I've played more Ticket to Ride than 99% of the world's population (I didn't do the math, but I'm fairly confident). After years of playing with friends and family, I've come to appreciate the underlying rules and strategies that emerge when you dedicate enough time to the (or any) game.
In May, I began tracking my family's gameplay, recording different metrics and variables, and then later analyzing this data. From June 1st to August 31st, we held a summer-long, 50-game Ticket to Ride Tournament. This is what came of this project...
The Basic Rules of Ticket to Ride
For those unfamiliar with the game, here's a quick rundown of how it works. Each player is assigned a color and given 45 trains in that color. In the tournament, I played as green. The goal is to score as many points as possible. You earn points in two main ways: by building railways (connections between cities that range from 1 to 6 train segments long) and by completing destination tickets, which involve creating a route between two specified cities. Shorter routes score fewer points, while longer ones score more. Additionally, there's a 10-point bonus for the longest continuous railway... more on that later.
To build railways, you spend the train cards you've collected and place your train cars. For example, if a railway is 5 segments long and its color is blue, you'll need 5 blue cards or a mix of blue cards and wildcards (e.g., 3 blue cards and 2 wildcards). There's a face-up pile of 5 train cards that you can choose from during your turn, as well as a face down "random" pile.
Each turn, you get one action, which can be:
- Drawing 2 train cards (either from the face-up pile, random pile, or one from each).
- Drawing new destination tickets (you draw 3 but only need to keep 1).
- Building railways.
That's the basic overview of the game and its rules.
Tracking Games: The Gamelog
At the core of this project was the Gamelog, a simple spreadsheet where I entered our scores and various other metrics following each game. These metrics included:
- Total Points: The final score each player achieved.
- Train Points: Points accrued from the length/quantity of trains placed.
- Route Points: Points earned from completing destination tickets.
- Route Quantity: The number of destination tickets each player had at the end of a game.
- Route Completion Rate: The ratio of routes completed to routes drawn, expressed as a percentage.
- Longest Route: Whether the player earned the bonus for the longest continuous train.
- Cars Remaining: The number of train cars left when the game ended.
This data was tracked for every game (with a few gaps in data such as cars remaining and route completion rate where certain metrics weren't tracked yet) and averaged out at the bottom of the sheet to give an overview of our trends over the season. This raw data became the foundation for everything that followed.
View Gamelog PDF
Visualizing: G(ame)-Analysis
Next came the G-Analysis sheet, which visually represented the data from the Gamelog, showing how different metrics changed over time. Graphs charted total points, route points, route quantity, and train points, allowing us to quickly see how our scores evolved throughout the tournament.
While visually interesting, the sheet didn't reveal many actionable insights beyond what could be inferred from the raw data. It's possible my limited experience with data visualization prevented me from noticing more subtle (or even non-subtle) patterns. The graphs didn't alter my understanding of our play styles... but they did provide a bird's-eye view of our progress and change over time.
View G-Analysis PDF
Understanding: P(layer)-Analysis
The most exciting part of this project was the P-Analysis sheet, where the data came to life. I broke down each player's individual performance using formulas and creating metrics, giving us a deep dive into the play styles and emergent outcomes.
Some key metrics from the Player Analysis sheet:
- Standard Deviations: Regular, positive, and negative deviations relative to each individual player's scores.
- Highest/Lowest Game Performance: The scores from the top and bottom 3 games.
- Points per Route: The average points gained per destination card drawn.
- Points per Train: The average points gained per train placed.
- Volatility: Variation in score calculated by dividing the player's standard deviation by their average score (expressed as a percentage—lower % = less variability).
- Sharpe Ratio: Adapted from finance, measuring the player's average score against the average of all players, where the player's average is the "return" and the cumulative (of all players) average is the "risk-free rate" (reasoning: to win in the aggregate, you should aim to beat the average score).
- Sortino Ratio: A variation of the Sharpe ratio that focuses solely on downside risk (negative deviations), measuring a player's worst performance relative to the established risk-free rate.
These metrics were also broken down by train points and route points, giving the players the ability to hone in on different play styles/strategies to maximize points and wins. Armed with this data, players (mainly me) could adjust tactics for future games... for instance, dialing in on consistency or embracing high-risk, high-reward strategies.
View (Noah Williams) P-Analysis PDF
The Results
After 50 games (with an average duration of 40 minutes per game), I scored a total of 6,255 points, winning 23 games. Player3 (anonymized for privacy) followed with 6,093 points and 19 games. Player2 with 5,622 points and 8 games. It was truly a hard-fought battle, with Player3 eclipsing my wins briefly before I pulled ahead. My highest score in a three-player game was 182 points (in a two-player non-tournament round, I reached 209 points!) where I drew and completed 10 routes.
Emergent Strategies and Language
One of the most fascinating aspects of playing so many games was the emergent strategies and terminology we developed—concepts not found in the rulebook but essential for higher-level play:
- Card Pull Order: Unless two face-up cards are exactly what you need, always draw one from the random pile first. You gain the advantage of partial certainty before making your next decision, instead of relying on blind luck (a similar problem to the Monty Hall Problem).
- Counting Cards: There are 12 cards of each color (black, white, red, orange, yellow, green, blue, pink) and 14 rainbow/wildcards (affectionately trainbow). By paying attention to what others play, what's in your hand, and the cards that are face up, you can reasonably guess what remains in the deck, allowing you to make more informed decisions.
- Antifragile Pathing: Paths vulnerable to disruption (like Nashville to Atlanta) can be blocked easily, dramatically increasing your costs. Identifying fragilities and building early (robust), or adapting to disruptions by pathing through destination ticket dense locations (antifragile) becomes critical to scoring higher points and avoiding losses.
- Avoiding Path Dependency: Part of "Antifragile Pathing" is avoiding path dependency, or avoiding relying on certain events occurring or not occurring to achieve your desired outcome. Someone suffering from path dependency is fragile to other players actions. If you need a certain segment connection, you are path dependent to that connection. If you need to pull a certain color of cards in order to build/play, you are fragile.
- Increasing Path Optionality: The inverse of path dependency, path optionality, refers to gaining and maintaining options throughout the game. What does this look like? Lets say there are three ways left for me to complete a route - but there's still a lot of game left. Because there are three ways I can complete that route, that route is not fragile. But, it could be. If someone takes 2/3 accessways, the route is now fragile. So - what is the solve? Gaining the ability to place and build on all three pathways such that you have the option to build whenever YOU decide is right, instead of having you hand forced. Ideally, layering options is the best strategy here.
- Route Efficiency: We coined the term "inefficiencies" to describe deviations or branches in your train path, which work against securing the 10-point longest route bonus. Optimal pathing allows for both efficient route-building and the completion of multiple destination tickets.
- Worth noting, longest route is typically a losing strategy as it "costs" more than it's worth if it limits your ability to complete destination tickets. The average value a destination ticket is 11.6... longest route is worthwhile only if it does not interfere with completing tickets OR other players are highly inefficient, so it's "free money" to be more efficient.
- Segment Efficiency: Relating to using the fewest number of cars possible to complete destination tickets, while generating the most points possible; Leaving more cars available later in the game (that can be used towards other destination tickets), while building longer segments to gain more points. Running low on cars can severely limit your options in the endgame, so segment/car efficiency becomes critical.
- Gambling: Drawing new destination tickets near the end of the game became known as "gambling" due to the heavy reliance on (sanitized) luck. If you drew tickets you could quickly complete or had already completed, you can achieve a massive boost in points... but if the destination tickets are impossible, you can wipe out the points you earned from previous destination tickets very quickly.
- If none of the destination tickets you pull are possible/are likely for you to be able to complete, take the lowest point value and "write it off".
- Mindreading: There are 30 routes total in the USA version of Ticket to Ride, and after playing you gain some level of familiarity with these routes such that you can reverse engineer what routes other players likely have from the path/route they have taken. You can use this to either disrupt their path, or if you have determined they likely do not have a route, you can use this information to aid in gambling (with the assumption being that a given route is still in the deck and can be drawn).
- Endgame Control: The first person to run low on cars controls the endgame. They have the option to gamble, or simply "end" the game forcing a final turn each from the other players. If you are ahead in points, ending the game fast ensures other players cannot catch up. Behind? Perhaps gambling may be worth it.
- Point Targeting: Aiming to achieve a certain number of points in either category of train/destination, and once achieving this number in a category, switching gears to dial in on the other type of points. In my case, I usually aimed to hit 50 route points, then would focus solely on points from building longer segments.
Cloneable for Your Own Use!
Want to tell (piss off) your family member that their "Sharpe" is too low? If this sounds fun to you and you enjoy Ticket to Ride, you can clone this project and track your own tournament.
And come on... who doesn't want to have a spreadsheet showing you're better at a board game than your friends? ;)