How are Catan dice probabilities calculated?
There are 36 equally likely ordered pairs when two fair six-sided dice are rolled. Five pairs total 6, so its chance is 5/36, or 13.9%. Seven has six pairs; 2 and 12 have one each. This calculator includes seven because it asks about dice totals, rather than producing terrain.
A drought is not a debt
Across ten independent rolls, a 6 misses every time with probability (31/36)^10: about 22.4%. The chance of at least one 6 is the complement, about 77.6%. Neither figure says how many ore cards you will receive: that also depends on your buildings, the robber and the bank.
Use the horizon honestly
A roll means any player's dice roll, not just your own turn. Expected hits are the number of rolls multiplied by the single-roll probability. They are not a countdown. These formulas apply to random dice in Catan and Colonist; balanced-dice modes, including Archipelago's cycle, require a different conditional model.
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.