I will add my two cents here. You can call all that I advised my son on and what he did last year gaming - with a very pejorative nuance. I call it a smart strategy that can increase your odds. Of course, I do NOT advocate misrepresenting yourself, your goals, etc. Nor do I think you should choose a major you don't like or a school you are not likely to thrive in. However, unless your heart it set on A PARTICULAR school, and there is a range of schools that you are interested in, you can employ a strategy that can maximize your odds.
I think your son did precisely the correct thing because he wanted to attend a private school! By using the word "gaming," I did not mean that an applicant should not put considerable thought into school selection (certainly didn't mean it in the pejorative sense). I apologize for not being more specific.
It is by no means a dishonorable thing to try to figure out "the system" (DS certainly did, and likely so has everyone else). This is not misrepresentation at all, simply a fruitless exercise akin to picking Powerball numbers. The best way to do it, IMHO, is simply rank your choices from best to worst and live with that choice.
In my view, if someone wants to attend a private school, then he or she should not be listing public schools in an effort to increase the odds of obtaining a scholarship (unless that is definitely a school that he or she would consider). As I recall, if you are selected for a scholarship and are awarded one to a state school, then good luck trying to transfer that to a more expensive school!! Will not happen. Conversely, if the applicant has no interest in a private school and wants to go the local state schools where most of his or her classmates are going or because the state schools, while less expensive, actually carry a higher prestige than the private school, then he or she should not list ANY private schools. My DS tried to figure things out initially but finally took the following approach:
"Dear Cadet Command, here's my list. I have rank-ordered them as you requested, but just know the farther you go down the list from my top choice, the less likely I will be to accept your offer and more likely will opt for another alternative."
There was a period last year when based on advice here on SAF that I thought DS's decision to list only high-price private schools doomed his chances of receiving a scholarship. Turned out not to be the case. Again, IMHO, trying to calculate the gambling odds (perhaps a better phrase than the term "gaming") is not helpful at the end of the day. At least that was my experience.
For AFROTC, school selection is not as important as major. I recall that one of the AFROTC PMSs urged my DS to select a major that would enhance his chances of obtaining a scholarship. DS ultimately declined to do that and received the AFROTC scholarship offer anyway. If DS had followed the PMS's advice, however, and chose to go AFROTC, then he would be stuck in a major that wasn't his choice and his grades would have likely suffered as a result of lack of interest (which could easily cause him to LOSE the scholarship if grades weren't up to par).
The only thing that I really think AROTC and NROTC really, Really, REALLY actually do try to do is accommodate and respect the applicant's requested choices, because they know that if they offer a scholarship to the applicant's, say, seventh choice of school, the odds of recruiting the student for AROTC instead of AFROTC (or no ROTC) diminishes accordingly. As you may recall, last year (and I suspect it happens every year), some applicants did not place a lot of thought into their school choices and ended up receiving scholarships to colleges
to which they never applied.
Whether a student receives an ROTC scholarship depends on the OML. Now, if someone can positively tell me that school choice has either an upward or downward effect on the applicant's OML ranking (which I understand that it does NOT), then I may reconsider what I have just posted. My understanding is that the decision to award a scholarship comes first, then CC decides to figure out which school to apply that scholarship (likely going for the cheapest one, although in my DS's experience last year, Cadet Command selected the MOST expensive school on his list, and it wasn't even his No. 1 choice!). For the life of me, I can't figure out why CC would have offered an AROTC scholarship to a school with a higher price tag, when that was not the school that DS had requested. And THAT goes to my point about the fruitlessness of trying to figure this out.
In short, I suspect that we polled 100 different SAF members on the best strategies for school selection, we would receive 100 different answers. And that's my point.