> that was with success on the first try of the first round (which is very rare).

This very much depends on the patient history (age, cause of infertility, …) and the clinic. Live births per intended retrieval can vary from 10%-60% conditional on the above.

In our case, it was suggested that the first transfer of the first cycle had a 15% chance of success. Whether that's "very rare" is perhaps a matter of perspective. It was low enough we assumed it would be a failure and we were surprised when it succeeded, but to a doctor it's a frequent occurrence.