Abstract Study question Which embryo selection model would be given high priority for single euploid blastocyst transfer, iDAScore® v2.0, KIDScoreTM D5 v3.2 or conventional morphological grading system? Summary answer Prioritize morphological grading over embryo score for single euploid blastocyst transfers, and reverse the priority for single non-PGT-A blastocyst transfers. What is known already The use of effective tools, such as AI, morphokinetic data and the Gardner criteria, for embryo selection within in vitro fertilization (IVF) has the potential to increase the possibility of pregnancy. Nevertheless, previous studies indicated that the best embryo these tools prioritize may be inconsistent and controversial. Therefore, this study demonstrates integrated reference tables of FHB+ rates for selecting of single embryo transfer (SET) clinically, and assess the association between iDAScore®, KIDScoreTM, traditional morphological grading and embryonic ploidy status. Study design, size, duration Retrospective study from November 2022 to October 2023 with morphokinetic parameters of time-lapse monitoring analysis involving embryos from 264 patients who underwent day-5 single vitrified-warmed blastocyst transfer with or without preimplantation genetic testing for aneuploidies (PGT-A) (total SET=264; euploid=158; non-biopsied=106) using Embryocope® Plus incubators. After SET, the rates of FHB+ of each group were analyzed. Mean female age was 35.2 years. Participants/materials, setting, methods Blastocyst morphology was scored in 3 groups: good (AA, AB, BA), average (BB), poor-quality embryos (BC, CB, CC). Blastocysts were ranked established on the scores caused by iDAScore or KIDScore. All cycles were stratified into 4 score groups (8.1-9.9, 6.1-8.0, 3.7-6.0, 1.0-3.6). Assisted hatching was conducted on day 3. Trophectoderm biopsies were performed on day 5, and examine the embryonic ploidy status using a next-generation sequencing-based PGT-A platform (Thermo/Ion GeneStudio™ S5 Prime). Main results and the role of chance In D5 non-PGT-A SET group, the FHB+ rates of good-quality embryos were higher than those of average and poor-quality embryos (49% vs. 40% vs. 0%). According to the embryo score group, the group with higher scores showed better FHB+ rates (KIDScore: 56.9% vs. 47.2% vs. 16.7% vs. 0%; iDAScore: 59.1% vs. 49.6% vs. 14.9% vs. 0%). The non-PGT-A results indicated that embryo score should be given high priority. In D5 euploidy SET group, the FHB+ rates of good-quality embryos were higher than those of average-quality embryos (78.12% vs. 56.00% vs. 44.44%). According to the embryo score group, the group with higher scores did not show distinct better FHB+ rates (KIDScore: 65% vs. 69.51% vs. 47.6% vs. 0%; iDAScore: 64.1% vs. 67.7% vs. 38.8% vs. 0%). The PGT-A results indicated that morphological grading could be given high priority. Based on the data, we hypothesized that assisted hatching might lead to distortion in embryo scores. Limitations, reasons for caution The study is limited by its retrospective single center study with small sample size of single embryo transferred even some of the groups have no embryo transfer. Therefore, a prospective multicenter validation is necessary. Wider implications of the findings This study provides distinct tables for clinical embryo selection with or without PGT-A. Our findings support the potential application of the integration of AI, morphokinetic data and embryo quality prediction systems, and indicate the possibility of making appropriate decisions in different age groups clinically. Trial registration number Not Applicable