It's called variable ratio reinforcement where positive reinforcement is only administered at an average ratio but random occurrences. This allows the trainer to cue more repetitions without filling the animal up too quickly. However, there are some drawbacks. If the animal is not 100% confident in the trick, they might give up and stop doing it. Also, if the ratio is such that reinforcement is too rare, the animal could become aggressive.
Also, I continue to use the clicker even though I'm not giving treats. The clicker is no longer a bridge but a secondary reinforcer. The parrot is working to earn clicks rather than treats and the reason it wants clicks is because they can be associated with treats. The parrot ends up working harder because it doesn't know when the treat will come.
Here is a discussion of variable ration reinforcement in greater detail.But until the parrot knows multiple tricks and is very proficient at the training process, you should maintain a continuous ratio of reinforcement where one trick gets one treat.
By the way, I made a stupid mistake when filming that video. We had to do many takes to get the time down and I got in a habit of reinforcing Kili for the same few tricks every time. You may have noticed that she was avoiding flipping the card. Believe me it is not because she doesn't know what to do. I can get her to fly across the room and flip the card at first glimpse of it cause she really likes doing that. However, in this trick routine I was consistently giving her treats for a few tricks beyond the card flip so she was trying to skip the card which doesn't reward and go to something else. If I wasn't so focused on the video and did things properly, I would be less predictable and more random about which tricks were rewarded. The video was incredible no doubt and I probably had better runs than the one shown (when I was practicing before we started videoing) because at first the bird really didn't know which tricks would get the treats and just tried everything with equal enthusiasm. What is really incredible is that I was getting a variable ratio of reinforcement of about 5 to 1 meaning I got her to do five tricks for every treat. That's lower than what I normally do (about 3 to 1) so after a while she was getting confused and frustrated. After we completed the video I went back and did the same string of tricks and rewarded each trick individually to gain her trust back.