Blog

Board Games: Winners and Losers

Lucas Connors
|
November 9, 2021

Most people that know me know that I am obsessed with board games. I've played hundreds of different games, over thousands of hours. I also like to keep a journal of sorts about the games that I play. I started recording my data consistently in 2018 after I was inspired by a friend of mine in the board gaming community who put together a bunch of visualizations on top of his own data. Today we're going to dive into a slice of the data from this journal, taking a look at winners and losers.

My Best and Worst Games

First, let's delve into the games I'm personally best and worst at. One metric we can use to evaluate how well a player plays a game is their win rate (ie. the percentage of time a player wins when playing a particular game). Let's first take a look at my top 10 games by win rate, filtering out any games that have only been played a few times.

Now one potential issue with using win rate as a metric is that it over-inflates games with a small number of possible win outcomes. Take the game Codenames for example. Either the blue team or the red team will win. Therefore, a player should win Codenames 50% of the time assuming the game is balanced and teams are evenly matched. On the other hand consider a 6-player game of Catan. If the game is balanced and players are evenly matched, a player should generally win 16.67% of the time. So a win rate of 25% in a 6-player game of Catan is actually a lot more impressive than a 50% win rate in Codenames. In the data above, all 10* games have only two possible win outcomes (they are either co-operative or team-based games with two teams).

Instead of using win rate, let's use a metric that inflates wins that occur in scenarios with many possible win outcomes called a "weighted win value". If a player wins a game with two possible win outcomes, that is worth 2 points. If a player wins a 100-player game with a single winner, that is worth 100 points. Players are expected to earn 1 point for each game they win on average, so if we take the total weighted win value a player has for a specific game divided by the number of times they've played it, we end up with a "Win Value Index" (or WVI).

In this analysis, we generally assume that all games are perfectly balanced (although we may stumble on some evidence suggesting otherwise!). Here are my best 10 games, using WVI:

With this metric we now see more competitive games appear, including Quixx, Reef, Dominion, and Perudo. The top result here, Horrified, is a co-operative family-weight game based on the Universal monsters. Despite cranking up the difficulty every time we've played, we have never come close to losing this game so I am not surprised to see this here.

Next let's take a look at my worst 10 games, using the same "Win Value Index" metric:

The top five results here are all games where I have no recorded win. Hearts of AttrAction and The Mind are notable entries here. Hearts of AttrAction is a flicking game where players attempt to collect magnets by having them attract to one another. My partner annihilates me at this one every time. The Mind is an incredibly simple co-operative card game, but immensely difficult to actually win. The Mind is really more about seeing how close you can get to winning rather than actually reaching the end.

Hearts of AttrAction, 2014 (Designer: Jeff Glickman)

The Starting Player

Most board games are turn-based, which means that unless the game is real-time or involves simultaneous play, someone has to be the first player to make a move. In some games, biases can exist in favour or against the starting player. In Chess for example, the player playing white wins 52-56% of the time instead of the 50% you might expect if the two sides were balanced. In this section, let's dive into starting player biases evident from games that I've played over the years. To do this we will compare the WVI of the starting player to the WVI of the remaining players and look at the games that produce the greatest delta.

The Resistance and Anomia are notable entries in this section. The Resistance is a social deduction game, conceptually similar to Mafia / Werewolf. For the purposes of my data, the starting player is the first player to be the Leader, whom selects the first team to be voted on. The Leader may (and often does) pick themselves to be included in the team, and so this finding intuitively makes sense because if some percentage of initial team proposals is accepted by the players, that initial team is more likely to provide a point for the starting player's team than if a random team were selected.

Anomia, 2010 (Designer: Andrew Innes)

Anomia is a simple party game where players have to think quickly to come up with example nouns that match the given category for the round. Players take turns by drawing a card from the deck and a "face-off" begins between two players when players draw matching symbols. Because players can only earn points in the game from "face-off"s, that means it is impossible for players to earn any points in the game until they have at least drawn their first card. Therefore, the starting player has the most opportunity throughout the game to have a "face-off" and I think this is why we see a bias exists for the starting player in Anomia.

Taking a look now at where the starting player has a disadvantage, the top result here is the bidding game For Sale. In For Sale, players auction off real estate and then later in the game attempt to sell their properties for maximum profit. Bidding games often lend themselves to being a disadvantage for the starting player, particularly when players are inexperienced and naturally lowball initial bids.

After For Sale we have Tsuro, which is a simple tile placement game in which players are attempting to survive for as long as possible by avoiding any collisions with other players or falling off the edge of the board. It intuitively makes sense to me that moving earlier in Tsuro is a disadvantage since players moving after you can take advantage of your starting position and provide you with fewer options in later turns. The rules actually say that the oldest player should be the starting player, which seems to indicate that the starting player disadvantage was known when the game was designed.

Tsuro, 2004 (Designer: Tom McMurchie)

Conclusion

We’ve seen that win rate is not a great metric for understanding how well a player performs when comparing different games to each other. We’ve also shown how data can demonstrate which games have a starting player advantage or disadvantage.

Have your own dataset you’d like to analyze? Share your use case with us and we’ll get you up and running on Cascade in no time

* Footnote: Two Rooms and a Boom technically has a variable number of possible win outcomes due to their mechanics of having different roles in each game. Regardless, in most cases even this game will end up with exactly two teams.

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