As far as sticks go, I think it is up to the dog's own character as to what it sees as valuable ...
Bramble loves running and fetching sticks - we almost always have two, so he will drop one to get ready and run or swim for the other ...
If he meets another dog, however, sticks go out of the window, and he immediately drops his stick to sniff the other dog - if they pick it up and run off with it, he simply looks bereft and wonders what went wrong ... He will reluctantly relinquish his stick if we only have one, but if we ignore it, he will simply pick it up and carry it, yet drop it at the first next interesting thing on his walk ....
We never let him lie there and chew a stick though, as, apart from the obvious risks, it upsets his tummy and he is sick if he has ingested stick ...
