## 4 Results
### Integration of the Causal Model into the Neural Network  
The integration of the causal model into the neural network represents a crucial step in this experiment. While traditional neural networks are great at finding complicated patterns in data, their lack of transparency makes it difficult to figure out what causes what [4]. By adding causal principles to the network structure, the model not only gets better at generalizing in changing environments, but it also makes it easier to understand the decisions it makes, which is critical in important situations like making strategic decisions in _StarCraft II_. This integration makes it easier for the system to suggest strategies by using both clear causal relationships and complex patterns learned from data, as shown in Table 4. When the outputs of the causal model were joined with the original data, they made an input vector with 30% more features. This led to a 95% success rate for the standalone neural network and a 1.1% success rate for the hybrid model.  
To understand whether the improvement in the hybrid model's performance was meaningful, we compared its F1-score with that of the standalone neural network across 10 independent runs. Using a paired \(t\)-test, we found that the hybrid model's 1.1% higher F1-score was not just a fluke--it was statistically significant, with a p-value of less than 0.0001. The probability of this improvement occurring by mere coincidence is exceedingly low.  
Figure 5 shows the F1-scores for both models across the 10 runs. On average, the standalone model achieved an F1-score of 0.9515, while the hybrid model reached 0.9628. While this may appear to be a minor distinction, in a game such as _StarCraft II_, where every decision is critical, even a 1.1% enhancement can significantly impact the outcome.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Aspect** & \multicolumn{2}{l}{**Detail**} \\ \hline Data flow & \(\bullet\) & Input: \\  & & – & Raw Features (Units, Resources) \\  & & – & Causal predictions (e.g., military units) \\  & \(\bullet\) & Concatenation: \\  & & – & Expanded vector (+30\% Features) \\  & & – & Combination of SCM and Original Data \\  & Model & Precision & F1-score \\ \cline{2-4} Performance & \multicolumn{2}{l}{Standalone Neural Network} & 0.9520 & 0.9520 \\  & \multicolumn{2}{l}{Hybrid Model} & 0.9630 (+1.1\%) & 0.9630 (+1.1\%) \\ Interpretability & \(\bullet\) & 75\% of recommendations consistent with causal rules & \\  & \(\bullet\) & Verifiable strategic coherence & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Architecture and evaluation of the hybrid model.  
The negative t-statistic (\(-6.62\)) indicates that the hybrid model's improved performance was not due to chance; it was consistently superior. This is further supported by the narrow confidence interval for the difference in F1-scores, which ranged from 0.008 to 0.014. This indicates that we can be 95% positive that the actual enhancement resides within this interval.  
This enhancement signifies that the hybrid model excels in suggesting methods that adjust to the game's evolving circumstances. Whether a player is low on resources or has a strong army, the hybrid model can adjust its recommendations more effectively than the standalone model.