 9 has thirteen production pips. Upgrading it adds thirteen expected cards per 36 fair rolls. It does not add twenty-six: the first thirteen were already available. A new settlement on 8, 10 and 3 adds ten expected cards per 36 rolls.
Include the road bill
In the default scenario the city costs five cards, while two roads and a settlement cost eight. Both purchases add one net victory point. These totals are useful for planning, but ore is not interchangeable with wood at no cost. Compare your actual resource access with the shopping-list and port tools before treating the cheaper total as the easier purchase.
Production is only part of the decision
A new settlement can secure a missing resource, a port or an important route. A city concentrates more production under the same robber threat. This model assumes fair dice, no blocked hexes and enough bank supply. Select zero for coast or desert. It does not validate placement geometry or include strategic value, awards, trades or changes to future expansion.
Rules, assumptions & further reading
Check the official CATAN rulebooks and Colonist’s base-game rules for the rules at your table. These calculations and worked examples are original mathematical models, not measured win rates. They do not read a live game or establish that a move is legal.