  We use machine learning (ML) and non-ML techniques to study optimized
$CP$-odd observables, directly and maximally sensitive to the $CP$-odd $i
\tilde \kappa \bar t \gamma^5 t h$ interaction at the LHC and prospective
future hadron colliders using the final state with a Higgs boson and a top
quark pair, $pp\to t\bar t h$, followed by semileptonic $t$ decays. We perform
phase-space optimization of manifestly $CP$-odd observables ($\boldsymbol
\omega$), sensitive to the sign of $\tilde \kappa$, and constructed from
experimentally accessible final state momenta. We identify a simple optimized
linear combination $\boldsymbol \alpha\cdot \boldsymbol\omega$ that gives
similar sensitivity as the studied fully fledged ML models. Using
$\boldsymbol\alpha\cdot \boldsymbol\omega$ we project the expected
sensitivities to $\tilde \kappa$ at HL-LHC, HE-LHC, and FCC-hh.
