Catan strategy: 6s and 8s or variety, ore or wood, and does your seat matter?

First, what a dot is worth

The dots under a number token count the ways to roll that number with two dice. There are 36 ways in total, so a 6 with its five dots comes up 5 times in 36 rolls. Add up the dots around a spot and you know how many cards it pays per 36 rolls.

And it pays on every roll, not just yours. With four players a 6 next to your settlement pays out 5.6 times every ten rounds on average. A 2 pays out once every 9 rounds: about 2 times in a whole game of 20 rounds.

6s and 8s, or every resource?

The oldest Catan argument. One side says take the best numbers and trade for the rest. The other says a resource you never roll is a resource you have to beg for.

We built six opening strategies on one shared bot (more on that below), so the only thing that differs is where they settle and what they value. The Pip chaser takes the most dots, period. Variety first takes as many different resources as it can. Balanced counts dots, gives extra credit for resources that are scarce on this board, for new resource types and for harbors. We sat each one at a table of three Balanced bots, rotated the seats and played 7,500 games per strategy, with simple trading between players switched on.

The Pip chaser does get the best numbers: 21.9 dots on its two starting settlements against 19.3 for Variety first. But it starts with 3.5 resource types against 4.8, and it wins -20% against a fair share. Without trading between players it is worse still: -40%. Variety first does better (-7%), and Balanced, which wants both, sits at a fair share against copies of itself. Starting on random spots, the baseline everyone should beat, comes in at -89%.

On this board the Pip chaser goes for the 13-dot spot on brick and wheat. Every other strategy settles for fewer dots and a third resource. In a draft between four Balanced bots on the same board, nobody takes that spot at all.

What one extra resource type is worth

To put a price on it, we let all four players start on random legal spots and play the same way afterwards: 60,000 starting positions, from hopeless to excellent. Then we compared positions with the same number of dots and a different number of resource types.

With 13 to 15 dots, players on two resource types come in at -32% against a fair share, players on four types at +39%. Three more dots with one type fewer comes out about even: 16 to 18 dots with three types (+46%) against 13 to 15 dots with four (+39%). A straight-line fit over all positions says one more type is worth 2 dots when players trade, and 3 when they don't.

Not every dot is equal either. In the same fit, measured in average dots, a dot of wheat is worth 1.3, ore 1, brick 1, sheep 0.9 and wood 0.8. A starting harbor was worth about 0.9 dots.

Ore and wheat, or wood and brick?

The second argument is about the whole plan. Wood and brick means roads and settlements: spread out early, grab Longest Road. Ore and wheat means cities and development cards: sit tight, upgrade, collect knights. We gave both plans the best shot we could: the opening strategy settles on its resources, the bot builds in its order, and we tried 12 settings for each plan before picking the best one for the main run.

Here is the race. Turns are your own turns, so turn 10 is the tenth time the dice come to you.

Wood and brick wins every race except the one that counts. It places a fifth settlement in 52% of its games and takes Longest Road in 65%. But with almost no ore its first city waits until turn 17, and once its settlement spots run out, everything that still scores needs ore. Ore and wheat has a city by turn 5, buys 8.5 development cards a game and takes Largest Army in 61% of games. Final score: +14% against -52%.

We tried to rescue wood and brick. The best of 12 play settings, re-run on 7,500 fresh games, is the -52% above. A milder opening that still likes good numbers and new resource types, with just a tilt toward wood and brick, came in at -26%. The best ore and wheat setting scored +25% in the smaller tuning run and +14% in the main one.

One level deeper: what if everyone goes ore and wheat?

A plan that wins against Balanced bots proves little if it only works because nobody else is doing it. There are three mountain hexes on the board. So we sat each strategy at tables where all three opponents play the same plan.

At a table of Pip chasers, ore and wheat is the best plan we have (+37%). At a table of ore and wheat players it is just one more player fighting over three mountains, at +5%, while Balanced wins +33%. Even wood and brick climbs to -6% there. Trading matters too: without trades between players, ore and wheat drops to -14%, because it has to get its wood and brick from somewhere.

Does seat order matter, with the snake draft?

In the setup the first player places first, the last player places twice in a row, and the order snakes back: 1-2-3-4-4-3-2-1. The idea is that seat four makes up for the worst first pick with the best second one. In 30,000 drafts between identical Balanced bots, it doesn't quite: seat one's first settlement averages 11.7 dots and seat four's 10.1. Seat four gets the better second spot (9.3 against 8.5), but ends up 0.9 dots behind in total.

Then the games. Between four identical Balanced bots, seat one wins 30% of the time and seat four 21%, against a fair 25%. With three players it is 38% against 30%. Using the price per dot from the random-openings test, the starting spots explain only about 33% of that gap. The rest is tempo: seat one rolls first, builds first and gets to every spot first for the whole game.

Are development cards worth it?

Counted as points, development cards are expensive. A card costs three resources, and only 5 of the 25 are worth a point.

But that undercounts the knight. Say the robber sits on your 6. It costs you 5/36 of a card per roll, on every player's roll, so 0.6 cards per round in a four-player game. Left alone it stays until the next 7, which is 6 rolls away on average: about 0.8 cards per settlement on that hex. A knight gets that back, steals a card, and counts toward Largest Army, which is two points.

In our games that adds up. The ore and wheat bot buys 8.5 development cards per game, plays 4.1 knights, takes Largest Army in 61% of games, and is the plan that wins most. Development cards are not a way to score. They are a way to turn ore, wheat and sheep into points when your settlement spots run out.

What we left out

Trading and robber politics are where real Catan games are won, and they are the hardest part to model. Our bots trade one card for one card, only when both sides need what they get, and they refuse anyone with eight or more points. Nobody haggles, offers two for one, or forms a trade embargo against the leader. Real tables trade more, which helps the plans that start short of a resource: ore and wheat players most of all, but also the Pip chaser.

The robber goes on the hex that hurts the leader most, by public points. Nobody threatens, bargains or holds a grudge. Bots don't block a spot just to deny it in the draft, and they don't count hidden victory point cards. So read these numbers as "best of the strategies we tested, against bots that play decently", not as a solution of the game.

How we tested

The rules engine plays the base game as in the 5th and 6th edition rulebooks: 19 terrain hexes (4 forest, 3 hills, 4 pasture, 4 fields, 3 mountains, 1 desert), 18 number tokens placed at random with the red numbers never next to each other, nine harbors (four 3:1 and one 2:1 per resource) shuffled over fixed spots on the coast, the snake draft with starting cards from the second settlement, production with the bank's 19 cards per resource (if the bank can't pay everyone, nobody gets that resource unless only one player is owed it), the robber and discarding half above seven cards, roads, settlements with the distance rule, cities, piece limits (15 roads, 5 settlements, 4 cities), 4:1, 3:1 and 2:1 trades, the 25 development cards with one per turn and none on the turn you buy it, Longest Road (5+, broken by an opponent's settlement) and Largest Army (3+ knights), and ten points on your own turn to win. Automated checks cover the board geometry, the dice, production and the bank rule, the robber, harbors, development cards, Longest Road cuts and loops, and invariants after every turn of full test games.

All bots share one core. Each turn it lists its options (a city, a settlement plus the roads to reach it, a development card, a push for Longest Road), values each in points plus the production it adds, divides by the turns it expects to need to afford it, and works on the best one, trading with the bank or a harbor when that completes the purchase. The strategies differ only in where they settle and how they weigh those options. Every configuration was played thousands of times with rotating seats and fixed random seeds: one strategy against three Balanced bots (90,000 games, with and without trading), against tables of rival plans (67,500), random starting spots (30,000), identical bots for seat order (36,000) and a tuning run (15,600).

Limits worth knowing, beyond trading and the robber: the bots are decent, not expert, and games between them last about 20 rounds. The value of a resource type depends on how much players trade, which is why we show both. Harbor positions follow a fixed pattern around the coast rather than the printed frame, and we only played three and four players. Exact numbers (dice, dots, costs, the robber) are exact; everything that comes from games is bot-dependent. More on how we test.