I can’t say much, except what I’ve observed. I have owned Standard Poodles for most of my life. They’re smart dogs. No, not the little ones, the big dog sized ones. You see them in the circus.
One, over a period of several weeks, figured out the remote control controlled the TV, and figured out how to turn it on.
Several of them have figured out how to open swinging, latched, and knobbed doors.
A few of them have responded to mirrors. My theory is that they do know their own reflection… and don’t care. My reasoning is as such: It’s the puppies that respond to mirrors, and bark and chase themselves in it. Really young ones. As they grow older, they no longer do this. However, they do respond to dogs on TV.
One, while watching Westminster, responded extremely strongly to a similar looking poodle. It later turned out to be his uncle. Furthermore, he likes to watch soccer and nature shows with bears. At one point, a man came out of a blind in the background. Noticing this, he charged the TV and attempted to inform the man in no uncertain terms to go back in the blind.
All of them have been able to ‘find mommy’ or ‘find daddy’. If not in a easily locatable area, some check by process of elimination through most likely areas.
They can judge relative size of two mounds of food. I don’t know if they can count, though.
With about 80 percent accuracy, they can ‘find the new toy’, given four old toys and a new toy. Repeated about fifty times over four years.
Anything else you can think to try? Oh, one more thing, insofar as judgement goes. Older dog, baby. Baby pulls older dog’s ear hard. Dog’s head whips around, mouth firmly closes over the baby’s hand. Not a mark on the baby. That’s judgement, if I ever saw it.