Can someone please explain the tradeoffs involved in opening and closing connections to SQLServer?

On the one hand, keeping a shareable connection open throughout a user session is surely a waste of an available connection into the server, with the consequent license cost.

On the other, it seems that opening and closing a connection repeatedly must create uneeded overhead. Is there a way to implement some sort of timeout, where if a connection goes unused for x seconds it is closed, but is otherwise available for sharing? Can we get VFP or Windows to do this for us?

How would one tell if there is a shareable connection already open?

TIA,

Alex