Summary
For my master’s thesis, I developed a modular Monte Carlo simulation framework for analyzing balancing problems from my own strategic board game. The combat system had grown beyond standard Risk-style dice combat through different factions, unit profiles, dice types and custom effects.
The framework supports heterogeneous dice setups, mixed dice pools, unit profiles, faction and class differences, and effects such as rerolls. Its purpose is not to automatically generate perfectly balanced units, but to support designer-driven balancing decisions through simulations, metrics and visualizations.
I designed and implemented the combat model, simulation logic, experiment setup, evaluation metrics and visualizations myself.
What This Project Shows
- Data-driven balancing
- Combat system analysis
- Monte Carlo simulation
- Scenario-based evaluation
- Balancing metrics and visualization
- Designer-driven interpretation of results
- Awareness of metric and model limitations
From Playtesting to Simulation
The project began with a concrete playtest problem in my board game. Players questioned whether asymmetric unit classes and different dice setups were actually fair, while the growing number of interactions made the system difficult to judge through intuition alone.
Rather than treating this as a purely mathematical problem, I used the thesis to investigate how simulation could complement playtesting and provide a more systematic view of combat balance.
Design Problem
Combat system expansion with new factions, unit levels and dice setups.
Risk-like combat is comparison-based rather than purely additive. Because dice are compared pairwise, changing a dice pool does not translate directly into a predictable increase in strength.
As the game expanded with different factions, unit levels, dice types and effects, small mechanical changes could significantly influence win probability, expected losses and combat duration. This made balancing through intuition alone increasingly unreliable.
Why Intuition Was Not Enough
Classic Risk-style combat: battle round.
In additive systems, different dice combinations can often be compared through expected values. Comparison-based combat behaves differently because additional dice can change the number of pairwise comparisons and therefore the entire outcome distribution.
Additive combat systems can often be compared through expected values.
This means that apparently small changes can produce unintuitive results. In some situations, an additional die can even become disadvantageous, making simple expected-value comparisons insufficient for evaluating the system.
In comparison-based combat, an additional die can change the number of comparisons and even become disadvantageous.
Simulation Approach
Requirements for extended combat mechanics.
I built the framework in separate modeling, simulation and evaluation layers so that new dice types, unit profiles, factions and effects could be tested without rewriting the combat system.
Modular architecture of the simulation framework.
The model layer defines dice, effects, unit profiles and factions. The simulation layer resolves battle rounds and full battles through Monte Carlo experiments, while the evaluation layer aggregates the results into metrics, scorecards and plots.
This makes it possible to compare manually designed variants under controlled scenarios and quickly evaluate how mechanical changes affect combat outcomes.
Evaluation
I compared manually designed variants against a reference faction across representative scenarios, including small fights, symmetric matchups and mixed unit compositions.
Metrics included attacker and defender win rate, expected losses, combat duration, deviation from the baseline, outliers and tolerance-band violations.
Results were summarized through scorecards and heatmaps to reveal both overall trends and scenario-specific problems. The goal was not to find a mathematically perfect setup, but to provide better evidence for balancing decisions.
Evaluation Results
Which Orc variant stays closer to the baseline?
Aggregated scorecard across selected heterogeneous scenarios: 1v1, 2v1, 2v2, 3v2 and 5v3.
Heatmap of scenario-level results for each variant. These results are aggregated into the scorecard.
Design Role of the Framework
The framework is a decision-support tool, not an automatic balancing system. It does not search for the “best” dice pool or generate optimal unit stats.
I define candidate configurations, simulate them and interpret the results in the context of faction identity, pacing, player expectations and playtest feedback. A numerically similar outcome is not automatically a better design if it weakens the intended player experience.
The simulation therefore provides another source of evidence for balancing decisions rather than replacing design judgment.
Limitations & Lessons
Balance is contextual rather than absolute. Results depend on the chosen scenarios, baseline and mechanics included in the simulation, and controlled combat experiments cannot represent every interaction that occurs during a full game.
The framework therefore cannot determine whether a unit is “balanced” on its own. Instead, it helps identify suspicious configurations, trade-offs and outliers that can then be evaluated through design judgment and playtesting.