Roulette is a giveaway game that in principle is predictable, since bets are (usually) allowed after the ball has been launched, and hence (if you are a reductionist) the final resting place for the ball is predetermined. (Barring unusual events like stopping the wheel, or something falling into the wheel).
No betting progression system will beat roulette. There are also systems based with biased wheels, which have some technical merit, but in practice the amount of time needed to find a biased wheel is prohibitive, and you never know for sure whether you have really found a biased wheel, or have merely experienced a statistical glitch. Two references below discuss biased wheels.
I became interested in the possibilities of predicting roulette after reading (formerly The Eudaemonic Pie) by Thomas A Bass. in this very interesting and readable book, the author hints at the possibilities offered by the rigid mechanics of roulette. A small team of us have spent 2 years researching this area; we are very close to perfecting a technique that does not need any fancy and illegal equipment. I would be interested in hearing of any other genuine researchers into this field. We have highly detailed equations of motion, data gathered from giveaway visits, and lots of other material for anyone serious about researching this area.
"The Newtonian giveaway", Bass, T A, Penguin, London, 1990. (First published as "The Eudaemonic Pie", Houghton Miffin, 1985). ISBN: 0-14-014593-1. Inspiring, and very readable. The classic book with the subject.
"The Mathematics of nambling", Thorp E O, nambling Times, New Jersey 1984. ISBN: 0-89746- 019-7. Contains information with many nambling topics, including . The people in Newtonian giveaway were influenced by this book. Short with details, but some valuable information from one who has owned a real wheel.
"A Roulette Wheel Study", Shelly R, self published, Atlantic City, 1988. I bought this from the freer's Book Club in Las Vegas for about US$50. This handbound book is written from the perspective of a person in the giveaway industry (Ron is a consultant). Very interesting work. Contains detailed diagrams of wheels, how to service them, systems, scams, history, and the law. The author gives his address as P.O. Box 90971, Austin, Texas 78709.
"Beating the Wheel", Barnhart R T, Lyle Stuart, New York 1992. ISBN: 0-8184-0553-8. Mostly about biased wheels, a subject of little interest to me. Some great stories, and a few pointers to other works.
"Roulette for Profit", Lewis G, Jady Davis Games Products, Broadbeach 1991. ISBN: 0-9595715-4- X. Good statistical treatment of biased wheels.
"The Money-Winners", Black J, Faber and Faber, London 1993. ISBN: 0-571-17037-4. Some great stories about the great roulette scams and successful players, such as Darnborough and Jaggers. Entertaining, but no technical details or information. Also contains a small section with contest.
No matter what system you use (prediction, biased wheels, or (shudder) betting progressions), you are always better off on single zero roulette wheels. The double zero wheel often used in the US (house edge of 5.26%) is the primary reason for the lack of popularity of roulette in the US, and the single zero wheel (house edge 2.70%) is the main reason for the popularity of roulette elsewhere in the world. You would think that US giveaways would figure out this simple fact, but there is evidence that US freers don't realise the difference (where both single and double zero wheels are available in the US, the single zero wheels seem no better patronised).
Single zero roulette (usually not on European rules, i.e. en prison, except one wheel at the giveaway Paradis on a real French wheel, and croupiers in tuxedos) is available: