The game runs at NTSC rates, which we'll round up to 60Hz. We'll also say that 6s of inputs need to be considered, and scores which are above 6s will be discarded. We'll finally say that the possible input states consist of the joystick in either left ("shifting") or neutral ("popping") position, and the gas button either up or down. This generates four possible input states.
The number of possible input states in total will be 60 * 6 = 360, and so the total input space is 4 * * 360 = 2 * * 720, which is a little big for brute-force exploration. Many of these states suck; after all, the total number of shifts is not ~300, but ~5. So a guided search is likelier to pay off.
Edit: Thanks HN for eating asterisks and having no math mode.
There's brute force and then there's brute force. You know that the joystick inputs have to be applied in a certain order, and you basically want the throttle on unless you're above a certain RPM, so the search space is more like 60^4 with a couple of parameters, which is plenty tractable.
