Background. RGB-trained capsule-endoscopy classifiers underperform on small-vessel vascular findings by conflating hemoglobin contrast with bile and illumination falloff. Thus, here we test whether a Monte Carlo-inspired analytic model can compute hemoglobin from RGB signal built upon extracted classifier. Methods. On Kvasir-Capsule (47,238 frames, video-level 70/15/15 split, 11 evaluable classes) we evaluate two software-only configurations against RGB-only EfficientNet-B0 across 6 seeds: (i) a prior P_blood = sigma(alpha * (H_norm - 0.5)) * Phi(r) fused as 2 zero-init auxiliary channels; (ii) a distillation head training a 3-channel RGB backbone to predict P_blood. Significance: paired DeLong, McNemar, bootstrap CIs with Bonferroni correction. Results. Across 6 seeds (n=6,423), the analytic prior provides a small but direction-consistent macro-AUC improvement: RGB-only 0.760 +/- 0.027, input-fusion 0.783 +/- 0.024 (paired Delta = +0.023, sign-positive on 5/6 seeds), distillation 0.773 +/- 0.028. The largest robust per-class lift is on Lymphangiectasia, where AUC rises from RGB 0.238 +/- 0.057 to input-fusion 0.337 +/- 0.019, sign-consistent across all 6 seeds. On rare focal-vascular classes (Angiectasia, Blood - fresh) the prior's per-seed effects are bimodal: seed=42 reaches Angiectasia AUC 0.528 -> 0.916, but the cross-seed mean is 0.646 -> 0.608 with sigma_PI = 0.23 - reported as a high-variance per-seed exemplar. Conclusion. A Monte Carlo-inspired analytic prior provides a small, direction-consistent macro-AUC improvement on Kvasir-Capsule across 6 seeds with the largest robust per-class lift on Lymphangiectasia; the distillation variant runs on plain 3-channel RGB and yields a free interpretability heatmap.