Catan dice probability calculator.

Answer

Two six-sided dice make each number with probability ways/36: 6 and 8 are 5/36 (13.89%) each, 5 and 9 are 4/36, down to 2 and 12 at 1/36. A settlement on 6 and 5 plus a city on 8 gives 0.528 cards per roll, pays out on 38.89% of rolls and has a 0.73% chance of nothing in 10 rolls.

Worked example

Settlement on 6 (5 ways), city on 8 (5 ways, x2) and settlement on 5 (4 ways). Expected cards per roll = (5 + 10 + 4) / 36 = 0.528. Chance any of the numbers 5, 6 or 8 is rolled = (5 + 5 + 4) / 36 = 38.89%. No payout for 10 rolls in a row: (1 - 0.3889)^10 = 0.73%.

How it works

The dice. Two six-sided dice give 36 equally likely outcomes. A total n can be made in 6 - |n - 7| ways, so 7 has 6 ways and 2 or 12 only 1. The dots under the number token on the board show this count.

Production. A settlement next to a hex collects one card of its resource when the hex number is rolled, and a city collects two. A roll of 7 produces nothing, because the robber is moved instead, so 7 is never counted. Expected cards per roll = sum of (ways x cards) / 36 over your spots.

Chance of any payout. This counts each distinct number once, so two spots on the same number do not double the chance that something pays. Dry-spell odds assume independent rolls: (1 - p)^rolls. Resource types, trading and the robber blocking a hex are not modeled.

Sources and basis (opened 2026-10-08): Catan (Wikipedia) for settlements collecting one card, cities two, and the 7 moving the robber; two-dice arithmetic otherwise, checked by enumeration in the test suite.

FAQ

What is the probability of rolling each number in Catan?

2 and 12: 1/36 (2.78%). 3 and 11: 2/36 (5.56%). 4 and 10: 3/36 (8.33%). 5 and 9: 4/36 (11.11%). 6 and 8: 5/36 (13.89%). 7: 6/36 (16.67%), which activates the robber instead of producing.

Why are 6 and 8 the best numbers?

They are the most likely totals that produce resources: 5 of 36 outcomes each. Only 7 is more likely, and it produces nothing.

How many cards will a settlement on a 6 give per roll?

On average 5/36 = 0.139 cards per roll, or about one card every 7 rolls. A city doubles that.

Does having two spots on the same number double the chance of a payout?

No. It doubles the cards you receive when that number is rolled, but the chance that the number is rolled stays the same.

What is the chance of a dry spell?

The chance that none of your numbers comes up in a row of rolls is (1 - p)^rolls, where p is the chance that any of your numbers is rolled on one roll.