> Yes, the analysis proves 5.51 is impossible, and it's been confirmed that 5.57 is the best possible time through the use of an emulator with preprogrammed inputs, meaning that it plays the game perfectly.

An emulator with preprogrammed inputs doesn't mean it plays perfectly. It just means that it plays reproducibly. Whether or not it plays perfectly depends on the preprogrammed inputs.

How did they choose the inputs?

Looking at the game manual, it comes down to deciding when to shift, and deciding how to use the gas pedal.

Shifting looks like it is easy to deal with in emulated testing. You have neutral, 1, 2, 3, and 4. You start in neutral. So, an optimal run will start with you shifting once at t=0. You cannot down shift, so your only choice when shifting is up, and once you reach 4 you can no longer shift.

From another comment, it seems the game works in ticks of 3/100th second. That means that for a 6 second race, there are around 1.3 million possible shifting timings, assuming that you cannot skip gears.

For using the gas pedal, it looks like if you are not red lined, there are no circumstances where it would be better to not give it the gas. When red lined but at a time when your shifting plan calls for staying in the current gear, I can't tell from the manual what you should do. It says if you go past that you risk blowing the engine. What it doesn't say is if you get more power when going past the red line, so that it may be worth it.

Assuming that red line is max power, then when at red line but not shifting optimum would be to modulated the gas so as to keep it right at the red line.

For each shift pattern, it should be relatively easy to figure out when the gas has to switch between steady and modulated. Putting it all together that would give 1.3 million candidate inputs, one of which should be optimum.

If going past the red line does give more speed (at increased risk of engine blow out), it is more difficult. If engine blow out is probabilistic, you have to worry about the possibility that someone could get insanely lucky.

At that point, you probably need to analyze how the random number generator works, and how it is used, and how user inputs affect it. One particularly worrisome possibility would be that the timing of user input affects it. For example, if whenever the user presses or releases the gas it uses a random number to pick from several sounds associated with that action, that could be bad news. It would mean that the earlier analysis that the gas would optimally in each gear start out as constant and then switch modulated at the red line is no longer applicable. It could be that there is a run where if someone releases briefly the gas during the "constant" phase, that happens to get the random number generator to a position where they will get very lucky on the engine blow out rolls later.

If that meant we had to try every possible gas pattern, instead of just "constant followed by modulated", we'd have a combinatorial explosion.

Probably the best to do in this case (the "past the red line gives more speed, and the random number generator has a lot of user provided entropy" case) would be to tweak the emulator so that the engine cannot blow out, change the gas pedal input to simply be full gas all the time, and see what the results are. That would at least give us a lower bound on what the luckiest person in the universe could conceivably achieve.