The change that is in Erdnase, was actually developed by Houdini.
That's highly debatable! Sorry for going a bit off topic here, but I see a lot of people saying this, and I don't think the literature really supports a definite conclusion one way or another. The only published reference to the move prior to Erdnase (as far as I know) is P T Selbit's
The Magician's Handbook (1901), where it says, "For the knowledge of the movement, I am indebted to Mr Harry Houdini." To me, this sentence doesn't say that Houdini is being credited for inventing the move, rather he's being thanked for teaching it to Selbit. From what we know of Houdini, he wasn't in the habit of being modest about claiming a technique that he had invented. So, while not absolutely definitive, I suggest that this reference implies that Houdini did not, in fact, invent the move.
There are two other prominent references in the literature to the move. The first is in Camille Gaultier's
Magic without Apparatus, where Gaultier specifically says that he doesn't know if Houdini invented the move, although he saw him demonstrate it. The reference which seems to be most clear that Houdini invented the move is in
Elliott's Legacy to the Conjuring Fraternity, where it is referred to as a move "by Houdini". This project was fraught with conflict between Clinton Burgess and Houdini, over Houdini claiming too much credit for the book as a whole, so I contend this could also cast doubt on his credit for particular moves contained in it. Additionally, given that it was assembled from Dr Elliott's notes, the note describing the change could easily have referred to the fact that the move was taught by Houdini, which became "by Houdini" to fit the formatting of the book.
I think it's clear that this change was not invented by Erdnase, although, as is often the case, he adds subtleties into his handling which aren't often taught in other descriptions and I suggest he learned it from a magician in person (possibly August Roterberg) rather than from the literature. The evidence that Houdini invented it is, however, flimsy. I believe he would have claimed unequivocal credit for it if he'd invented it, and he doesn't. There are several such moves beginning to appear in the literature around this time and I think the origin of many of them, including this one, is probably lost to us. We can credit Houdini with introducing the wider magic world to the technique, as we do with Le Paul and "his" spread, but if we're going to be sticklers for historical accuracy, I think we should reserve judgment on whether Houdini really was the creator.