Another story from If Dogs Could Talk that has implications for agility training:
Csanyi set up an experiment in the lab with three groups; children aged 4 to 6, graduate students, and adult dogs. In the room were three large screens. The experimenter would place a ball in a plastic bucket, watched by the participant. He would then go behind each of the screens in turn, putter about for a moment, and emerge to show the participant whether the ball was still in the bucket or not. The he (in the case of the grad students) or the dog's owner, or the children's kindergarten teacher, would give a signal to find the ball. The grad students only made one error, and the dogs and children both had success rates that were much higher than could be achieved at random.
In the next stage of the experiment, the experimenter quite obviously put the ball in his pocket, showed the participant the empty bucket, and then disappeared behind each screen in turn pretending to leave the ball and showing the empty bucket after each.
All three groups had a few smartypants who immediately indicated that the experimenter had the ball in his pocket. But 50% of the grad students, 55% of children, and 75% of the dogs ostentatiously searched behind the screens for the ball before returning to the experimenter.
When the children and students were asked, they said that they felt that searching behind the screens was the essence of the game, regardless of where the ball was. Csanyi says "I see no reason to doubt that the dogs had similar ideas."
This and other experiments showed that dogs can learn the rules through patterning.
The problem is that we are often unaware of what the rule is that the dogs are learning. I think there are some dogs out there who know the rule "Walk up the ramp, across the top, jump off, mum puts me back on, I wait and she gives me a treat."
Morgan Spector said something that I mis-remember but it was like "Once is an aberration, twice is a pattern, three times is a lifestyle."