Distance
Playable nowHow many hexes apart two islands are, and how to work it out yourself.
You can do this now.
Counting hexes
The map is a grid of hexes. The distance between two islands is the fewest steps from one hex to a touching hex that gets you from one to the other. Cities on the same island are 0 apart.
An island's address is its coordinates. In 48:27, q is 48 and r is 27. Either number can be negative.
The formula
- Take the two addresses, q1:r1 and q2:r2.
- Work out Δq = q2 − q1 and Δr = r2 − r1.
- Distance = ( |Δq| + |Δr| + |Δq + Δr| ) ÷ 2
The same number is the largest of |Δq|, |Δr| and |Δq + Δr|, which is quicker in your head.
What distance decides
- Sailing time: 5 minutes plus 5 for every hex, or 2 minutes to another city on the same island. Loading at the Port comes first and does not depend on distance.
- Which listings an Auction House sees: those within its level + 1 hexes, or 2 hexes more once you have researched Trade Routes.
Examples
- 0:0 to 3:-1: Δq = 3, Δr = -1, Δq + Δr = 2. (3 + 1 + 2) ÷ 2 = 3 hexes.
- -2:0 to 0:2: Δq = 2, Δr = 2, Δq + Δr = 4. (2 + 2 + 4) ÷ 2 = 4 hexes.
- 1:-3 to -1:-1: Δq = -2, Δr = 2, Δq + Δr = 0. (2 + 2 + 0) ÷ 2 = 2 hexes.
A level 1 Auction House
Green dots are places an island can be. AH is the Auction House's island, and it sees listings on every island in the shaded hexes.