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Settlers of Catan: Theory and Practice

These are the notes from Blake’s 5-day project on Settlers of Catan strategy at Not Back to School Camp 2012.

Here’s the final video we produced (in a hurry):

 

Catan Probability

What do the dots mean? Dots = average number of rolls out of 36

2:…1

3:…..2

4:…….3

5:………4

6:………..5

7:………….6

8:………..5

9:………4

10:…..3

11:…2

12:.1

How often a specific number will be rolled in 60 rolls (roughly one typical game):

2: (2.78% * 60) = 1.67

3: (5.56% * 60) = 3.34

4: (8.83% * 60) = 5.30

5: (11.11% * 60) = 6.67

6: (13.89% * 60) = 8.33

7: (16.67% * 60) = 10.00

8: (13.89% * 60) = 8.33

9: (11.11% * 60) = 6.67

10: (8.83% * 60) = 5.30

11: (5.56% * 60) = 3.34

12: (2.78% * 60) = 1.67

Gambler’s fallacy: the idea that a certain number is “hot” during a game. E.g. if the 4 is getting rolled a lot, you should build toward a 4 instead of a more statistically probably number.

Probability combinations (e.g. 5-9-11) get mixed up by random placement of the desert. 5-6-9 is killer combo (& not always present).

Basic Approaches

Balance Strategy

Pluses: get a little of all resources, maximize numbers

Minuses: no particular plan for getting victory points

Wood-Brick Fast Expansion + Longest Road

Pluses: Quick access to many resources, ability to cut enemies off from territory early

Minuses: Potential to get frozen out of city-building materials late. Your crops will lose value over the course of the game.

Works well for late-placement if there are wide areas with few settlements. Use roads early both to expand and to cut off your enemies.

Ore-Wheat Cities + Dev. Cards + Largest Army

Pluses: multiply earnings from early settlements; benefits from development cards

Minuses: more concentrated = vulnerable to robber

Monopoly Strategy

Pluses: Monopolize a single resource on the board = high trade value with other players; trade for what you need

Minuses: Robber target

Port Strategy

Pluses: Build multiple times on a single abundant resource on the board + 2:1 port, trade for what you need

Minuses: Only two numbers/resources per settlement/city. Feast/famine.

No matter your strategy, you’ll likely need 4 total settlements/cities to win. (Why? Count the possible victory points.) Expansion is always necessary.

Initial Placement

Which phase of SoC is most critical: initial, mid, or late game? Initial, due to exponential nature of game. Capital investments produce more profit.

Initial goal = increase production growth. SoC is an exponential growth game! Early investments multiply. Hold off on longest road unless immediate opportunity must be taken. Hold off on pursuing largest army.

Another result of exponential growth: early handicaps matter. Poor roles or robber can truly set you back.

Placing on identical number tiles = distribution trade-off. Same number w/ two paired resources (brick/wood, ore/wheat) can be helpful. Also 2:1 port. But feast/famine, especially due to statistical clumping of rolls. (In 100 coin flips, 95% of the time there will be a run of 7 or more.)

You get resources from your second settlement. Consider what you can build with that second placement.  Can you build a road with which to cut off an opponent?

Maximum initial dot combination placement = 13 (if placement rules are followed)

Avoid initial port placements, in general.

Road building: be wary of moving toward high-value hexes. Consider # of players first. When in doubt, build toward the sea and/or 3-4-10-11 tiles.

Catan board generator (for Windows): http://www.birdieman.com/catanboard.htm

Basic Trading Strategy

Trade is exploitation. Please exploit. Don’t give easy trades.

Think about “Pareto optimality”: win/win, win/lose, lose/lose

Trade as close to your turn as possible so that you have a better chance of using it (instead of losing it, or gaining it anyways on a roll). If you have an advantage, trade on your turn.

Trade to stay below 8 cards.

When two even trades exist, trade with the less threatening player.

You can trade for anything, though it’s not binding. Favors. Revenge. Garlic bread.

Optional house rules: Futures, Trading Development Cards

Trading mind games

Visual incentivizing

Tell them how to trade; tell them their strategy.

Trade even when it won’t distinctly advantage you. Why? Because if someone else makes that trade, they might advantage each other.

Disparage the terms of your enemies trades. Point out how “bad” of a deal other experienced players have offered. Make it obvious that your trades are “fair”.

Various Mid-Game Strategies

If not going for longest road, use the triangle fork settlement building strategy, which costs you 3 road per 2 settlements (rather than 4).

Development cards

Ask yourself: How many resources cards are you spending on average to purchase one victory point?

Dev card probabilities (most recent edition). Remember that these change as the game progresses and if you pay attention to what cards have already been drawn, you can increase the probability that you’ll draw a certain card.

Knight: 56%

Monopoly: 8%

Road Building: 8%

Year of Plenty: 8%

Victory Point: 20%

If you draw a knight, tell people it’s a knight. Good defense.

It you draw anything else, tell people it’s a victory point. Don’t reveal monopoly, road-building, or Discovery — each has sneaky end-game value.

Remember to use a knight card before you roll.

Robber

Early game robber will piss someone off, no matter what. Consider pissing only one player off to minimize revenge factor. When in doubt, place the robber on the player to your right so that it spends the most time there (and not back on you). Esp. good if you have a knight in your hand.

When you get robbed, ask what the other player wants. If it’s something you don’t need, you both benefit from not allowing them to pick randomly. If it’s something you need to keep, make them choose randomly anyways. (If you do the above strategy enough times, you can lie at the end of the game to preserve your winning hand when robbed.)

Guilt others into not putting robber on you w/ “fairness” argument.

Offer a resource you don’t need in exchange for someone not putting the robber on you. (Warning: can lead to devastating bidding wars)

Sneaky Shit

Embargo!

Put the dice in front of the next player to hurry an indecisive (and threatening) player.

Trade away a lot of one resource, then Monopoly it back.

Act like you’re trading for a certain resource, then Monopoly it.

Act like you’re trading for a certain resource, then Knight the person who has it.

Have another player “hold” cards for you to avoid discarding on a 7

Don’t tell someone when they miss picking up a resource

Irrational threats (“If you put the robber on me, I will dedicate the rest of the game to defeating you, even if that means I lose too!”)

Elect yourself “point announcer”. This serves to remind people who their enemies are when you aren’t winning and to remind them of your “even-handedness” when you are. Make sure to include any unrevealed development card as a VP for your count.

 

[Thanks to Catan player Matt Sanderson for many of these strategies.]

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