Hi Ropunzel,
I think how I responded before covers your two concerns: 1. “arbitrary points” and 2. " Each trade you enter presents an independent and new risk," by which I think you’re referring to each pyramid level. You’re absolutely correct. Each pyramid level is “an independent and new risk.”
Here is what I wrote, which addresses each of those two points:
“Strong trend” covers adding a level as a “new independent trade,” and “strong new entry signal” addresses “arbitrary points.”
Norm
Oh by the way:
Did you see I posted about Bill WIlliams’ other book on my thread??? It was bugging the life out of me that I wasn’t seeing some stuff that formed a part of his methodologies in these other books of his. Only dawned on me last night that he had three books. And the one to which I’m referring is arguably his best work by far. And for sure didn’t lose the plot half way through as happened in the other two.
Main reason I mention it is because in THIS book he talks extensively and in depth about Fractals and certain other things (I remember now thinking that these other two books were just brief summaries of the first book) and those are good places to add to positions as the trade matures.
Hi Dale,
On your recommendation, I downloaded Trading Chaos - Second Edition, but I don’t know what other BW book you’re referring to. If you don’t mind, would you just tell me the title, and I’ll see if I could find it as a free download, the only kind of download I’ll download at this point. 
Thanks,
Norm
Do you REALLY think I’d just give you a title and say go find it yourself???
Here you go:
Thanks Dale,
I downloaded it. I’ll check it out as I’m able.
Norm