Each dot under a number on a Catan token stands for one way two dice can land on that number, so more dots means more rolls that pay you. You'll meet those dots the moment you place a starting settlement, and they decide something most new players leave to gut feeling: how many cards that spot should hand you over a game. Here's the whole system in one chart, worth a screenshot or a printout to keep beside the board.

Number Dots on the token Ways to roll it Fraction Chance per roll
2 ● 1 1/36 2.8%
3 ●● 2 2/36 5.6%
4 ●●● 3 3/36 8.3%
5 ●●●● 4 4/36 11.1%
6 ●●●●● 5 5/36 13.9%
7 No token: moves the robber 6 6/36 16.7%
8 ●●●●● 5 5/36 13.9%
9 ●●●● 4 4/36 11.1%
10 ●●● 3 3/36 8.3%
11 ●● 2 2/36 5.6%
12 ● 1 1/36 2.8%

Thirty-six ways to land two dice

The base game comes with 2 dice and 18 number discs, and the discs are just the dice math printed small. Count each die separately and two dice can land 36 ways. Only one of those makes a 2: a 1 and a 1. Five make a 6: 1+5, 2+4, 3+3, 4+2 and 5+1. So a 2 gets one dot and a 6 gets five, and the percentages My Kind of Meeple lists follow directly from that count.

The gap in the chart is the odd part. A 7 is the most common total in the game, at six ways out of 36, and it has no token because it pays nobody. It triggers the robber instead, and anyone holding more than 7 cards discards half. The likeliest roll on the table is the one you can't settle on.

That leaves 6 and 8 as the best numbers you can own. One extra way to roll sounds like a small edge over 5 and 9, but 5/36 against 4/36 is a quarter more production. Against a 2 or a 12 it isn't close: a 6 comes up five times as often. Meeples Corner estimates a typical game at about 71 rolls. On average, that's about 10 sixes, 8 fives and 2 twos.

One popular shorthand needs a small correction. Official Game Rules names 6, 8 and 9 as the numbers that roll most often, but 9 only belongs on that list if 5 does too. Both have four ways, so don't pass up a 5 because it isn't one of the "hot" numbers.

Totaling a corner

A settlement sits where up to three hexes meet, so its strength is the dots on those tiles added together. Take the corner Colonist.io's strategy guide picks as the best on its example board, touching 5, 6 and 9. That's 4 + 5 + 4, or 13 pips, and the guide notes it's the only 13-pip spot on that map.

The total has a plain meaning: it's how many cards the corner should produce, on average, every 36 rolls. A 13-pip settlement earns about 13 cards per 36 rolls, and that one conversion turns a row of dots into something you can compare. To skip the adding, the helper below deals or paints a board and shows the pips at every corner.

Find the best starting spots

Deal a random board and every corner shows its pips, with the five best open spots numbered.

The five best open corners, rankedA corner's pipsTaken or too close

Best open corners
#PipsNumbersResources

Pips are the ways two dice make a number, out of 36: a 6 or 8 has 5, a 2 or 12 has 1. A corner's pips divided by 36 is the cards it pays per roll, before the robber.

Your own board, the placement order and each player's starting handOpen the setup helper

Where you'll meet these totals

Almost every strategy guide quotes pip totals, usually in passing. My Kind of Meeple sets the most useful target: at least 11 pips for a starting settlement, with 9 to 10 acceptable. Its examples of strong spots, 8-9-5 and 6-9-5, both come to 13, the same total as Colonist's best corner, so treat 13 as about as good as you'll see.

Meeples Corner has the clearest comparison, setting an 8-5-10 corner against a 3-11-4 corner. Run both through its 71-roll estimate and the difference stops being abstract.

Two corners over one game

Assume each settlement is in place from the first roll, the robber never touches it, and the game runs about 71 rolls. The cards figure is pips × 71 ÷ 36.

8-5-10 corner5 + 4 + 3 = 12 pips
Expected cardsabout 24
3-11-4 corner2 + 2 + 3 = 7 pips
Expected cardsabout 14

A gap of about 10 cards from a single placement. The 71-roll figure is one blog's estimate, so read this as a sense of scale and not a forecast.

More pips or more numbers?

The case for chasing the biggest total is a good one, and Colonist puts it bluntly: "Colonist is a game of production. More is better." The arithmetic above backs that up, and a player who ignores pips will lose cards to one who counts them.

But the total doesn't tell you how those cards arrive, and that's where I'd step off the pure-pips view. Meeples Corner suggests pairing settlements to cover six different numbers, such as 8-5-10 plus 6-9-4. That's 24 pips, and because no number repeats, 24 of the 36 possible rolls pay you something: 67%.

Now say your two settlements sit on 6-9-4 and 6-9-10 instead. That's also 24 pips and the same cards on average, but the only numbers that pay are 6, 9, 4 and 10, which is 15 rolls out of 36, or 42%. You'd collect in bigger bursts with longer droughts between them, and a game has only so many rolls to even that out.

So here's the rule I'd use. One pip is worth about 2 cards across a 71-roll game, which is real but small. Given the choice, give up a pip to add a number you don't already have, or a resource you can't otherwise get. Official Game Rules recommends covering at least four of the five resources between your two starting settlements, and Colonist's warning is the right one to remember: "Don't assume you will be able to trade for any one resource." A large pip gap is different. Nothing about diversity rescues a 7-pip corner when a 12 is open.

What the dots can't tell you

They aren't a forecast. Colonist points out that 2s and 12s sometimes outroll 5s and 9s in a given game, and only settle toward the odds over the long run. A settlement on good numbers can still sit idle for a stretch, and that isn't evidence the chart is wrong.

They also aren't a measure of what a card is worth. Dots tell you how often a tile pays, not whether you want what it pays in. Meeples Corner counts three ore and three brick hexes against four each of wool, wheat and wood, so a modest number on a scarce resource can matter more than its dot count suggests. A pip total is where the comparison starts, and resources are a separate check.

What changes at the table

Stop judging corners by how the numbers look and count them. Before you place, total your top two or three spots against the 9 to 11 range. Check whether your second spot repeats numbers from your first. Then look at what the tiles produce. That's three small steps, and only the first needs the chart.

It also gives a child something concrete to do at the table, since adding three small numbers and comparing the results doesn't require any strategy. Whether an 8 or 9 year old is ready for the rest of the game is a separate question.

The math tells you what a corner is worth, but it doesn't tell you which corners will still be open when your turn comes. That depends on who goes first and the snake-draft placement order, where these totals turn into a decision.