If you're wondering what a half A press is, read this before commenting to ask. I use a special notation that allows for half A presses. Specifically, if you enter a level already holding the A button, then that A press only counts as half. It's actually pretty important to distinguish between the A button being PRESSED and the A button being HELD. While pressing A allows Mario to execute several kinds of jumps, the holding of A allows Mario to swim in water, do little kicks up slopes, grab the owl, and twirl slowly. So if a star requires the A button to be held, the pressing of the A button could have been done at some point in the past, and just held until that moment. For instance, let's say there are two stars: one that requires the A button to be pressed (x1 A presses), and another that only requires the A button to be held (0.5 A presses). Individually, these stars would both require a full A press. But if these stars were collected one after the other, then the A button could be pressed during the former, and held all the way through to the next star to be used in the latter. In this manner, these stars together would only use 1 A press, whereas they would take 2 A presses if done individually. So during a 120 star run, you would round these half A presses down, but on a star-by-star basis you would round them up.