JACQUES D. answered 09/22/20
I guess the important thing to remember is that we use the electronic configuration (based on Aufbau Principle as electrons fill the lowest energy levels for the atomic orbitals of hydrogen). We "explain" that the 4s is higher energy than the 3d, so they get filled first, but when there are 3d electrons present, they shield the farther 4s more than other 3d's, thereby resulting in "s before d" ionization for most transition metals (Fe being the poster child). We do some more hand-waving with regard to the Group 6 and 11 TMs by saying that the half or full d-shells are particularly stable which result in the anomalous +1 ions (when most TMs have +2 as the first state). The interactions of the orbitals is just not included in the hydrogen QM orbital solutions.
Chemistry has a lot of "formal" and heuristic approaches that really only cover particular cases and always have exceptions. The rules of thumb are necessary because atoms are inherently complex systems and their behavior can only be well-modeled by full quantum analysis which is not easy in general, or accessible to high school students.
In the end, I always say that chemistry is all about exceptions and all the models are only as good as you need for your purposes and not to be confused with what really happens (which may be a surprise) . Looking at inorganic chemistry texts, gold usually takes on the +3 state mostly in coordination complexes like [AuCl4]- , but it also does make salts with Cl, Br, and I. Apart from coordination structure, I believe the clue that silver does not go +3 indicates that the +3 state in gold may largely be about taking 3 electrons from a big atom until it's too charged to take another one - like the lanthanides. (configuration not being so important for larger atoms because the energy differential between higher orbitals are so small.
I always found the Ni group as the column with the "keeps-me-humble" configurations with s2d8 (ok), s0d10 (Oh, I guess that can happen - Cool!), s1d9 (I'm either going to quit or let this one go...)
Take care,
Jack