Dogs can reliably count to the number of treats they usually get at once.
Most treat oriented dogs will happily take an extra treat, and keep looking for them if there's a potentially indeterminate number.
My experience is that for small treats, 1/2 sized treats are just as good as ones that you haven't split. It's not like you're feeding the dog, you're treating it to reward/train. This is often with high value treats like bits of lunch meat that's ripped up to give them. (This is like a couple of grams for a 20kg dog, a snap and a gulp and it's gone.)
If the dog is used to getting 2 treats after an activity, that's what they'll wait for. If they're used to one treat after coming in, that's what they'll wait for.
If you, for some horrific reason, don't have the usual number of treats at the right time, you will be hounded for them. If you split them so that there are the right number but a smaller overall quantity, They're fine with it.
My experience is: * Dogs now how many treats they get for a specific context, including that there might be a long string of them. * Within reason, it's the number of actions rather than the volume. * Be very careful what actions you're actually rewarding.
Dogs are pretty smart. I'd be surprised if the smarter ones aren't on the verge of tool use. (collie pups are scary smart. greyhounds on the other hand.... not so much)
(source, dog fosterer, ~15 in the last couple years. )
Would genuinely love for someone to point out a reputable scientific paper that goes into this and actually draws some conclusive evidence.
Many human cognitive abilities are unconscious, like, in most cases, face recognition, so while I am not typically doing deliberate conscious mental math when distinguishing between my mother's face and my drinking buddy's face, it doesn't make sense to call it a "conditioned reflex" either, it seems to me. My brain is doing some sort of thought that I am not consciously aware of. That doesn't mean thought isn't happening.
I think they might have been thinking of a conditioned response, but then again you can't classically condition an animal to do something it's not already capable of. It's only the associations that are changed
The fact that they're showing different behavior in different circumstances shows some basic idea of quantity, and what is the expected quantity, and at least the difference between 1, 2, n-1, and indefinite quantity.
My dog would take it up the stairs, stand it on end, and cartwheel it down the stairs - dispensing all the treats at once for easy consumption. Kind of blew my mind that she came up with it. Her brother never figured it out.