Settlement

Warning: Beta*This page was written with information available during the beta and may no longer be accurate.*

Settlements are a type of Points of Interest where players can play building cards to construct and upgrade buildings, earning Victory Points for their team, increasing the yields of harvest dices, and improving the trade rates at the bank.

Once every 6 hours per settlement, each player can roll harvest dice. The combined number from the two dice dictate which tiles will produce resource based on the number on the tile. The two tiles marked with an asterisk () will produce resources with every roll. However, if the player rolls a 7, the robber will appear and give the player resources based on the development level of the opposing factions on the settlement.

## Settlement Diagram

Public settlements are built by all three teams, with each team building in their own sector of the settlement.

When the settlement is first discovered, each team has three resource tiles already built. The types of resource is determined by the resource balance in the local region. The two tiles closest to the center will be the Wild tiles, and match the result of any dice roll other then a 7. The third tile will be a "5-pip" tile: either a 6 or an 8. Each team's Monument is also already built when the settlement is discovered, and there are 2 more building locations available to construct buildings with development cards. Only Common (tier 1) development cards can be built while the settlement is just discovered (tier 1). There are 3 more spaces available to build resource tiles.

The settlement can be expanded with Settlement Upgrade development cards. At Tier 2 (Village) an additional 6 resource tiles can be built, there are 6 more building spots are available, and Uncommon (tier 2) buildings can be constructed. At Tier 3 (City) there are 8 more resource tiles that can be built, there are 8 more building spots, and Rare (tier 3) buildings can be constructed.

## Math and Stats

***Note:** You don't need to know or care about the math, you can skip to the easy recap below.*

### Probability

A build spot can have 1, 2 or 3 adjacent tiles, which shall be referred to as Tile A, Tile B, and Tile C in this section.

The probability of a given number being rolled is given in the following tables.

Let

A

{\displaystyle A}

 be the number on Tile A, and

P
(
A
)

{\displaystyle P(A)}

 be the probability of the number on Tile A being rolled.

P
(
A
∩
B
# )

{

0
,

if
A
≠
B

P
(
A
# )
P
(
B
)
,

if
# A
B

{\displaystyle P(A \cap B) = \begin{cases} 0, & \text{if } A \neq B \\ P(A) = P(B), & \text{if } A = B \end{cases}}

P
(
A
∩
B
∩
C
# )

{

P
(
A
# )
P
(
B
# )
P
(
C
)
,

if
# B
C

0
,

otherwise

{\displaystyle P(A \cap B \cap C) = \begin{cases} P(A) = P(B) = P(C), & \text{if } A = B = C \\ 0, & \text{otherwise} \end{cases}}

The probability of a building spot being rolled depends on the number and probabilities of its adjacent spots.

* In the case of a building spot with a single adjacent tile, the probability is simply equal to that of the adjacent tile being rolled.

P
(
A
# )
P
(
A
)

{\displaystyle P(A) = P(A)}

* In the case of a building spot with two adjacent tiles, the probability is given by the following formula:

P
(
A
∪
B
# )
P
(
A
)
P
(
B
)
−
P
(
A
∩
B
)

{\displaystyle P(A \cup B)=P(A)+P(B)-P(A \cap B)}

* In the case of a building spot with three adjacent tiles, the probability is given by the following formula:

P
(
A
∪
B
∪
C
# )
P
(
A
)
P
(
B
)
P
(
C
)
−
P
(
A
∩
B
)
−
P
(
A
∩
C
)
−
P
(
B
∩
C
)
P
(
A
∩
B
∩
C
)

{\displaystyle P(A \cup B \cup C)=P(A)+P(B)+P(C)-P(A \cap B)-P(A \cap C)-P(B \cap C)+P(A \cap B \cap C)}

### Expectation

The probability calculated above does not take into consideration the fact that, on a building spot where more than one tile has the same number, if that number is rolled the rewards of that building would be given more than once. The *expectation*, also known as *expected value*, *average*, or *mean*, takes this into account.

Considering the gain of all building spots to be equal, the expectation of a building spot is simply the sum of the probability for each tile to be rolled.

* In the case of a building spot with one adjacent tile:

E
(
A
# )
P
(
A
)

{\displaystyle E(A) = P(A)}

* In the case of a building spot with two adjacent tiles:

E
(
A
∪
B
# )
P
(
A
)
P
(
B
)

{\displaystyle E(A \cup B) = P(A) + P(B)}

* In the case of a building spot with three adjacent tiles:

E
(
A
∪
B
∪
C
# )
P
(
A
)
P
(
B
)
P
(
C
)

{\displaystyle E(A \cup B \cup C) = P(A) + P(B) + P(C)}

Note that if the numbers on the adjacent tiles are all different, then the probability and expectation are equal.

### Easy recap

Add up the number of pips (dots) under the number of the tiles adjacent to a building spot, the sum is how likely that building spot is to be rolled.

Divide that number by 36 to get the probability/expectation, then multiply by 100 for a percentage.

This works as long as the numbers are all different.

### Harvest Dice

Note how the number of pips (dots) under the number shows the number of dice combinations that result in this number. It's thus effectively an indicator of how likely that number is to be the result of the roll.

Harvest Dice roll result probabilities

1
36

{\displaystyle \frac{1}{36}}

2
36

{\displaystyle \frac{2}{36}}

3
36

{\displaystyle \frac{3}{36}}

4
36

{\displaystyle \frac{4}{36}}

5
36

{\displaystyle \frac{5}{36}}

6
36

{\displaystyle \frac{6}{36}}

### Building Spot Stats (unique)

*The following tables are generated and further manual edits might be lost in an update.*

#### Double Tiles

(table missing until the wiki decides to work)

#### Triple Tiles

(table missing until the wiki decides to work)