Catan dice odds
Two dice make 36 combinations. That single fact sets the value of every hex on the board, and it is the whole of Catan probability.
Each Catan hex carries a number token from 2 to 12, and the dots under the number are called pips. A pip counts one of the 36 combinations that two six-sided dice can roll. A 6 carries five pips, so it pays five times more often than a 2, which carries one.
Every number token
| Number | Pips | Ways to roll | Chance | Bar |
|---|---|---|---|---|
| 2 | 1 | 1 | 2.8% | |
| 3 | 2 | 2 | 5.6% | |
| 4 | 3 | 3 | 8.3% | |
| 5 | 4 | 4 | 11.1% | |
| 6 | 5 | 5 | 13.9% | |
| 8 | 5 | 5 | 13.9% | |
| 9 | 4 | 4 | 11.1% | |
| 10 | 3 | 3 | 8.3% | |
| 11 | 2 | 2 | 5.6% | |
| 12 | 1 | 1 | 2.8% |
The 7 is missing from the table because no hex carries it. It is the most likely total of all, at six combinations and 16.7% of rolls, and it moves the robber instead of paying a resource.
Where the 36 combinations come from
Each die has six faces, so the pair has 6 × 6 = 36 outcomes. The grid below lists the total for every pair. Count how many cells hold a number and you have its pip count.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
The middle diagonal is the 7, shaded grey. The 6 and the 8 sit either side of it in clay red. The further a total sits from 7, the fewer cells it fills, and the fewer pips it earns.
What the odds mean at the table
A settlement sits on a corner, and an inland corner touches three hexes. Add the pips of those three hexes and you get what the corner pays per roll. That sum is the single most useful number when you place your first settlement.
- 15 pips is the maximum for one corner, and it needs three of the 6, 8 and 5 class of hex around it.
- 10 to 12 pips is a strong opening corner.
- Under 8 pips only pays if the corner holds a resource that the rest of the board is short of, or if it reaches a harbour you plan to use.
The long run against one evening
These percentages describe an infinite number of rolls. One game holds roughly 60 to 80. A 5-pip number should land about 9 times in that span, but landing 3 times or 16 times is ordinary. Plan around the odds, and do not treat a quiet 8 as broken.
Common questions
Which number is the most likely in Catan?
Ignoring 7, the 6 and the 8 are the most likely. Each comes up on 5 of the 36 dice combinations, which is 13.9% of rolls. The 7 itself is the single most likely total at 6 combinations, but it carries no number token because it moves the robber.
What are pips in Catan?
Pips are the dots printed under the number on a hex. The count equals how many of the 36 two-dice combinations produce that number, so a 6 shows five dots and a 2 shows one.
How many pips does a good settlement have?
An inland corner touches three hexes, so its pip total can reach 15. Anything from 10 upward is strong. A corner in the low single digits will starve you unless it holds a resource nobody else has.
How often does a number come up in a game?
A four player game runs about 60 to 80 rolls. A 5-pip number therefore lands roughly 8 to 11 times, and a 1-pip number lands about 2 times. Short games swing far from those averages.
The generator prints the pip count under every token, and it shows the pip total per resource for the whole board. Draw a board and read the balance before anyone places a settlement.
Open the board generator