Catan Settlement Odds & Resource Calculator

How it works

P(number) = (6 − |7 − number|) ÷ 36 · pips = 6 − |7 − number| · cards per roll = Σ pips ÷ 36 (× 2 for a city) · P(7 within n rolls) = 1 − (5/6)ⁿ

Two dice produce 36 equally likely combinations, and the number of combinations that sum to each value forms the familiar pyramid peaking at 7 — six ways — with 6 and 8 at five ways each and 2 and 12 at one. Catan prints that count as dots on each token, so the dots on the hexes around a settlement are literally the number of dice outcomes that pay you, and dividing by 36 turns them into cards per roll. Multiplying by the rolls in a game gives the expected haul, while the probability that at least one hex hits shows how often a spot produces anything at all — the figure that matters for early tempo. The 7 has no hex but the most combinations, which is why a hand above seven cards is exposed roughly one roll in six.

Worked example

A settlement on 6, 8 and 5 has 5 + 5 + 4 = 14 pips: it produces on 38.9% of rolls and yields 0.389 cards per roll, about 27 cards over a 70-roll game. A rival spot on 4, 9 and 10 has 10 pips and about 19 cards a game. Holding 8 cards, there is a 16.7% chance of losing 4 of them on the very next roll and a 42% chance within three rolls.

Frequently asked questions