How the dice drive production
In a typical settlement board game, the board is made of resource tiles, each marked with a number from 2 to 12. On your turn, two dice are rolled. Every tile showing the rolled total pays out to the players who have a building next to it. Your income therefore depends on two things: how often your tiles’ numbers come up, and how many different resources you collect.
The key fact is that two-dice totals are not equally likely. There are 36 equally likely combinations when you roll two six-sided dice, and different totals can be made in different numbers of ways.
| Total | Ways to roll it | Chance |
|---|---|---|
| 2 or 12 | 1 | 1 in 36 (about 2.8%) |
| 3 or 11 | 2 | 2 in 36 (about 5.6%) |
| 4 or 10 | 3 | 3 in 36 (about 8.3%) |
| 5 or 9 | 4 | 4 in 36 (about 11.1%) |
| 6 or 8 | 5 | 5 in 36 (about 13.9%) |
| 7 | 6 | 6 in 36 (about 16.7%) |
You can check the table by adding the ways: 1+2+3+4+5+6+5+4+3+2+1 = 36. Counting these combinations is the idea behind a sample space of equally likely outcomes.
Many games of this type give the 7 a special role, such as triggering a blocking piece or a penalty, instead of paying out any tile. Check the rules of your own game, but the count of ways to roll it is still 6 in 36.
Reading the number tokens
Number tokens on the board often show small dots, one for each way the total can be rolled. A 6 or 8 has five dots, a 5 or 9 has four, and so on down to a single dot for 2 or 12. The dots are a quick reminder of the table above.
A simple placement score is to add up the dots at each corner where you could build. A corner touching a 6, a 5 and a 9 scores 5+4+4 = 13 dots, which means 13 of the 36 combinations would pay you something. Because a single roll produces only one total, these outcomes cannot overlap, so you can add them directly: 13/36 is about 36% per roll. A corner touching a 2, a 3 and a 12 scores 1+2+1 = 4, or 4/36, about 11%.
This is a useful guide, not a prediction. Over a short game of perhaps 60 to 80 rolls in total, actual results often drift well away from the averages, a point explored in discussions of short-run results. A high-dot corner is better in expectation, but a particular game can still go against you.
Variety matters as much as frequency
Maximising dots alone can be a trap. If all your high-probability tiles produce the same resource, you will collect plenty of it and be unable to build anything that needs a different one. A balanced position with moderate numbers on several resources can be more useful than one excellent number on a single resource.
It also helps to think about which resources your goals require. A plan that needs many of one resource type rewards a different placement from a plan built around variety. The right choice depends on your intended route, and reasonable players disagree on which is best.
What the numbers mean for trading
Trading is where the probabilities turn into decisions. A resource you rarely receive is scarcer for you, and so more valuable to you than one you collect in abundance. A fair trade, in a rough sense, gives away something you have plenty of in return for something you lack.
Some rules of thumb follow:
- Value depends on your position. The same card is worth more to a player who needs it for an immediate build than to one who has no use for it.
- Scarcity is table-wide. If no one has a good number on a resource, everyone will want it, and its price in trades tends to rise.
- Your opponents can do this arithmetic too. If you offer a trade, they will often work out what you need from your board and your hand.
- Helping a rival is a cost. A trade that is fair between two players can still be bad for you if it moves the other person closer to winning.
A trade can be thought of as comparing what each side gets in terms of weighted averages of how useful each card is to them. Because the usefulness is different for each player, both sides can leave a trade feeling they gained. This is a feature of the game, and one reason negotiation is often seen as a skill beyond pure luck.
Where chance and choice meet
Dice decide what arrives, but you decide where to stand and what to swap. Good placement raises the average number of resources you collect, and sensible trading helps you convert those resources into what you need. Neither removes the randomness. A player with excellent numbers can still go many turns without income, and a player with weak numbers can sometimes have a lucky streak.
It is worth remembering that rolling a number many times in a row does not make it less likely on the next roll; each roll is independent of the previous ones. Believing otherwise is a version of the gamblers fallacy, and it can lead to poor trades based on a feeling that a number is “due”.