Noobingalltheway: In no way in any kind of average working can a score of 66 push an average of 71.5 UP
If it's a system that takes your best "X" scores, out of your last "Y" rounds (as in best 10 scores in your last 20 rounds), then a 66 can definitely make your average go up.
Example: using the "best 10 of your last 20 rounds" methodology, IF your very first round was say, a 60, and your current average is 71.5, then when you shoot a 66, the score of 60 will be replaced as one of your 10 best, since it's no longer one of your last 20 rounds. If it gets replaced by the 66 you just shot, then your average will go up by 0.6 to 72.1.
Anyone who maintains a golf handicap in real life should be only too well aware of this fact.