There's more than one way to skin a cat, or so the saying goes. I'm relieved to report that I haven't tried any of them. I have, however, tried out a lot of different ways to hold the bow.
When I was a student, it seemed that every time I went to a new teacher, I had to learn a new bow hold. For one teacher, the philosopher's stone was pronation. Another had me space my fingers wider apart on the stick. Yet another deplored the way I draped my (long, thin) fingers over the frog, insisting that I should hold it in the pads of my fingertips. As we can see in this recent article from The Strad, the topic of different "schools" and methods can become fraught and argumentative. But you know what? All the bow holds I learned were good ones, and I use aspects of all of them today as I continue to evolve in the way I play the cello.
The fact is that a lot of different methods of holding the bow can work, as we can see from watching videos of the world's top cellists. As a teacher, I try to stay open-minded about a student's bow hold, unless it simply doesn't work. On page 27 of Cello Practice, Cello Performance, I wrote:
"Human bodies vary hugely, so there can be no single correct method for holding the cello and bow, but it is only logical to play with both hands in a relaxed, rounded shape. The thumbs should oppose the middle fingers, both on the stick of the bow and the neck of the cello. The fingers of both hands should, in most circumstances, keep their natural spacing--after all, the cello and bow were designed with the human hand in mind!--and not wedged together as in a salute, or forced widely apart in a tense grasp."
That said, I wonder if some of the things we've always been taught about holding the bow really are true. One of the top ones is the part of the frog on which almost everyone places the thumb, i.e. the top corner where it joins the stick. The first picture shows how I was taught to hold the bow:
The problem with this is that the "bump" at the end of the frog tends to dig into the pad of the thumb, and after long hours of playing, it gets very tender. I got to the point of having a permanent indentation in my thumb from the bow, as well as a sensation of stabbing pain in the flesh of my thumb when I picked up the bow.
That was when I started experimenting with putting my thumb into the hollow of the frog. Beginning cello students often assume that this hollow is meant for the thumb, and get corrected by their teachers. But really, why shouldn't we put our thumbs there, as long as the overall bow hold maintains reasonable relaxation and naturalness? I tried this out (pictured below):
I found that when I held the bow this way, I was able to execute all the bow strokes just as well, with the added benefit of no more pain.
Here's how it looks from the front (pictured below). If you oppose your thumb with your middle finger, the thumb doesn't poke through the bow. In fact, I feel that my hand is better "connected" when I hold the bow this way. Try it and see.