Advanced Ovarian Cancer (AOC) is often diagnosed at an advanced stage with peritoneal carcinosis (PC). Fagotti score (FS) assessment at diagnostic laparoscopy (DL) guides treatment planning by estimating surgical resectability, but its subjective and operator-dependent nature limits reproducibility and widespread use. Videos of patients undergoing DL with concomitant FS assessments at a referral center were retrospectively collected and divided into a development dataset, for data annotation, AI training and evaluation, and an independent test dataset, for internal validation. In the development dataset, FS-relevant frames were manually annotated for anatomical structures and PC. Deep learning models were trained to automatically identify FS-relevant frames, segment structures and PC, and predict video-level FS and indication to surgery (ItS). AI performance was evaluated using Dice score for segmentation, F1-scores for anatomical stations (AS) and ItS prediction, and root mean square error (RMSE) for final FS estimation. In the development dataset, the segmentation model trained on 7,311 frames, achieved Dice scores of 70$\pm$3% for anatomical structures and 56$\pm$3% for PC. Video-level AS classification achieved F1-scores of 74$\pm$3% and 73$\pm$4%, FS prediction showed normalized RMSE values of 1.39$\pm$0.18 and 1.15$\pm$0.08, and ItS reached F1-scores of 80$\pm$8% and 80$\pm$2% in the development (n=101) and independent test datasets (n=50), respectively. This is the first AI model to predict the feasibility of cytoreductive surgery providing automated FS estimation from DL videos. Its reproducible and reliable performance across datasets suggests that AI can support surgeons through standardized intraoperative tumor burden assessment and clinical decision-making in AOC.