Maybe I should restate my question. Assume a receiving antenna is in
the center of a sphere and the received signal is coming in equal
amounts from all points on the surface of the sphere. Which receiving
antenna would capture more power, an omni or a high gain beam? There
are no noise and no losses.

Ron

Ron wrote:

Assume an incoming rf signal has exactly the same strength in all 3
dimensions i.e., completely omnidirectional. Question: would an antenna
having gain capture any more signal power than a completely
omnidirectional antenna with no gain?

Ron, W4TQT