\section{Additional numerical summary}\label{app:results}

\begin{table}[h]
\centering
\caption{Mean exact root gap and true regret of the generative policy across factorial cells.}
\begin{tabular}{@{}llrr@{}}
\toprule
Transition entropy & Return dispersion & $V_\gen-V_\ctrl$ & Generative-policy regret \\
\midrule
Low  & Low  & \GapLowLow{}  & --- \\
High & Low  & \GapHighLow{} & --- \\
Low  & High & \GapLowHigh{} & \RegretLowHigh{} \\
High & High & \GapHighHigh{} & \RegretHighHigh{} \\
\bottomrule
\end{tabular}
\end{table}

The omitted low-dispersion regret entries are visually near zero and are available in the machine-readable results. Reporting exact gaps and policy regret separately is important: a positive normalization/value gap need not materially change the action policy.
