Each spin of the wheel is independent of the previous one and in a spin each number is equally likely to be called. Therefore it is impossible to devise a strategy guaranteed to win. Despite this many strategies have been devised over the years. Their advantages and drawbacks are discussed below.
Doubling Strategy
The player plays on any one of the even money bets (say on red) and doubles his bet after every loss. A red number will sometime be called and then the player will recover his previous losses and win a profit equal to his original bet. This strategy sounds very good but has serious drawbacks. If a player starts with a small amount say $10, he will win $10 at the end of doubling sequence. If the player loses 6 consecutive times his total outlay at would have been $630 and he will need $640 for the next bet. If the player wants to win something substantial he has to start with a high initial bet and play with a huge bankroll. Mathematically he stands to win as much as he can expect to by placing the same bet each time, so this does appear to be an exercise in futility.
The Martinez Strategy
This is not a strategy to win. Martinez called it the 'dopey experiment' and said it provided a lot of fun. The player divides his bankroll into 35 parts and bets on a particular number for 35 turns. If the selected number wins on any spin then he wins an amount equal to his bankroll, and can treat the unplayed money as free. For example he starts with $35 and plays $1 on the number 3. The number 3 is called in the fifth turn he will win $35, and having wagered only $5, he will have $30 as 'free' money. If the player is lucky, his number will be called early on and he will have more free money. In the worst case his number will not be called at all and he will lose his bankroll.
The First and Third Column Strategy
This strategy was born from the observation that the red and black numbers are not uniformly spread over the columns. The middle column has only four red numbers. Hence by betting $1 the first and third columns and $1 on black the player covers all but four numbers. His payouts are as follows. For a red number in the first and third columns he quits, for a red number in the middle column he loses $3, for a black number in the middle column he loses $1 and for a black number in the first and third columns he wins $2.