How to Play
Introduction
We built the Gurobean Optimization Game as an educational tool. Where the Burrito Optimization Game introduces the idea of mathematical optimization, Gurobean goes a step further: it shows what happens when decisions must be made in systems that are uncertain, dynamic, and nonlinear. Players run a coffee shop (choosing how much to brew, how to price drinks, and how to staff and serve) and discover that a good decision can’t be judged by a single outcome.
If you’re looking for an overview of how to play, see the Game Guide. If you’re an instructor looking for tips on teaching with the game, you’re in the right place. This guide outlines how you might structure a lesson, introduces the high-level concepts the game illustrates, and suggests some “aha!” moments to aim for during gameplay. It also points to the downloadable lesson plans and slide template you can adapt for your own class.
The Gurobean home screen. Players jump straight into the game or take on Championship Mode, and the billboard sums up what the game explores: nonlinear optimization, simulation, and decision-making under uncertainty.
Lesson Plans and Slides
For anyone teaching the game in a classroom or training setting, we’ve put together resources you can download and adapt:
Technical lesson plan: for operations research, engineering, computer science, and advanced analytics students (Part 1 of this document).
Business & Analytics lesson plan: for MBA, executive education, and applied analytics audiences (Part 2 of this document).
Slide template: an editable deck that introduces the game and the ideas behind it, which you can adapt for new learners.
Intended Audience
The game has several intended audiences. For example:
Data scientists: Gurobean helps explore the question of “what’s next?” after forecasting. Once you can predict demand, how do you act on it, under uncertainty, with limited resources?
Operations research and simulation students: a hands-on lead-in to stochastic optimization, queueing, and simulation before the formal models arrive.
Business and analytics students: experience first-hand why feasible plans can perform very differently, and why analytics supports decisions without eliminating risk.
Anyone who needs to see that uncertainty and nonlinearity are hard: if you think a complex, random system is easy to optimize by intuition, try running the shop by hand and watch the queue grow.
Younger students (bonus audience!): a friendly way to show that math and computation drive real-world decisions, not just textbook equations.
You may want to adapt the ideas below for the particular group of learners you are working with. The two lesson plans give audience-specific versions of everything that follows.
Sample Lesson Plan
The lesson plans contain audience-specific timings and discussion prompts. At a high level, every version follows the same arc:
A round in progress (here, the start of Round 6). The HUD shows the day, score, and newsfeed; the Constraint and Profit monitors; the BREWROBI brewing station; and the decision sliders with their feasibility indicator. Alinea introduces each round’s new wrinkle: here, that average wait time and lost customers now matter alongside profit.
Before class
Read the Game Guide and play through several rounds yourself.
Note where the simulation surprises you, especially a round where a strong-looking decision performs poorly, or where a single run beats Gurobi.
Optionally, have students play the opening rounds beforehand to learn the controls.
In class
Introduce the game as a decision-making system: sliders are decisions, resources and capacity are constraints, customer arrivals are random, and performance is measured by simulation.
Play the early rounds, predicting outcomes before running each simulation.
Discuss what was easy, what was surprising, and why repeated runs differ.
Play the later rounds where pricing, queues, and congestion appear and intuition starts to break.
Discuss why profit stops behaving smoothly, and how you might design an algorithm to solve the problem.
Choose one: continue into the uncertainty-focused rounds, or pause for an “optimization & simulation 101” primer.
After class
Run a Championship (see below) for homework or in class.
Coffee break
Go get some coffee! ☕
Learning Objectives
High-level takeaways
If nothing else, players should come away from the game having learned these things:
Feasibility is necessary, but not sufficient. Meeting every constraint doesn’t make a plan good; performance is a separate question.
A single outcome doesn’t measure a decision. Because demand is random, the same choice produces different results on different runs.
Intuition breaks down in complex systems. Nonlinearity, congestion, and feedback make systems behave in ways simple reasoning misses.
Optimization and simulation are partners. Optimization picks the decision that is best on average; simulation reveals how that decision behaves over time.
"Aha!" moments
There are many insights you can highlight while students play. Some occur organically; others need a little instruction to set up. Here are some examples.
Feasibility vs. performance
When sliders turn red, the solution is infeasible; it violates a resource or capacity limit. Students quickly learn to get back into the feasible region. The deeper lesson is that being feasible is only the entry ticket: among all the feasible decisions, performance still varies enormously. “Is this allowed?” and “Is this good?” are different questions.
Feasible (top, green) vs. infeasible (bottom, red) slider settings. Red values flag a broken constraint; the player must adjust until every limit is satisfied.
Trade-offs
Every decision pulls in more than one direction. Brew too little and customers leave empty-handed; brew too much and coffee becomes waste. Serve too slowly and the queue grows; raise prices and margins improve but demand falls. There is rarely a single dial to turn; good decisions balance competing effects.
Diminishing returns and saturation
Increasing a decision usually helps, until it doesn’t. The first additional unit of capacity or brewing has a large effect; later ones have less, because the system saturates. Ask students to find the point where pushing a slider further stops helping (or starts hurting).
Let it run: warm-up vs. steady state
Unlike the Burrito game, Gurobean computes nothing instantly. Each simulation starts with an empty shop, and the early metrics swing wildly while the system “warms up.” This is a perfect, visible example of transient vs. steady-state behavior and the need for a burn-in period before results are meaningful. Encourage students to wait before judging a decision.
Warm-up vs. steady state: the shop opens empty (top) and the early numbers are unstable; once customers fill the queue (bottom), the metrics settle into representative behavior.
Same decision, different day
Run the same sliders twice and the outcome changes. Customer arrivals and preferences are random, so any single run is just one realization. This is the moment to introduce the idea that we should evaluate a decision by its distribution of outcomes, not by one lucky or unlucky day.
Expected value vs. a single run
At the comparison screen, students sometimes beat Gurobi on a given run, as in the Round 7 result below, where the player’s plan came out 8% ahead of the optimal expected value on one five-day simulation. This is not a bug; it’s the central lesson. Gurobi chooses the decision that performs best on average across many possible futures, and a single simulation is just one of those futures. The question isn’t “who got lucky this time?” but “which decision would you trust before knowing what randomness will occur?” This is a natural bridge to stochastic optimization, regret, and the value of the stochastic solution.
Round 7 comparison. The player’s solution earned more profit than Gurobi’s on this particular five-day run, yet Gurobi’s remains optimal in expectation, as Alinea explains, “even with the same settings, the simulation won’t play out the same way twice.”
The comparison screen also plots each solution on the expected-profit curve. Filled markers show expected profit; hollow markers show what actually happened in the simulated run, so students see both where a decision sits in theory and how one random run played out.
Nonlinearity breaks intuition
In Gurobean, pricing, congestion, customer loss, and capacity feedback on one another, so the profit “curve” bends: more brewing or a higher price helps, until it doesn’t. Small changes can swing queue lengths and lost customers in ways that are hard to anticipate. Reasoning by inspection, which worked for a linear problem, no longer suffices.
Crucially, the shape of this curve is not fixed. It changes with the round, with the scenario’s fixed quantities (such as the beans and water available), and with the prices in play. Three things move as the shape changes: where the peak sits (the best slider value), how high it reaches (the best achievable 5-day profit), and how sharp it is. A broad, flat peak is forgiving, so a roughly right decision does nearly as well as the optimum; a sharp peak is unforgiving, so a small miss is costly. A binding resource limit can also cut the curve short, placing the best feasible choice at the constraint rather than at the curve’s natural peak. The lesson plans include a discussion activity built around this idea.
Why simulation is necessary
When effects interact nonlinearly and the system is path-dependent, there is often no closed-form formula for performance. Instead, we estimate outcomes empirically by simulating the system many times, exactly how real operations are analyzed in call centers, hospitals, and transportation networks. Gurobean lets students feel why a formula isn’t always available.
How might an algorithm work? Why enumeration fails
Ask students how they’d automate what they did by hand. Someone usually suggests “just try every combination.” It’s a good moment to show why that’s doomed: even if a computer could test a billion candidate policies per second, discretizing a handful of sliders into a few dozen settings each produces combinations that climb into the trillions within a few rounds, and each candidate must be simulated many times to estimate its expected performance, not merely evaluated once. This motivates why we need solvers and smart algorithms rather than brute force.
Deterministic, stochastic, and robust thinking
Use the comparison screen to introduce three ways to optimize under uncertainty: plan under a forecast or the mean (deterministic), optimize expected performance (stochastic, what Gurobi does in Gurobean), or protect against the worst case (robust). Discussing which is appropriate, and when, connects the game directly to the field.
Championship mode
Gurobean offers two kinds of Championship, both reached from the Championship screen. Each rewards consistent, well-reasoned decisions rather than a single lucky run: enter a match code to join a private Class Championship, or tap Enter Weekly Match to join the public, worldwide competition.
The Championship screen. Entering a match code joins a private Class Championship; “Enter Weekly Match” joins the global, weekly competition. Players also choose a display name before joining.
Class Championship
Like the Burrito game’s Championship, an instructor can spin up a private competition for a class on a shared scenario, with the optimal solution kept secret. To run one:
Choose a match code and share it with your class.
Ask students to open the Championship screen, enter the match code, choose a display name, and click Join Match.
Everyone plays the same scenario; the best total scores appear on the class leaderboard.
Review the standings together afterward, and enjoy running your Championship!
Global Championship
The Global Championship is a public, worldwide competition with a shared global leaderboard, so your students can measure themselves against players around the world. Players join it with the Enter Weekly Match button, no match code needed, after choosing a display name. As the name suggests, a new global match runs each week, each with a fresh scenario, so classes can return for a new challenge on a regular cadence.
Because it refreshes every week, the Global Championship makes an easy recurring assignment, for example, a weekly class challenge with bragging rights against the rest of the world, or a standing extra-credit option throughout a term.
Game Tips
Gurobean has a built-in guide, Alinea, who surfaces tips throughout play, not only on the solution and comparison screens. Whenever the player changes a decision or the circumstances shift, an exclamation (!) pops up on screen with a contextual hint; Alinea also introduces each round’s new wrinkle and, at the comparison screen, explains why the results came out as they did. Together these tips flag teachable moments and reinforce the game’s intended learning outcomes: feasibility, uncertainty, nonlinearity, and the role of simulation. As an instructor, you can let Alinea raise the prompt, then pause to expand on it with your class.
When the player acts or conditions change, an exclamation (!) appears on screen; opening it reveals Alinea’s contextual hint, a built-in cue for the teachable moments above.
