Source-linked AI summary
Turn-Based Combat Arena: A New Framework for Multiagent Training and Game Balancing
V. M. Vasyuta, V. V. Malitskyi, O. S. Kushnir, B. I. Horon, V. A. Franiv
TL;DR
The paper presents TBCA, a configurable turn-based strategy game framework for ML studies, and investigates how to balance its units. It reports consistent and fair unit parameters from balancing based on victory impact or semi-random team play, while noting that some balance metrics are noisy or can misrepresent imbalance.
Problem
Only a few variations of turn-based strategy games have been widely considered, while these games offer a simpler but strategically diverse domain for studying strategic behavior.
Source: §2.2 · p. 4Method
The paper introduces TBCA, a configurable turn-based strategy game framework, and formulates unit-parameter balancing as a 10-parameter optimization problem using CMA-ES across different loss functions.
Source: §1 · p. 2, §5 · p. 10Results
Balancing based on victory impact or semi-random team play leads to consistent and fair unit parameters.
Source: §5 · p. 10Takeaways & Limitations
TBCA supports game-balance analysis through multiple metrics and optimization of unit parameters.
Source: §5 · p. 10d2-based balance metrics have measurement error up to 14% even with 5,000,000 simulations per evaluation, making them less practical as optimization loss functions.
Source: Pairwise win-loss matrix for the… · p. 7
Abstract
from arXiv · showhide
This paper is the first in a series on Turn-Based Combat Arena, a configurable framework for turn-based strategy games designed to support the efficient training and evaluation of machine learning agents. The proposed framework enables flexible modification of game rules and parameters, allowing rapid experimentation across diverse scenarios. Its architecture is optimized for high-throughput simulation, supporting tens of thousands of games per second and enabling the storage and processing of billions of gameplay records on a single machine. The problem of balancing the game, and particularly the parameters of game units, is investigated in detail. We evaluate several optimization approaches and show that multiple methods converge to comparable solutions, suggesting robustness in identifying balanced game configurations. These results indicate that the framework can serve as a practical platform for both game design analysis and agent training.
1 Introduction
Turn-based strategy games offer a domain for studying AI and game-theoretic questions, but only a few rule variations have been widely considered. The paper introduces TBCA as a configurable framework for ML studies, with high-throughput simulation and a focus on game balance.
1 Introduction
- Games provide controlled environments with clear rules and objectives for developing and evaluating AI algorithms.The paper notes that computer game milestones have served as AI testbeds since the early 1990s.Source: §1 · p. 1
- Many early superhuman game-playing systems combined databases of prior games for openings and endgames with tree search through intermediate states, requiring extensive computational resources.The paper cites checkers, chess, and Arimaa as examples of games with large state spaces.Source: §1 · p. 1
- Turn-based strategy games are proposed as a simpler but still strategically diverse domain, where complex mechanics or agent parameters need not obscure basic strategic behavior.The introduction also identifies balance, strategy diversity, and behavior complexity as open questions.Source: §1 · pp. 1–2
- Only a few variations of turn-based strategy games have been widely considered, despite the many possible rule variations.Existing examples include TUBSTAP, STRATEGA, and ADAPTA.Source: §1 · p. 2
- TBCA is a highly configurable game framework designed for ML studies, with simulation throughput of tens of thousands of games per second and capacity to process billions of battle records on one machine.The paper also investigates game balance as a central problem.Source: §1 · p. 2
2 The Game
TBCA is a configurable turn-based battle game with unit statistics and combat rules designed to support varied strategies. Its state-space complexity can be adjusted through game parameters, spanning simple configurations to ones whose optimal strategies remain unknown.
2.1 TBCA rule set
- TBCA uses configurable units with health, attack and defense modifiers, attack range, and movement points; attack and defense can compensate for tactical advantages from range and mobility.The study uses five unit types, with each unit type having its own configurable parameters.Source: Players · p. 3
- Unit types are primarily randomized at the start of each battle in this study, so players must adapt strategies to changing teams.The game also permits deterministic unit types for predefined teams and more strategic play.Source: Players · pp. 3–4
- Damage depends on the attacker’s attack modifier and target’s defense modifier, with a configurable random factor; a surviving target may retaliate for half the direct-attack damage when in range.A melee attacker always faces retaliation, whereas a longer-range attacker striking a melee unit does not.Source: Damage mechanics · p. 4
- Unit turns are ordered by movement points, while ties are randomized; on a turn, a unit may move, attack, move then attack, or skip.Repeated idle turns can trigger a configurable draw threshold, preventing games from continuing indefinitely.Source: Movement decider · p. 4, Draws · p. 4
2.2 State-space complexity
- The complexity calculation accounts for team-unit configurations and spatial arrangements subject to at most one unit per cell.The study assumes a shared initial health level for all units.Source: §2.2 · p. 4
- The selected configuration’s state space exceeds chess’s (10^43) and lies between Hex (10^57) and Thurn and Taxis (10^66).The game’s complexity can be tuned by changing maximum health, the number of unit types, or the number of units per team.Source: §2.2 · p. 4
3 Framework Architecture
The framework is designed to support high-throughput simulation, metrics collection and data incorporation, and integration of new ML models. Its architecture combines a parallelizable battle engine, a database with an in-memory staging step, and a WebSocket API for AI players.
3 Framework Architecture
- The architecture targets high simulation throughput, effective metrics collection and rapid data incorporation during reinforcement learning, and easy integration of new ML models.Source: §3 · p. 5
- The stateless battle engine supports parallel simulation and benchmarks at 55,000 games/s, or about 6 · 10^6 states/s, on a single machine.The benchmark used a Docker container limited to 16 CPU cores and 16 GB RAM; the machine had an Intel Core i5-13500K and 32 GB RAM.Source: §3 · p. 5
- DuckDB is used for large-scale battle records, with stated capacity of 300–400 million records in about 100 GB of local disk space.An in-memory stage accumulates battle statistics and periodically flushes them to the database to address the limited update rate of column-oriented storage.Source: §3 · p. 5
- The real-time WebSocket Battle API sends players the current battle state and next acting unit, then accepts a permitted action and its parameters.Players may optionally attach a label to decisions, which is stored with battle statistics for later behavioral analysis.Source: §3 · p. 5
4 Game Balancing
The section treats unit-parameter balance as central to fairness, strategic depth, and avoiding systematic bias in simulation data. It compares candidate balance metrics and optimization outcomes.
4.1 Balance metrics
- Pairwise win rates are considered too coarse to capture unit strength, so the section also considers kills and damage as more granular measures.The pairwise kill measure averages kills by one unit type against another and ranges from 0 to T.Source: Pairwise win-loss matrix for the… · p. 6
- Damage-based d² metrics have much higher measurement error than k² metrics, and σn and εa can be small even when a game remains highly imbalanced.The reported errors reach 14% for d²-based metrics versus 0.3% for k²-type metrics; short battles can also produce low σn and εa in an imbalanced setting.Source: Pairwise win-loss matrix for the… · p. 7, Battle-level metrics · p. 7
- Because single-type comparisons miss teammate interactions, the authors add semi-random-team comparisons and randomly composed-team metrics, including survival rate and victory impact.The proposed random-team metrics include the mean squared deviation of unit-type survival rates and of victory impact.Source: Battle-level metrics · p. 7, H units · p. 7, Unit type-specific metrics · p. 7
4.2 Pre-balancing setup and methodology
- The setup varies attack and defense while fixing tactical parameters and the damage function, and uses a rule-based agent that attacks or moves toward attack range.Tactical settings and damage parameters were chosen to reflect the units’ tactical properties.Source: §4.2 · p. 8
- CMA-ES evaluates 10,000 battles per candidate; exhaustive search across the 10 integer parameters would require about 8.2 · 10^17 games, estimated at 2.6 · 10^6 years.The optimization treats parameters as continuous, then rounds them to integers for loss evaluation.Source: §4.2 · pp. 8–9
4.3 Analysis of balance parameters
- Most optimizations favor the highest attack for F and SR, the lowest for LR, lower defense for SR, and higher defense for H; parameter similarities also persist across metrics and setups.The authors relate these patterns to unit tactical properties.Source: §4.3 · pp. 9–10
- Survival rates cannot be balanced across all unit types, strict kill-death balance reaches a minimum of 0.462, and semi-random teams yield consistent values across the defined metrics.Semi-random-team balancing also produces relatively fair victory-impact values.Source: §4.3 · p. 10
- Victory impact σw is preferred because it is more unambiguous and avoids assumptions about semi-random team composition.The authors recommend optimizing attack and defense using either semi-random team play or victory impact.Source: §4.3 · p. 10
5 Conclusion
TBCA is a configurable turn-based strategy game and high-performance simulation framework, with unit balancing studied through multiple metrics and optimization. The paper reports that victory-impact and semi-random-team balancing produce consistent, fair unit parameters.
5 Conclusion
- A special case with 5 unit types and 8 units per team has state-space complexity of about 10^60, higher than chess.The game has numerous tunable parameters for exploring different configurations, mechanics, and strategies.Source: §5 · p. 10
- The simulation framework achieves tens of thousands of games per second and supports storage and processing of billions of battle records on one machine.It includes in-memory battle-statistics accumulation, a real-time WebSocket API for AI players, and a rule-based agent with diverse behaviors across unit types.Source: §5 · p. 10
- Balancing based on victory impact or semi-random team play leads to consistent and fair unit parameters.The study formulates unit-parameter balancing as a 10-parameter optimization problem and applies CMA-ES across different loss functions.Source: §5 · p. 10