Could a series that had succeeded on every continent (except, of course, Antarctica) including North America -- in Canada -- make it this time in its most elusive, yet potentially most important, market? After races in locations as diverse as Detroit; Phoenix, Arizona; Long Beach, California; Watkins Glen, New York; Las Vegas and Indianapolis, among others, what can the new site, Austin, Texas, do to ward off the hex that seems to hover over the series in the United States since it was first run in the country in 1959?
For a start, it's a changed Formula 1 that arrived in 2012.
''The Formula 1 racing that we are bringing to Austin this time is not the same as that which ran at Indianapolis,'' said Timo Glock, a driver at the Marussia team, referring to the last stint for Grand Prix racing in the United States, from 2000 to 2007.
Thanks to new technical rules, Formula 1 races have been transformed in the past three seasons from the frequently predictable processions of the past to often wild melees with plenty of overtaking up and down the pack. An example was the Abu Dhabi Grand Prix on Nov. 4, when the championship leader, Sebastian Vettel of Red Bull, was able to weave his way up from last place at the start to third at the checkered flag.
To capture the American imagination, however, many ingredients must be present in -- or added to -- a series that differs greatly from the numerous local motor-sports offerings, such as Nascar, sprint car, drag and IndyCar racing.
A major problem is that most Formula 1 races in the United States are run either late at night or early in the morning because of the global audience, which means they attract only the most devoted U.S. fans.
Another issue is merchandising. Carlo Boutagy, a native of Canada who has lived in the Middle East and who runs the F1 FanZone, a park for fans outside the track at several races -- although it won't be present in Austin -- said the series must centrally develop its merchandising if it wants to be on a level with American sports.
In Formula 1, each team handles its own merchandise business. Generally there is little merchandise available for fans, and what there is tends to be costly, not very interesting and not easy to obtain. ''If you go into many homes in the United States where there are hockey fans, N.F.L. fans or baseball fans,'' Boutagy noted, ''you find rooms full of merchandise from the sports.''
Also, there is little done to entertain fans beyond the track action at a Formula One race. Any entertainment is provided by local promoters, such as variety acts performing on stages outside the grandstands and activities for children at the Bahrain race.
In fact, Formula One is not much of a family affair, unlike most American sports, as tickets for the race are usually much more expensive than those for other sporting events. In Austin, the tickets are among the series' cheapest: Three-day general admission is $159, but a seat in the grandstands costs $269 to $499.
Austin has several assets that could make it a permanent and successful home to the series in the United States. It is the first purpose-built track in the country for Formula 1. Previous sites were either temporary street circuits or pre-existing tracks for other events, such as the legendary Indianapolis Speedway.
''Indianapolis has its history and its big race, with the Indianapolis 500 and even the Nascar race,'' said Anne Bradshaw, a Briton who is running the media center in Austin, as she did for the first Grands Prix at Indianapolis.
She noted that Indianapolis did not need Formula One, while Austin's Circuit of the Americas was built for the occasion, as well as to benefit the local community and to be used for other events when not used for the Grand Prix.
The track itself at Indianapolis was a disappointment for Formula One. Only part of the oval was used for the race, the rest of the circuit being a flat and uninteresting inner portion of road circuit in the infield. The 20-corner, 3.4-mile, or 5.5-kilometer, track at Austin received excellent marks ahead of the first race this weekend, including a first corner on a steep hill that Bradshaw compares to the great ''corkscrew'' at the Laguna Seca circuit in California.
''I get a nose bleed just climbing up it,'' Bradshaw said.
Probably the best way to make the series a success in the United States is to have an American driver and even an American team. There have been only two American world champions -- Phil Hill in 1961 and Mario Andretti in 1978.
The last American driver, Scott Speed, raced in 2006 and 2007. In 2010, an attempt to start an American team called USF1, based in North Carolina, failed before the season began for lack of financing.
The Texas location could prove successful thanks to another kind of ''local'' team: The Sauber team team has sponsors from neighboring Mexico, including Telmex and Cuervo Tequila, and a Mexican driver, Sergio Pérez. Pérez has finished on the podium three times this year, and will move to the leading McLaren team next year.
''I think it is the closest race for eight years for me to my hometown of Guadalajara,'' Pérez said. ''I expect many Mexican Formula 1 fans to attend, and this, for sure, will give me an extra boost. Of course I also hope there will be a Mexican Grand Prix one day, because I am aware of the great enthusiasm for Formula 1 in my country, but for now I regard the race in Austin as my home Grand Prix.''
Most of the series' sponsors dream of success in the United States. Christian Horner, director of the Red Bull team, which is owned by the Austrian energy drink company that sells well in the U.S. market, and which is leading both the drivers' and constructors' championships this year, said this year it was the race for which his team had received the most interest from sponsors to attend.
Many seek to attend the elite Paddock Club, where the teams entertain clients, sponsors and wealthy fans.
Norbert Haug, the director of McLaren Mercedes Motorsport, said that the United States is the world's biggest market for Mercedes cars -- with 245,231 cars sold in 2011 and 215,596 sold through the end of September -- and that the company was looking at how to profit from the race on a marketing level.
In the end, perhaps Austin, the quirky capital of Texas, is just the place for the apparent mismatch between Formula 1 and America, given the city's motto: ''Keep Austin Weird.''