I Analysed 47,000 Games of Catan. Here's How to Win Every Time (mathematically) 🎲🐑

About this video

• Video Title: I Analysed 47,000 Games of Catan. Here's How to Win Every Time (mathematically) 🎲🐑
• Channel: Ioana Roman
• Speakers: Ioana Roman
• Duration: 00:17:39

Overview

This video mathematically analyzes over 47,000 recorded games of Catan to determine what factors contribute most to winning. It debunks the idea that Catan is purely luck-based, instead presenting it as a structured, stochastic dynamic optimization problem with elements of probability, game theory, and empirical analysis. The video explores various game mechanics, from dice probabilities and settlement placement to development cards and trading strategies, to identify statistically significant advantages.

Key takeaways

• Catan is not purely based on luck; it's a strategic game with well-defined probabilities and optimization opportunities.
• The game can be modeled mathematically, considering resource vectors, graph theory for board layout, and market dynamics for trading.
• Turn order has a surprisingly balanced impact on win rates, with the third player having a very slight edge.
• While Longest Road and Largest Army bonuses correlate with winning (increasing win rates by approximately 9% and 4% respectively), they are not guarantees of victory.
• Missing a single resource at the start of the game has a minimal impact on win rates due to the game's trading and port mechanisms.
• A simple classifier trained on initial placements could only predict winners with 27% accuracy, indicating that most of the game's outcome variance occurs after the initial placements.
• Development cards, particularly the Monopoly card, can significantly shift game outcomes by acting as resource shocks.
• "Inefficient" trades (giving up more resources than received) can be strategically beneficial, often used to gain tempo or secure key objectives.
• The game rewards scaling (e.g., through cities and development cards) more than simple expansion (e.g., building many roads).
• Catan is a path-dependent game where interactions, timing, and adaptability are crucial, rather than being predetermined from the start.

Based on the data analyzed, the video suggests that a strategy focused on scaling through cities and development cards, rather than just expansion through roads, is more effective for winning Catan.

Key points supporting this:

• Resource Exposure: Winners tend to have slightly higher exposure to wheat and sheep, resources crucial for development cards and cities.
• Roads vs. Cities: Exposure to brick and wood (for roads) is almost identical between winners and losers, suggesting that while important, road building might not be the fundamentally dominant strategy. The game may reward "compounding city growth" over extensive road networks.
• Development Cards: The use of development cards, particularly the Monopoly card, has a significant impact on win rates, acting as "resource shocks" and "systemic liquidity extraction."
• Trade Efficiency Paradox: Players who appear to make "inefficient" trades (giving up more than they receive) often win more. This is because they are not optimizing the trade itself, but rather their overall position, trading for tempo, securing key objectives, or blocking opponents, which leads to long-term gains.
• Path Dependency: The game is highly path-dependent, meaning decisions made throughout the game, especially in terms of trading, development card draws, and timing, are more critical than initial placements alone.

In essence, the "best" strategy involves leveraging resources for city upgrades and development cards, making strategic trades (even if they seem inefficient short-term), and adapting to the game's evolving dynamics, rather than solely focusing on expanding territory with roads.

The video indicates that missing a single resource at the start of the game has a surprisingly small impact on win rates.

Here's what the analysis showed:

• Minimal Dip: Missing any one resource barely moves the needle in terms of win probability. Win rates remain around 25%, with only slight dips observed when missing ore or wood.
• Resilience through Trading: This resilience is attributed to the game's built-in correction mechanisms, primarily trading. Players can use ports and player-to-player trades to acquire the resources they lack.
• Economic Perspective: The game is viewed as an economic system that adapts. It doesn't easily collapse due to the absence of a single input because trading infrastructure (like ports) exists to resolve such imbalances.

Therefore, while having all resources might be ideal, not having one specific resource from the beginning is not a death sentence and can be overcome through strategic play and trading.

Using a Monopoly card has a significant and positive impact on a player's win rate.

Here's a breakdown of its effect:

• Without Monopoly: If a player plays zero Monopoly cards in a game, their win rate is around 25% (the baseline).
• With One Monopoly Card: If a player plays just one Monopoly card, their win rate jumps up to approximately 40%.
• With Two Monopoly Cards: If a player plays two Monopoly cards (the maximum possible in a game), their win rate approaches 55%.

The video explains that Monopoly cards function as "resource shocks," effectively redistributing accumulated resources from all other players into the player's inventory. The effectiveness of a Monopoly card is also influenced by timing; late-game plays, when players have accumulated more resources, are dramatically more effective than early-game plays. It's described as a "systemic liquidity extraction" mechanism that can decisively shift game probabilities.