Haven't read the paper yet but this is so weird because when I was a kid I noticed this phenomenon myself. I noticed I could reliably flip a coin such that when it landed it would land on the same side as it was flipped from. I was getting like 80% accuracy and I didn't even know what I was doing to achieve it. I could just usually feel when I flipped it that I "did it right". I used it a couple times to win coin toss decisions but then sorta forgot about it and relegated it to a statistical fluke. It would be amazing of there was some merit to it.

There's a "fair coin", and then there's a "fair flip". It's actually pretty difficult to do a truly "fair flip".

Sounds like maybe you were doing something like this? https://news.ycombinator.com/item?id=42184069

Maybe you were like one with the coin and always pushed it the optimal way for like the same type of movement and direction and rotation for the same amount of rotations in air etc like perfected an initial condition and kept it stable like it rotated 6 times and landed the same way