I’ve been requested to weigh in....
I’ve read the papers on the AMP website looked at their videos etc. I offer the following:
AMP agrees with my position that we are “flash” annealing the neck and shoulder area and the temperature must be just higher than 500C (1000 F) to have any effect. It just so happens that a “dull red heat in a darkened room” is about 1000F (
https://en.m.wikipedia.org/wiki/Red_heat#cite_ref-2) So, this means that unless you see a dull red glow from your case necks, you’re probably wasting your time and gas.
They indicate that case wall (weight distribution) affects their program to be used. They also have data to indicate that brass hardness can still vary substantially even amongst the precision brands. However no indication that this variance is localized or if it materially affects bullet pull. With flame annealing the only variable here is time in the flame and there isn’t the granularity in the actual heat input. Also, with flame annealing, heat distribution could potentially be an issue.
They advocate that you should anneal every shot for consistently low bullet pull. However, Brian Litz indicates that annealing everyshot didn’t make any difference. AMP also indicated that neck expansion is only one (of several, I presume) factors in bullet pull. So, perhaps, would be annealing or lack there of, but I have no data. They also said that there has to be enough cold work present to get annealing by stating that you should size new brass or wait til the second firing.
So, to sum it all up and to answer the OPs question, if my goal was to save the brass because it is rare, or has a lot of preparatory work in it, then I’d anneal every third time. If I wanted to maintain SD on bullet pull anneal every second time. If I was reforming to make a wildcat, anneal before caseforming, then after and every third time thereafter.
But $1400 buys a big bunch of Lapua brass. At 6 firings each, that amounts to 8400 shots.