^That is, unless you're racing in the Formula GT Championship. If anyone wants to give the following a try here ya go, worked for me as I expected...(if you have the NTSC version, this MIGHT work for you, or not, if I'm wrong in my beliefs. But it's worth a shot if you're anxious to get an F1).
I read on a site somewhere that if you use a Lancer Evolution in the Super Speedway enduro, you'll win the F090/S. Sure enough, I took my Evo VI (T.M.E.) to that race and won the F090/S in black/orange. With this F1, I did all of the other enduros and never won a single F1 (perhaps you're more likely to win one if you don't annihilate the competition, like I did with the F1).
Just yesterday, I gave the Roadster Endurance a go. I came up with the idea that if I used a slower car (technically, a car with a lower P/W ratio), that I'd have a good chance of winning the F688/S). I bought a Miata MX-5 (for 17,000 cr. ; there's 2 plain ol' MX-5s), and gave it an oil change and some T1 tires (front and back). So I entered the race and was behind the leading LS by like 6 - 8 sec. after the end of the 2nd lap I think (keep in mind my disadvantage in HP, and T1 tires, and most importantly, lighter weight - the combo of lightweight/low HP will keep you out of the pit lane for awhile. Anyways...), but he pits in every 3rd lap; the 2nd best car (the Miata 1.8 RS) pits every 9th lap. I worked my pit strategy in such a way that I pit in 6 times fewer than the LS, and 2 times less than the 1.8 RS and at the same time as them: I pitted every 18th lap. My tires would barely get orange (I never went-off course, but did go over the rumble strips often). Anyways, with that car/pit strategy, I won the race by less than 10 seconds. And, like I thought (being at a disadvantage in p/w ratio, but pitting less) would increase the chances of winning an F1. Think about it...it's like GT4 in a way...the more difficult the race, the more points it's worth. And in GT3, the harder it is for you to win (and you do win) the better your reward. And indeed, I got the F688/S. I have the NTSC version, so this set-up might not work if your playing another...or maybe I'm all wrong in my beliefs here. But the bottomline is, use a car that is fair, or hard to win with, if you want an F1. This seems to make even more sense, when I recall the first time I did this race with a Miata LS (the best or fastest, one you could possibly use in this event) and got the least desirable prize car, the MX-5 Miata in that special color.