What are Matrix Games?
What are Matrix Games?
What are Matrix Games?
There are as many ways to apply games for learning as there are types of games. And the modalities, objectives, and outcomes for different learners and program needs make applied games-based learning an even more diverse field.
However, the latest, fanciest, and most high-tech solutions aren’t always necessary to achieve your needs as an instructor or the outcomes of your learners. Sometimes, all it takes is a focus on simplicity, dialogue, and a rigorous examination of critical thinking to get the most out of learning through matrix games.
This article will first define matrix games as a argumentation based system for games-based learning that makes applied games approachable and applicable to a wide variety of different disciplines. Matrix games also make games-based learning much more approachable for even the most apprehensive instructors.
The article will cover the major elements of matrix games and how they are structured as well as how argumentation forms the basis of these games and how they can be leveraged as both an instructor and approached as a learner.
However, the fun of matrix games isn’t’ limited to arguing with others. Whenever there are indecisive moments or times when there is no consensus, instructors can also use the randomness of dice to develop a sense of unpredictability in outcomes that often replicate the expectations of practical learning applied to the field.
The article will also cover matrix game participants, preparation to play matrix games, hosting matrix games, and debriefing matrix game play. These games will then be critically examined according to their applications, strengths, and weaknesses.
The article will close on first steps that you can take in designing your own matrix games and how that design can be best focused for teaching, training, learning, and development for your specific needs.
Matrix Games Defined
Let’s get started with defining matrix games and discussing some of their history. They were first developed for teaching and learning by Chris Engle in 1992. Education was a main consideration for its inception, and matrix games were created as a simpler and more flexible format compared to rules-heavy wargames and role-playing games which were their original inspiration.
The same reasons that make role-playing games approachable and adaptable is included in the structure and system of matrix games. That is, roles are defined in such a way to help participants learn through experience and simulated events without creating real-word situations. This is especially helpful for instructors in disciplines where recreation is not feasible or attainable for historical events or speculative activities.
This approachability is accomplished through structured storytelling and arguments which are usually adjudicated by an “umpire” (a term borrowed from its wargaming origins), but for the purposes of this article (and your own applications) can be delegated to the instructor. This direct relationship provides a way to scale matrix games and apply them to settings where learners can use their creative reasoning and create a more enjoyable experience that prioritizes narrative flow over rigid mechanics.
From the learner’s perspective, matrix games allow players to create arguments and build narratives together with other players. However, actions, activities, and other means of changing direction and outcome of the story form the basis of the debates that make the core loop of matrix games.
Therefore, matrix games are activities hosted by an umpire (instructor) and played with learners that are based on narratives that include conflicts and problems. Players engage with each other and the narrative. They then take actions that are argued between all parties and decided through a combination of umpire decision, chance through dice, and improvisation.
Elements of Matrix Games
Ultimately matrix games are made up of a few different elements. Most of which are shared with other commercial games.
Those include the story (or narrative) of the game that lays out the relationships between characters, problems, and goals. This narrative structures the overall experience of the matrix game and the theme that it occupies.
Next are the resources or technology in which the game is played. For the most basic and relevant matrix games these include a physical gathering space around a table. These games can also take place via web conference platforms for remote settings. Lastly, matrix games include mechanics. Often the same mechanics that are included in other tabletop games. Though (for the most part) matrix games are made up of the actions and argumentations of players and the resolution of actions through conversation, debate, and the overall decision of the umpire (instructor).
These arguments are the central element of matrix games, as they represent the ability for players to listen, debate, and determine the course of the game based on the setting and structure of the narrative. This is accomplished in concert with the guidance of an instructor as the umpire. While some may view this as overtly fungible, they represent a key aspect of these games as goals, directions, and decisions can be examined and dissected through careful reasoning and analysis rather than just an ultimate focus on “winning conditions.”
This structure often works in tandem with a more advanced aspect of matrix games, in which there is no fixed order of play. Rather, players can propose or modify any action at any time (including – but not limited to) the rules of the matrix game itself. Such a structural change can be daunting for novice practitioners. But more seasoned facilitators will see this as a means of delving further into the structure of the material that further promotes critical reasoning.
Structure of Matrix Games
While more advanced matrix games can be played without a fixed order of play, many first-time facilitators may choose to start with a specific format in mind. These typically include play over 2-3 hours with several “rounds” of action and response between players. Such a format provides the means for players to acclimate to this type of game and open up avenues for deeper discussions, collaboration, and problem solving.
This is because for players to make, define and promote their own arguments, they must become more familiar with the material dictated by the instructor. Doing so allows them to better explore a given scenario in greater depth because they are challenged to understand the context surrounding it.
This is actualized through game play with players taking turns proposing a single action they intend to take and then providing 2-3 reasons why the action should succeed. Opposing players can then challenge the proposal by offering counterarguments for why a proposed action might fail.
Instructors can interpret this format by weaving players’ actions into the narrative, shaping the direction of the scenario, and influencing future decisions. Some selected player actions could be historical and follow the decisions made by leaders during a historical battle. Whereas others can depart from these historical realities and instead explore different paths for what could have occurred. The latter represents more interesting decisions and dilemmas which affect the future of the scenario dramatically.
This core loop of argumentation, debate, and counter argumentation continues until the “problem” of the game or scenario is resolved. Of course, it is the direction of the instructor to determine the definition of “resolved. “However, if running low on time or resources, facilitators can also narrate how a scenario might end by providing reasons for how a narrative might play out.
However, the core reason why matrix games are such adept applications for developing critical thinking is not based so much on the resolution of the scenario, but rather on how players progress through it via robust argumentation.
Argumentation in Matrix Games
Argumentation can sound like a complicated process. But players simply indicate what they want to do next within the narrative of the game and then the umpire (or instructor) along with peers determine if the action can be resolved.
Disagreements are bound (and expected) to arise, and those are handled using dice or some other kind of random number generator that is used in concert with the instructor’s judgement to determine the result of the action.
The scope of the arguments within the game can cover anything relevant to the story’s scenario such as weather, politics, logistics, or morale. More skilled and experienced players can even argue for changing the rules of the matrix game. However, the basis of good argumentation is the structure set by the umpire. Typically, this has encompassed the “three reasons” system. Simply put, this includes players providing three positive reasons why an action would succeed. Conversely, peers would provide at least three reasons why the action would not succeed.
This is where the influence of the instructor acting as the umpire can have a critical and educational effect. The quality of arguments can influence the odds (and thereby the results) of the action. In practice this means that arguments which are provided with no counterargument automatically succeed. Whereas weak counterarguments make it so that the original argument has a high (though not guaranteed chance) to succeed.
The effects of these arguments mean that one side must win, and the other must lose. In effect the action either succeeds or fails based on argumentation (or saving that), chance through dice rolls or other means.
Special attention should be paid to argumentation as it forms the crux of the matrix game process. Well-structured and reasoned arguments can often earn approval and consensus from both parties: a sign of critical approval. Whereas bad arguments can earn the criticism and scorn of players, and the instructor, for being poorly reasoned or rationalized.
More advanced iterations of matrix games can also include “secret arguments” which are written privately to the instructor or umpire. However, these are recommended for more seasoned players as they can often slow down the game.
Similarly, larger and more strategic changes in the can be structured to succeed only if multiple sequential arguments are won in order. This, and secret arguments, can and should be reserved for future iterations of matrix games where players and instructors have had the chance to master basic rules and structures.
Dice and Randomness in Matrix Games
It can be said that nothing is ever “guaranteed” in matrix games. Instructors as umpires can decide that even unopposed arguments are still liable to fail due to chance via dice roll. Purists would argue that such a judgement makes the experience unstable, but relying on chance helps balance the accuracy of matrix games against undue complexity.
If argumentation represents the crux of matrix games, then dice represent the fickle hand of fate and its influence on even the best planned and well intentioned players. Such is the outcome of many historical campaigns and events when bad luck has had an outsized impact and forever changed the course of history.
Despite this, random chance through dice can have a positive effect on argumentation and critical thinking providing players with reasons to plan accordingly and determine that not all decisions are “locked” and are still subject to failure due to no failings on their part. In fact, this makes it so that players are encouraged to make the strongest arguments they can, to ensure the best-case scenario for their success.
Umpires and instructors can further influence these dice rolls by indicating that certain high or low results (i.e. a natural 1 or 6 on a D6) means an automatic success or failure, regardless of the strength of the argument. This means that success, failure, and even ambiguous changes to the game state are all valid results.
Matrix Game Participants
As has been discussed so far, there are at least two different kinds of matrix game participants. One group represents the students (players) who engage with the scenario and story and make decisions in that space. These players can be further divided into “teams” offering arguments for or against specific actions.
In addition, the instructor (or umpire) provides the same structure and format that a game master would provide in role-playing games. This is the individual who adjudicates decisions, results, and directions of the story based on the actions of players and their teams.
However, a more granular approach that one might take is assigning specific roles to players that help broaden their perspectives. While having a strategic analysis of a particular historical battle, political conflict, or other kinds of real or fictional event is important, it is also worth it to consider the kind of impact that that individual living and interacting within the story can have within the larger narrative.
With this in mind, it’s important to structure players’ roles and responsibilities throughout the game. Many matrix games are made up of 6-8 players and are paired with the instructor or umpire serving as a facilitator. However, these numbers can be scaled up for larger groups with a confident and savvy instructor.
Scaling can take place by breaking up players into “teams” that are assigned roles representing different “actors” on that team. Those teams could be as large as entire countries or organizations. Scaled down, it can also represent offices, units, or even individuals operating within the same scenario.
The scale of matrix games is influenced not only by the number of participants, but also through the engagement and communication between the instructor and players. Not only are they responsible for adjudicating actions but also serve the ultimate purpose of matrix games which is learning through experience. This is best accomplished through the argumentation framework previously discussed, as well as debriefing and reflection of such activities.
The best reflections and debriefing can be structured as integral parts of matrix games through the adjudication of arguments. By paying careful attention to what arguments are made, how they are debated, and the resulting challenges and decisions provide prime examples to be articulated in the debrief.
After all: remember that even well-structured and reasonable arguments can still be subjected to the randomness and whim of dice rolls. This demonstrates that nothing in the game is for certain: a result that can provide an interesting point of reflection and discussion during debriefs.
Preparing to Play a Matrix Game
One of the main hallmarks of matrix games are that they require little to no resources and are highly dependent on the knowledge and application of instructors who are usually already subject matter experts in a particular area. Therefore, the actual resources demand of matrix games is quite low.
Physically played matrix games require no more than a secured room (classroom) and perhaps boards representing the physical relation of different units and characters in the game (although this is not a requirement). Additional optional components include dice and spaces to hold private and separate discussions between players and their respective teams.
However, matrix games can also be played online virtually through web conferencing software. In this case, the requirements change to digital documents representing boards as well as breakout rooms for private player discussions.
Both modalities will require some kind of briefing or background material for players. For best effect, participants should receive and review preparation material on the scenario, story, and their roles in addition to specific objectives (if any) in the game. Such materials make it feasible to start the game immediately based on players’ pooled knowledge of the scenario.
Hosting Matrix Games
Matrix games can be deceptively simple or very complicated depending on your game literacy, patience, and propensity for applying games for learning. However matrix games are one of the most flexible and adaptable formats for games-based learning and can be applied in a variety of approaches.
Matrix games can be broken down into the following steps for facilitators. First, facilitators should explain and recap the scenario and the surrounding story. This includes where it takes place, the ongoing event or conflict, and the people and the individuals involved.
Next, facilitators should briefly explain the rules of the matrix game. While overall implementation is subject interpretation, the most common scenarios include having one individual or “team” of persons represent an organization or unit. Then then narrate an action they would take and provide 1-3 reasons why the action would succeed. The opposing (or remaining) players or teams then make counter arguments on why the particular action would not succeed.
Based on the strength and presence of arguments and counter arguments, the facilitator then makes a decision on the action’s success (or barring that rolls dice or uses a random number generator to determine a result) and then narrates the change in the game state for all involved. The opposing team then has an opportunity to make an argument and the process repeats itself. Facilitators can take their time to briefly explain these rules but also be flexible enough to demonstrate how the game works in the first few “turns” through demonstration.
This demonstration can often serve as the catalyst for a more becoming teaching moment as it provides players and teams with the opportunity and agency to make a choice, defend it, and then move the game forward. Instructors can facilitate this process gradually allowing more confident players to try first and then ask more reluctant ones to join the conversation as the game progresses.
Debriefing the Matrix Game
Matrix games are much like other applied games in that much of the learning takes place through active debriefing. This means that at the conclusion of the game, players step out of their roles and reflect on what actions they have taken and how actions (and feedback) have informed or connected back to insights from learning objectives and training materials.
These debriefs are critical as they serve as an opportunity for instructors and players to dive deeply into the results of the game, and how players’ actions have affected its outcomes. Specifically, this can include a critical examination of assumptions that players made, and how those assumptions affected what actions they could take and how they argued for or against them.
Additionally, facilitators could challenge participants to examine their strategies, and what they did in order to accomplish any objectives that were issued to them. This directly aligns with evaluating risk assessments and how proposed actions were weighed against their positive outcomes and negative results.
Finally, all debriefs benefit from a prolonged discussion with peers and instructors on the overall structure, flow, and pace of the game as well as how outcomes from the experience could be applied to real problems and challenges, they may be facing outside of the game.
Applications of Matrix Games
This article has examined what matrix games are and how they can be used. The most popular ways that they are played are for specific educational and training scenarios. While they do share many of the same characteristics of tabletop role-playing games, they are meant to be played as part of a learning experience.
And to that end, matrix games are flexible and scalable in achieving that goal. they can be played in a small seminar with as few as 4 players, to an entire cohort of classroom players. They can be played in-person, online, during one session, or over multiple days.
No matter how you choose to play your matrix game, you’ll always need some kind of clear framing for your story or scenario. This might come out of your learning objectives that examine some kind of historic event set in a specific time (i.e. during the Napoleonic wars). Or it can be more fanciful and explore a scenario based on a historical period (i.e. the cold war) or a made-up scenario that serves as an analog for your teaching space (i.e. first contact with an alien species).
Matrix games are often used by the military as a means of experiential learning to develop and hone warfighting skills by testing assumptions in a simulated environment. This provides a means for individuals to critically examine their actions and the arguments and counterarguments that go into determining their validity. While you may not be teaching at a service academy or at a war college, you may still use the framework of matrix games for achieving the same kind of critical aims.
This is what makes matrix games are especially valuable for applied gaming: their flexibility. If a topic can be debated, then it can be transformed into a matrix game. Therefore, the overall framework can be applied to a wide variety of teaching and training concepts and disciplines.
Strengths of Matrix Games
The flexibility of argumentation is one of the biggest strengths of matrix games. It provides a method of interaction and engagement for players and means in a structured environment that is thematic to the story or scenario.
While arguments alone don’t mean much in terms of critical thinking, determining what makes certain actions plausible, viable, and applicable is. This kind of strategic thinking is cultivated, tested, and applied by learners through matrix game play. Its format forces players to separate thinking and decision making that they may feel is “intuitive” from what is truly deliberate and analytical.
Therefore, the overall value of the matrix games is to promote this kind of rigorous decision-making process, strategic insights, cooperation, and adapting thinking. All of which can be attained by enthusiastic and capable facilitators who design and structure matrix games that align well to stated learning objectives.
Weaknesses of Matrix Games
Matrix games are not a panacea for applied games in all contexts. They have their weaknesses. One of which is the threat of “unlimited choices” for participants. One of matrix games’ greatest strengths are that players can make choices so long as they can make arguments for their success and defend against counter arguments. But this does not help determine and select what arguments to make.
This structure can position matrix games as overwhelming for players that are not familiar with the material, story, or scenario and may not have the context to make educated decisions about what they can and should do. These materials promote analysis paralysis for players given the structure of the game.
Therefore, matrix games represent valid choices for applied games when participants know and understand the underlying scenario and context of the game situation. Instructors can address this by providing context materials about the game ahead of time for players to study. Facilitators can also situate the decisions that players can make within the scope and scale of the overall narrative.
For first time players, instructors can also offer a starting “menu” option that players can take at the start the game. After they become more comfortable, they can then expand their options past the original menu once the game is underway.
In addition, poorly designed or implemented matrix games may also run into the issue of oversimplifying complex geopolitical scores or misleading participants into “easy” solutions. Instructors are therefore encouraged to act as umpires and referees for the game and provide the necessary context and background for supporting actions based on their expertise of the subject matter area.
Getting Started Designing Matrix Games
Matrix games are interesting because they can be both large and engrossing, but also small and intimate. They can be incredibly detailed and offer a complex and evolving narrative, or they can be simpler re-creations of historical events for study and analysis.
Therefore, getting started with matrix games begins with the selection of a particular story or scenario. Ones that work best are historical scenarios that are “problem” driven with at least two opposing “factions” or teams that seek an objectives that conflict with one another. This forms a good framework for starting a matrix game that can be inclusive for learners as well as serve as a low barrier of entry to begin play.
It’s important when first starting that the design philosophy around matrix games is to focus on the specific scenario and the learners engaging with it rather than getting held up around the rules and mechanics of the system. The system exists to serve the learning purpose of the matrix game, and not the other way around. This represents a significant departure compared to how other game systems work.
This focus on both the scenarios and the learners is critical for instructors as they know the subject material and their learners how the game can be best adapted to meet their needs. Instead of focusing on the minutiae of the rules, instructors should invest time and effort into focusing players’ attention on the conflict that requires resolution and how the overall problem is at the center of the scenario. This is important because play stops when the conversation around the problem and its resolution stops. Therefore, continuing to keep the conversation moving and argumentation occurring is critical to continuing the momentum of the game.
This approach specifically materializes in the matrix game through the story and the characters within it: the roles that learners play within the game. Therefore, care should be taken to determine who players roles, their objectives, their capabilities, and philosophies.
All of this resolves around the premise that matrix games can be both easy and challenging to design and run. Therefore, one of the best ways to become acclimated to the workflow integral to their application is to first play and participate in a matrix game, then run a matrix game for your learners, and then finally choosing to write and create one from scratch.
Matrix Games for Learning
Overall, matrix games are a powerful solution for teaching and learning, especially in disciplines that require critical thinking and argumentation as a means of development. Philosophically, matrix games are most closely aligned with Kant’s philosophy on models of perception as well as Hegel’s dialectic on thesis-anthesis-anthesis-synthesis framework.
Their flexibility makes it so that instructors can adapt them to support higher order learning through rigorous problem, solving, analysis, and decision making. This is most closely determined by the instructor and designer through the structure of the game which rewards logically consistent strategies, and provides a means for players to defend their decisions with both evidence and professional knowledge.
One of the hallmark moments of many matrix games is being able to discover, highlight, and address flawed assumptions and then adapt actions accordingly. This is most often seen through role-play within the game as it allows players to understand their own motivations as well as that of other players. Doing so allows them to adapt their strategies to shifting dynamics.
These kinds of interactions make the most sense pedagogically, as it requires players to source the basis of their arguments through course materials and academic literature to justify their choices. Doing so bridges the gap between theoretical knowledge and real-world decision making.
In summary, matrix games are best approached with learners through three core components. The first of which are addressing assumptions and evaluating the underlying beliefs that justify the approaches of players. The second are the “ends” and the results of arguments and how they best meet the needs and expectations of desired outcomes. The last are the “means” or ways that players achieve those outcomes within the contexts, constraints, and structure of the matrix game. This is a format which gives maximum agency to the player with overall structural authority to the instructor, facilitator, and umpire of the game.
Takeaways
This article explored matrix games in depth. It started out by defining them as well as covering the basic elements that compose matrix games. Their overall structure was reviewed as well as how argumentation constitutes a core aspect of its implementation. Both aspects are used to move the game forward as well as highlight it as a tool for applied learning through games.
Dice and randomness still play a critical part of matrix games, so its role was described as well as how participants engage with and actively participate in the game. Preparation of matrix games was also covered including detailed steps in addition to hosting and eventually debriefing matrix game play.
This article closed on some of the best applications of matrix games, covering both their strengths and weaknesses and how both can be best addressed through designing a matrix game from scratch. The result of which is a flexible and novel approach to using games for teaching and learning in a variety of different disciplines and modalities.
This article covered matrix games. To learn more about gamification, check out the free course on Gamification Explained.
Dave Eng, EdD
Principal
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Cite this Article
Eng, D. (2025, November 11). What are Matrix Games?. Retrieved MONTH DATE, YEAR, from https://www.universityxp.com/blog/2025/10/31/what-are-matrix-games
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