Picture author: Conor Ogle, source: Wikipedia
So, if you start with $10 you will eventually win $10 and get your bets back. The strategy is flawed to begin with, but this one of the reasons casinos use zero and double zero in addition to capping the maximum bet. Given that you would have 50/50 chance and very large amount of money to use for betting, you would beat the casino every time. And that's not OK for casinos.
But let's assume for a while that there would be a casino with roulette which has no zeros and no cap for maximum bet. I.e. betting on black/red would really be a 50/50 chance. This would be then equal to coin tossing (head or tails), which is typically used as an example in many books on probability.
The biggest flaw in the martingale strategy even in case of 50/50 chance winning is that it requires very large amounts of money to get even a small win. Let's assume you want to win $10. The table below gives you the probability (p) of loosing "n" bets in a row. It also shows what bets you need to place using the strategy.
Even though it is very rare (1 in million) to see 20 heads (or 20 black) in a row, it is not impossible. In fact, in the roulette book, the writer said that he had witnessed a streak of over 20 of the same color. Assuming that you would win on the 20th bet, you would still need some 5,2 million dollars to claim your 10 dollar victory.
To make odds better, the writer introduced a "system of five". Meaning that you wait until there has been eg. five times black and then you start applying martingale using red. Unfortunately, this strategy does not increase you chances of winning at all. Even if you would wait until 10, 15 or 20 of the same, you chances would not increase.
You still would have chance of 50% in loosing the next bet and the table above does not change one bit from that point forward. I believe it is a very common error to think if you see someone get 10 times heads in coin tossing, the probabiliy of next heads is low. The probability of seeing 10 heads in the row is 9,77% (i.e. low), but in case that is already in the past then it won't matter. The next toss carries 50%/50% probability for tails/heads in the same way that every single toss does.
Similarly I believe that technical analysis does not give significant advantage, because what has happened in the past won't matter now or in the future. You might get lucky and it works for awhile, but eventually you will loose if that is the only strategy you have. Naturally, technical analysis can be used as a tool among others to determine what is going on in the market. I.e. understanding what has happened until now.
Basically the casinos and the online brokers have the same design. The more you play, the more you will loose to the "bank". Therefore, it is no wonder that many brokers and the like advocate technical analysis. The more trades there are the more money they will make. People implementing true buy and hold strategy are lousy customers for brokers.
Still, if you want to gamble with your money, it is much more wise to gamble in stock markets than to do so in a casino. Because your odds are much much better and you can limit your losses more easily.