Not Really True
My observations have been made in neutral play counts; and as I have said, a very small sample, so I am not drawing conclusions. When Aces highly outnumber the 3s, my bet is the minimum, so it does not really matter what happens. When 3s highly outnumber the Aces, I tend to get an Ace more often on large bets. What I am saying does make sense, and zero information is not accurate. Whether or not I can turn this into something useful is another question. This play may not be a good example, since the increased likelihood of getting an Ace is balanced by the decreased likelihood of getting a 3. Obviously, I have noticed that I am doing poorly because of the large bets, due to the probability of excess aces before the deal. The corollary question was whether it would be better to not double an 11 in these situations. Even though you may have impliedly answered the question, it is still better to double and receive a 3 because it takes that card out of play.
The double 11 play was just the example that made me think of the question. The question is can this betting side count be used, on ANY play, to adjust the play count? I do not side count cards separately, like most players do. I would appreciate any info.