Catan dice roller

How to use this dice roller in your Catan game

The tool rolls two six-sided dice, one red and one yellow, the same colours as the dice in the current edition of the base game. You can press Roll, or pick the dice up with your finger or mouse, drag them and let go over the tray. Once they stop, the total appears: that is the number that produces in Catan.

It works well on a phone in the middle of the table. It is handy if a die has gone missing, if someone wants to see the game statistics, or if you are playing over a video call and everyone needs to see the same result.

How the dice work in Catan

Every turn starts with a roll of both dice. The total decides which terrain hexes produce resources, and it produces for every player, not just the one rolling.

• Each settlement next to a hex with that number takes 1 card of that terrain's resource.
• Each city next to that hex takes 2 cards.
• If you have two or three settlements around the same hex, you collect for each of them.
• The hex with the robber on it produces nothing, even when its number comes up.
• If the bank does not hold enough of a resource to pay everyone, nobody receives that resource that turn, unless only one player is affected.

Number tokens

The base game has 18 number tokens marked 2 to 12. There is only one 2 and one 12; every number from 3 to 11 appears twice, except 7, which has no token at all. The desert never gets a number, and it is where the robber starts.

Under each number is a row of dots, also called pips. They show how many combinations of the two dice make that total: 2 and 12 have one dot, 6 and 8 have five. The more dots, the more often the hex produces. The 6 and 8 are printed in red and in larger figures so you can spot them straight away.

If you set up the board at random instead of following the letters on the back of the tokens, the rules say the red tokens must not end up on neighbouring hexes. If they do, swap tokens until they are apart.

What happens when you roll a 7: the robber

Seven is the most likely total with two dice and, for exactly that reason, it produces nothing. Instead the robber is activated, always in this order:

1. Discard: every player holding more than 7 resource cards (so 8 or more) chooses half of them, rounded down, and returns them to the bank. With 9 cards you discard 4; with 11 you discard 5. Anyone with 7 or fewer loses nothing. Development cards do not count.
2. Move the robber: the player who rolled the 7 must move the robber to another hex or to the desert. Leaving it where it is is not allowed.
3. Steal: that player takes one random resource card from an opponent with a settlement or city next to the new hex. If there are several, they choose whom to rob.

The turn then carries on as normal with trading and building. While the robber sits on a hex, that hex produces nothing when its number is rolled.

A knight card also moves the robber and lets you steal, but nobody has to discard. Discarding only happens on a rolled 7.

Catan dice probability table

Two six-sided dice have 36 possible combinations, all equally likely. The probability of each total is the number of combinations that make it, divided by 36. The dots on the number tokens are exactly that number of combinations.

A few useful figures that follow from the table:

• 6 and 8 together come up in 10 rolls out of 36, or 27.8%.
• A 7 comes up on average once every six rolls. In a four-player game, the chance of at least one 7 in a full round of the table is 51.8%.
• The dots on all 18 tokens add up to 58, a quick way to gauge the total output of the board.

The dots are how you rate an intersection: add up the dots of the hexes around it and you know how many rolls in 36 pay you something. A settlement touching a 6, an 8 and a 5 has 14 dots: it collects on 14 rolls in 36, or 38.9%, about 23 times every 60 rolls.

Why players go for 6 and 8 (and when that is not enough)

Of the numbers that have tokens, 6 and 8 produce the most: each comes up on 5 rolls in 36. A settlement on a 6 hex collects, on average, two and a half times as often as one on a 3 and five times as often as one on a 2. That is why opening settlements tend to go next to red tokens.

There are some caveats worth keeping in mind:

Streaks and variance: why the 6 sometimes never shows

Every roll is independent of the ones before. Dice have no memory: a 6 that has not appeared for ten rolls is no more likely on the next one. Believing otherwise is the gambler's fallacy.

Odd streaks feel impossible, but their odds can be worked out. The chance that a number fails to appear in N rolls in a row is (1 − p) to the power of N, where p is its probability per roll:

In other words, a 6 going 20 rolls without showing happens one time in twenty. With so many tables playing, it happens to someone every day. What is genuinely rare is neither a 6 nor an 8 in 20 rolls.

Over a 60-roll game you would expect about 8.3 sixes, yet there is a 6.7% chance of 4 or fewer and a 6.6% chance of 13 or more. A 2 or a 12 may never appear at all: the chance of no 2 in 60 rolls is 18.4%.

That is what the chart on this page shows. With few rolls the bars stray a long way from the expected values; as the game goes on they drift towards the familiar pyramid shape with 7 at the top. A game of Catan is usually too short for that shape to fill out completely, which is why luck plays such a big part.

Expansions that change the dice

Cities & Knights: the event die

Cities & Knights, first published in German in 1998 as Städte und Ritter, adds a third die: the event die. It has three faces with a ship and three with a city gate, one blue, one green and one yellow. Each turn all three dice are rolled together and resolved in this order:

1. Event die. On a ship, the barbarian ship moves one space towards the island; when it reaches the end of the track, the barbarians attack. On a gate, players may be able to draw a progress card of that colour.
2. Red die. It decides who draws that progress card: you need a red die symbol showing the rolled value in the matching colour section of your city improvement chart. With the first yellow improvement, the market, you draw a yellow card if the red die shows 1 or 2. Higher improvements add more values.
3. Red plus yellow. The total works as in the base game and decides production.

In numbers: the ship comes up on half of all rolls and each gate colour on one roll in six. With the market, the chance of drawing a yellow card on any given roll is 1/6 × 1/3, or 5.6%.

One rule about the 7 is often forgotten: in Cities & Knights the robber stays in the desert until the barbarians attack for the first time. Before that, a 7 still means discarding if you hold too many cards, but the robber does not move and nobody is robbed. The Alchemist progress card lets you choose the result of both numbered dice before rolling; the event die is rolled as normal.

Event cards that replace the dice

Catan has an official alternative to dice: a deck of event cards. It appeared in 2005 alongside the Atlantis scenarios and was later included in the Traders & Barbarians expansion. There are 36 cards, one for each possible combination of two dice, so the spread of numbers matches the table above: six 7s, five 6s, five 8s and so on, down to a single 2 and a single 12.

• Shuffle the 36 cards, set 5 aside face down, put the New Year card on top of them and the rest of the deck on top of that. When New Year turns up, everything is reshuffled. The 5 cards left unplayed keep some uncertainty towards the end of the deck.
• The six 7 cards carry the robber attack event, with the usual discard.
• There are 11 different events and nearly half the cards have one. Epidemic, for example, on 6 and 8 cards, means cities produce only 1 resource that turn.
• If you want a perfect distribution, the rules allow you to play all 36 cards without New Year and reshuffle at the end.
• With Cities & Knights you still roll the event die, and for progress cards you use the red die value printed on the card.

The deck evens out streaks: once the full deck has been played, every number has come up exactly as often as it should. In exchange, the events bring luck back in another way.

Catan history and trivia

This page has no connection with Catan GmbH or Kosmos. Catan is a registered trademark of its owners and is named here only to describe the game.