I know that solving Verity was an absolute bear, and therefore I understand why everyone was quick to jump on the first algorithm that was proven to work consistently (give everyone doubles of what they're holding; distribute one to each).

However, now that we understand the mechanics of the encounter much better, is there any reason to keep using this strategy?

To the best of my knowledge, there are only three possible shadow states upon entering the inside room:

  1. The shadows on the wall are two copies of the shape your guardian is holding.
  2. The shadows are one copy of your shape and one copy of another shape.
  3. The shadows are both shapes your guardian is not holding.

We also now know that it's mandatory to give away both the shadows you start with.

Given this knowledge, it's very easy to distribute shadows to the shape-holders who need them in one single step.

Scenario 1. This is what people are used to. One shadow to each of the other guardians.

Scenario 2. First look at the shape that is different from the one you're holding. Only one of the other guardians can use that shape. For example, you are holding S and the wall shows ST. The guardian holding T cannot escape with a T on the wall. Therefore, you give your T to C and your S to T.

Scenario 3. Just give to unlike. If you're S and your wall is TC, give T to C and C to T.

This guarantees that everyone has the shapes they need to leave after only one phase of dunking.

It also means that all the correct codes can be assembled before the witness notices you (so no forgetting your place) and that you don't need to check in with one another to confirm that people have their duplicates and are ready to distribute. Furthermore you will only have to kill one ogre and two sets of knights.

I do understand that the guide videos are already out there and people like to do what they know, but it would be cool to see this more streamlined method gain in popularity.

TL;DR: Give your shadows directly to the people who can use them. The shape you're holding can go to either, so start by giving away any shapes different from what you're holding. This guarantees a two phase inside.

Note: It is my understanding that it is impossible for the shadows to be duplicates of a shape you are not holding upon entering the room. In other words, if your guardian is holding S, the shadows cannot start as TT or CC. This is important because the strategy breaks in this instance. Please correct me if anyone has ever experienced this state.

EDIT: Thanks, all, for the helpful discussion. I'm sorry I was wrong about Scenario 3 being possible. The point of my post was to learn the answer to my original question, and I managed to do that and more. In fact, I see that we inspired another two reddit posts based on the comments. Good stuff. And good luck with your master clears.