Many of the answers here are partially correct, but many also are repeating commonly held fallacies, and other contributors simply don't know what they're talking about. The total conversation makes it clear that there is still a large gap in knowledge within the industry, though not nearly as bad as it was pre-internet.
To be clear the 1/3 "guideline" refers to the depth of the notch
the 80% guideline refers to the total length of the hinge relative to the diameter at the cut, so if the tree is 50" in diameter at the cut, the hinge should be 40" in length, no matter how deep a notch is required.
One detail that I have never heard mentioned when it comes to the 80% recommendation is: should that 80% (40" in the above example) length be measured at the front of the hinge or the back of the hinge? They will be significantly different. Since that distinction has never been addressed, perhaps we should just say that the 40" should be the average length or middle of the hinge. Either way, whether the one-third rule or the 80% rule, the question remains "WHY?"
The 10% hinge width is another guideline that is not well understood. I'd guess that not one instructor of 50 in the world could accurately address all the factors involved in those two guidelines. Since even the "experts" lack a complete understanding, it's just easier to say "do it like this" without an explanation. Thus in 2022 the question is asked and the above answers are still incomplete. It's actually phenomenal that with such a fundamental skill this question has been so rarely addressed in all these years. And there are so many of the unlearned masses that have never even bothered to think about "the why", yet they often hold vehement beliefs about "the rules", and get all righteous and indignant with anyone who might suggest or demonstrate otherwise. Sounds a lot like mass formation psychosis to me. An entire industry where everyone, for decades, has just done it the way they were taught, without ever questioning why.
It is understandable that there is going to be inertia within the educational institutions in the industry. They are not going to advocate for changing "The rules" because they don't want to assume responsibility for situations where a little knowledge becomes dangerous. There are far too many factors that make a complete teaching on the subject very complex. Few if any of the "instructors" have this complete understanding, to begin with. But even if they did, it would be very difficult to accurately convey that knowledge, especially to newbies, because there are just too many factors involved. Thus you 're not going to learn much about advanced falling techniques from professional educators. As such, Youtube has become a major factor in pushing the boundaries of acceptable techniques.
Unfortunately, it's easy to pass on bad habits or show advanced techniques that could be extremely dangerous when improperly applied on YouTube. One example would be the unnecessary tip tying shown by August and Reg. While they may appear to do it safely, Human (Corey) almost got himself killed by improper application of the technique... literally 6" from death. He claimed to be a big Hunicke fan, and admitted to cutting Humboldts regularly because that's what he saw the west coast guys doing. Watching him come that close to death is a very sobering reminder of just how serious the consequences of incomplete understanding can be in this business. He had no idea that the piece he was about to cut could helicopter around the back of the tree and smash his skull in.
When falling or taking tops there are going to be many factors that can make a difference in how deep a notch to cut. Just to name a few:
1) how big is your bar relative to the cut?
2) are you falling with wedges or pulling with ropes, and if using ropes how much pull do you have in the system, how high are they set?
3) How much side lean are you fighting?
4) Does the tree or top have front lean, no lean, or a slight back lean etc?
5) what degree of accuracy is needed?
6) how prone is the species, given the lean of the tree, to barber chair?
7) what are the obstacles involved should you lose the tree to side lean?
8) how much of a hurry are you in?
9) are you trying to jump the top?
And the list could go on....
And for those that like to think about such things, here's another question for YOU...
WHEN DON'T YOU NEED A HINGE?