Catan — rules

4-player Settlers of Catan. Implemented mechanics: settlement and city placement, roll-distribution, robber, road network, bank trade, 1-for-1 player trade, development cards, Longest Road, Largest Army. Multi-card trade bundles are not modeled.

Board

• 19 hexes arranged as a radius-2 hexagon, generated deterministically per seed. Resource tiles: 4 wood, 3 brick, 4 sheep, 4 wheat, 3 ore, 1 desert. Number tokens 2–12 (no 7) shuffled across non-desert hexes.
• 54 vertices and 72 edges connect the hexes. Each vertex is shared by up to 3 hexes; each edge by up to 2.
• The robber starts on the desert.

Initial placement

Snake order (seats 0→1→2→3, then 3→2→1→0). Each turn the seat places one settlement at a legal vertex, then one road at an unoccupied edge adjacent to that settlement. The second settlement (round 2) grants one of each resource from its adjacent hexes as starting hand.

A vertex is legal for a settlement only if it is unoccupied AND no neighboring vertex (through one edge) is already occupied (the standard distance rule).

Main loop

Each player turn proceeds in four phases:

1. Roll — roll. Two dice (deterministic per turn from match seed) produce the roll value.
2. Resource distribution (skipped on 7) — every adjacent settlement on a hex matching the rolled number gets 1 of that hex's resource. Cities get 2.
3. Main actions — any number of build_* and trade_bank:* actions the player can afford and has space for, then end_turn.
4. Discard + robber (only on a 7 roll) — players with > 7 cards auto-discard floor(n/2) of their largest pile (deterministic). The roller then chooses a hex to move the robber to and (if the new hex touches another player's building) chooses one of those players to steal a random resource from.

The robber blocks production on its hex until it moves again.

Building costs

A settlement must be at a vertex connected to one of your roads (the road-connection rule). A city must replace one of your own settlements.

Trade

Two ways to convert resources:

• Bank trade — pay N of one resource to the bank, take 1 of any other (trade_bank:<give>:<get>). The default rate is 4:1; a settlement or city on a generic 3:1 port drops every resource's rate to 3, and one on a resource-specific 2:1 port drops that resource's rate to 2. The board ships 4 generic and 5 specific ports (one per resource). your_trade_rates in the public state shows the best rate the viewer can pay per resource.
• Player trade — offer_trade:<target_seat>:<give>:<get> proposes a strict 1-for-1 exchange of a single resource each way with a chosen opponent. The target's only legal moves are accept_trade (cards swap, both hands update) or decline_trade (no swap). At most 2 offers per turn to keep negotiation finite.

Victory

First player to 10 VP wins (standard Catan target), counting base VP plus Longest Road, Largest Army, and face-down VP cards.

If no player reaches the VP target within 160 dice rolls, the highest-VP player wins; ties broken by resource count, then seat order.

Development cards

Buy a card on your main turn for 1 sheep + 1 wheat + 1 ore (buy_dev_card). The deck has 25 cards: 14 Knights, 5 Victory Point cards, 2 Road Building, 2 Year of Plenty, 2 Monopoly. You may play at most one non-VP card per turn, and never a card you bought this turn.

• Knight (play_dev:knight) — move the robber and steal as if you had rolled a 7 (no discard step). Counts toward Largest Army.
• Road Building (play_dev:road_building) — place two free roads (engine enters road_building_first then road_building_second, each accepting a free_road:<edge> action).
• Year of Plenty (play_dev:year_of_plenty:<res1>:<res2>) — take any two resources from the bank in one action.
• Monopoly (play_dev:monopoly:<res>) — every opponent gives you all of their cards of the named resource.
• Victory Point — kept face-down; counts +1 VP for the holder. Not playable as an action.

Largest Army

The player with 3 or more played knights gets +2 VP. Transfer follows the same rules as Longest Road: ties keep the bonus with the current holder; a strict overtake by one player transfers it; an overtake by a tie vacates it.

Longest Road

The player with the longest continuous chain of their own roads, provided that chain is at least 5 segments, gets +2 VP. The chain must be a simple trail (each road used at most once) and breaks at any vertex where another player has a settlement or city — you can finish a chain at an opponent's building but cannot extend through it.

Transfer rules:

• The current holder keeps the bonus on tie or sole lead.
• A new unique leader strictly longer than the holder takes the bonus.
• If the holder is overtaken by multiple players tied at the new max, the bonus is vacated until one player extends further.
• If the holder's chain drops below 5 (e.g. an opponent settlement splits it), the bonus is lost.

public_state.longest_road_holder, longest_road_length, and per-seat longest_road_lengths track the bonus. total_victory_points is the authoritative tally for the victory check.

Forfeits

Any action outside the legal set forfeits the match for the offender (no points credited; the leader on VP at forfeit is the winner).