Analytics and board games

Playing, learning and having fun all at the same time.

By Evan S. Levine

Formula D is a simulation of a car race in which players decide which gear their car is in.

Formula D is a simulation of a car race in which players decide which gear their car is in.

Sometimes useful tools for outreach and teaching can be found in unexpected places. That’s particularly true for analytics, since it is an interdisciplinary field that combines aspects of statistics, engineering, economics and psychology. One of the most interesting places I’ve seen analytics concepts appear is in modern board games [1].

Now, it’s certainly true that the connection between games and analytics has been evident for a long time. For example, the concept of probability was developed in the 16th century by Cardano to model games of chance. Von Neumann and Morgenstern’s “Theory of Games and Economic Behavior,” a foundational book on game theory, is full of examples from chess, poker and bridge. Raiffa’s “Negotiation Analysis,” a classic text for decision support, includes numerous small games and experiments. In Analytics magazine, the “Thinking Analytically” column [2] often features game-inspired puzzles to solve. In other words, the links between games and analytics have been explored by many researchers and have inspired the development of many analytical and mathematical ideas.

When the connection between games and analytics is used for educational purposes, the games teachers and authors select tend to be classics such as poker or chess. These are beloved games, and there is value in the fact that many students are already familiar with how they are played. Instead of spending time explaining the rules, the teacher can spend time explaining the actual analytic concepts he or she wants to illustrate. However, these classic games are relatively static; some of them, like chess, have been studied to the point that the full depth of the game is only evident to an expert. Others, like checkers, have been “solved,” meaning that the optimal move is known from any position. In my opinion, these are not attractive qualities for games used for teaching analytics and decision-making. I like the examples that I use in teaching to not necessarily have a right answer, for the moves to be debatable from multiple points of view, and for the intricacies of the decision-making to be readily apparent.

That’s part of what I find attractive about using modern board games for analytics outreach and education. Modern board games (a term I use to distinguish them from classic games such as chess and poker) have recently been undergoing a golden age of design quality and sales. Some experts argue that this golden age is a result of cross-pollinating German style mechanics with Western-style storytelling [4]. Regardless of the reason the golden age is occurring, the larger number of people playing board games is a phenomenon we in analytics can take advantage of.

In Pandemic, participants are globetrotting disease experts fighting cooperatively to contain outbreaks and find cures.

In Pandemic, participants are globetrotting disease experts fighting cooperatively to contain outbreaks and find cures.

Analytics and Board Games

The discrete choices and definitive outcomes present in most board games make them excellent laboratories to train students to think analytically. As an obvious example, consider the tremendous computational effort expended to develop computer programs to play chess well enough to beat the top grandmasters. These programs evaluate a set of discrete choices and identify the most advantageous move, a structure similar to using analytics in a professional context to provide decision support. Beyond the straightforward algorithmic skills that playing board games teaches, why else are these games relevant to teaching analytics?

First, by playing a board game an analyst can appreciate the perspective of the decision maker. Sure, the stakes are relatively low compared to the consequences of professional analytics, but any person who’s ever played a board game with their friends will tell you that when playing a game the stakes are real. Furthermore, when making real decisions, sometimes strange events can occur that are difficult to predict solely from the rules of the game. For example, poker players are familiar with the concept of going “on tilt,” when emotional stresses overwhelm the rational decision-making process. Decision-makers sometimes exhibit similar behavior in a professional context, and analysts need to know how to handle such behavior when it occurs. Students can learn how to do this by experiencing the behavior for themselves.

Second, a well-designed board game demonstrates a key analytical skill: the reduction of a complicated system to a model that consists of simple rules. Unlike video games, board games’ closest rival, the rules of a board game are transparent because they must be enforced by the players and the structure of the game itself. This means that the rules of the model are generally readily apparent to the players. I will discuss several examples of these models in modern board games below, but many classic board games do not have this quality. For example, it’s hard to envision what real world system Candyland and Chutes and Ladders are modeling. Chess suffers from a similar malady; the action in a game of chess rarely evokes a medieval battle because the board and the way the pieces move are so stylized.

There is a need for games that teach analytic thinking, help analysts appreciate the perspective of a decision-maker, and demonstrate the reduction of a complicated system to a model with simple rules but do not have the negative characteristics of classic games discussed above. That’s where modern board games come in.

Betrayal at House on the Hill is a semi-cooperative game because the “bad guy” isn’t known at the outset

Betrayal at House on the Hill is a semi-cooperative game because the “bad guy” isn’t known at the outset.

Structure of Board Games

The marketplace is full of a tremendous variety of board games; introducing some technical terminology makes it easier to recognize and understand their similarities and differences. A simple distinction can be made between a board game’s theme and its mechanics [4]. In essence the theme of a board game is the flavor associated with the game, and the mechanics are the rules that govern the model.

To illustrate this distinction, consider the classic board game Monopoly. Monopoly’s primary mechanic is known as “roll and move”; the player whose turn it is rolls the dice and moves that number of spaces. Consequences result for that player (and possibly others) depending on which space the player lands. This mechanic is distinct from the game’s theme, which portrays the players as hotel barons in Atlantic City building real estate empires. Both theme and mechanics contribute to the players’ enjoyment of the game. However, the mechanics are much more relevant to analytics than the theme.

A board game’s victory conditions are typically related to its mechanics. For example, in Monopoly, the winner is the last player who is not bankrupt, having managed acquisitions and avoided other players’ properties. Another common victory condition is to accumulate the most points by the time a predetermined number of rounds have been played.

Not all board games involve players competing to meet the victory conditions. There are also cooperative board games, wherein players work together to best the challenges the game’s system lays out. Pandemic, in which the participants play as globetrotting disease experts fighting cooperatively to contain outbreaks and find cures, is an accessible example of a cooperative game. Semi-cooperative games also exist; in these games a subset of the players cooperate to best one of the other players. Betrayal at House on the Hill is a particularly interesting example of a semi-cooperative game because which player the other players are working against isn’t determined until partway through the game.

Dominant Species, a game that simulates the evolution of creatures, uses a worker placement mechanic

Dominant Species, a game that simulates the evolution of creatures, uses a worker placement mechanic.

The Relationship of Mechanics to Analytics

There are a variety of mechanics present in modern board games, and different mechanics evoke different aspects of analytics. An individual game may contain multiple mechanics; in fact, some of the most interesting games explore the interaction between dissimilar mechanics. My descriptions of these mechanics should not be seen as absolute law, as slight alterations to how the mechanics commonly work often result in the most innovative games.

Roll and move is a classic mechanic present in Monopoly and Chutes and Ladders. For a more modern instance of roll and move, consider Formula D, a simulation of racecars traveling around a track. Players decide which gear their car is in. For lower gears a player rolls four- or six-sided dice to determine how many spaces his or her car moves, while higher gears give correspondingly larger dice. Tough decisions result from players maneuvering their cars through curves; a car must end at least one of its turns in a curve or it will crash. Choosing the best gear involves weighing uncertainty, probability and risk.

Card drafting is a mechanic in which a player chooses one or more cards from a hand that will later be passed to another player. Players must balance drafting the best card for their own strategies against allowing powerful cards to be passed to opponents further down the line. 7 Wonders is a competitive game in which there are as many hands as there are players. Cards are simultaneously being passed around the table, with each player able to choose one card per turn. The objective is to maximize the difference between your and your opponents’ scores, so sophisticated tradeoffs are required regarding whether to play the best card for your own score or to prevent your opponents from obtaining cards that are more favorable to their strategies. Some of the available information is asymmetrically hidden. This mechanic evokes the maximization of utility given a fixed number of alternatives, when the utility of the alternatives is uncertain.

Worker placement is a mechanic that involves similar decision-making to card drafting, but none of the alternatives are hidden. Making the available actions visible to all players removes some of the uncertainty present in card drafting. In games with a worker placement mechanic, players have a limited number of action tokens they can place at the start of each turn. In Agricola, a game themed around 17th century German farmsteads, available actions include gathering resources, building fences, plowing fields and enlarging a farmhouse. Similar to card drafting, players must balance choosing the best action for their own plans against blocking other players from taking the most advantageous actions for them. Dominant Species, a game that simulates the evolution of creatures, is another modern board game that uses a worker placement mechanic.

In Agricola, players balance choosing the best action for their own plans against blocking other players from taking advantageous actions.

In Agricola, players balance choosing the best action for their own plans against blocking other players from taking advantageous actions.

Deck building is a mechanic in which players choose cards from a set to add to their personal deck. Through this process each player’s deck gradually expands, gaining new powers. In Dominion, players draw a new hand of cards from their deck each turn. When certain cards are drawn in combination, powerful effects occur, and players can choose to add more cards to their deck. With this mechanic, players are essentially competing to build the best process to produce these powerful effects. Each player’s deck is a laboratory for experiment and the most efficient deck will typically win (some randomness enters the game via the drawing of cards from each deck). Deck building evokes the analytical idea of process optimization.

Bluffing has been a part of board games probably since they were invented, but modern board games have put a particularly fine spin on the concept. Take Skull and Roses, a competitive game with extremely simple rules that hide a wealth of subtlety and strategy. Each player starts the game with four tiles: three roses and one skull. Players place tiles face down one by one until a player decides to make a bid regarding the number of tiles he or she can turn over without turning over a skull. That bid then travels around the table until everyone has passed. The player with the winning bid must start by turning over his own tiles, meaning that if he has put down a skull to trap someone else, he has instead trapped himself. This game beautifully illustrates some of the concepts of game theory; a player’s best move depends strongly on the past and future alternatives chosen by other players.

The final mechanic I’ll mention is deception – the hiding of a player’s true objectives. Deception is required in The Resistance, a semi-cooperative game in which players win by carrying out successful missions. However, some of the players are saboteurs who can cause a mission to go awry. The players must figure out who the spies are before it’s too late; the trick is that any amount of talking is allowed among the players at any stage. Players will accuse each other of being spies, spies will accuse good guys of being spies, and the result is a landslide of competing logic and Bayesian reasoning. I once played a game of The Resistance that started a weeklong discussion of Bayesian inference and how it should have influenced one of the decisions made. During that particular game I didn’t make the optimal decision, but the experience taught me something about how to apply Bayesian logic. That’s not bad for an evening of fun with friends.

Conclusion

These are just a few of the mechanics used in modern board games; games that involve new mechanics and new ideas are being released all the time. If you’re interested in learning more about board games, a wealth of resources available. To explore the mechanics of games, I highly recommend the textbook Characteristics of Games by Elias, Garfield, and Gutschera. To learn about the games themselves and find video reviews and playtests, try Board Game Geek [5], Shut Up and Sit Down [6] and Tabletop [7].

Board games can be a potent participatory tool for teaching students about analytics. They can also be useful hooks for recruiting new analysts to our field. In short, they can play an important role in the growth of analytics, while being fun at the same time.

Evan S. Levine (applyinganalytics@gmail.com) is the lead for analytics at the New York City Police Department’s Counterterrorism Bureau. Previously, he served as chief scientist at the Department of Homeland Security’s Office of Risk Management and Analysis. The views expressed in the article are those of the author and do not necessarily represent those of his employer.

Notes & References

1.     By “board game,” I really mean any game that is played around a table either with a group of friends or by a single player. The presence of a physical board isn’t a necessary component.
2.     http://viewer.zmags.com/publication/e0d5d66f#/e0d5d66f/84
3.     See the excellent introductory talk by Quintin Smith entitled “Board Gaming’s Golden Age” for more discussion (http://vimeo.com/52293009).
4.     This is just one of many frameworks with which board games can be analyzed.
5.     www.boardgamegeek.com
6.     www.susd.pretend-money.com
7.     www.tabletop.geekandsundry.com