Like all betting strategies, in the long run the math is against you. This way of playing (aka "Martingale") will be successful only in the short term. Yes, you will see it work say, 9 times out of 10, but the winnings from your 9 successful session will not cover your losings from the 1 losing session you are bound to come across sooner or later. Casinos always have the edge on your money rather than the other way around. Statistically, this is like selling a lottery ticket. You have a large chance of a small win (the selling price of a losing ticket), but a small chance of a big loss (owing the holder of a winning ticket).
Due to the addition of an extra zero in American Roulette, the house edge is increased to an unfavorable 5.26% compared to its European counterpart. European Roulette has halved house edge due to its use of a single zero, making it 2.7%. If you’re a fan of American Roulette, by all means take a spin; but it’s good especially as a beginner to keep in mind that the house has a greater advantage of taking your money.
On an American wheel, there are 38 spots: numbers 1-36, plus 0 and 00.  Your odds of winning a one-number bet are 37 to 1 (37 ways to lose, 1 way to win).  But if you win, the casino doesn't pay you 37 to 1, they pay you less: 35 to 1.  The difference between the true odds and what they actually pay you is 2/38, or 5.26%.  You can do this same calculation for the other bets, and it comes out the same.