This is the Martingale system, it will 100% work if you have infinite money and can bet infinite amounts.

To make things worse, Vegas now have triple 0 roulette tables. Three zeros in a row. In the same place. Do not play Roulette if you want to win. The only bet in a casino isn’t to the casinos favor is on Craps and it’s called ODDS. But to get to able to play it you have to win against 1.41% house edge first. And it is capped about 10x or 5x of original bet.

If you want to have the best odds against a casino that is hard work and not solid strategy. Counting cards can make money but honestly the amount of work it requires - you are better on the stock market or even in crypto.

Do not gamble against the casino.

The only reason to gambe is to have fun and safe risk with money you decided to spend and to never see again.

Another way of thinking about it is betting your entire bankroll for 99.9…% certainty that you will win $1.

Say you go into the casino with $1000.

Bet:

$1 lose.
$3 lose.
$9 lose.
$27 lose.
$81 lose.
$243 lose.
$729 oh wait you can't bet that much, you only have $457 left. Dang, do you bet $457 or find another $272? 

Bet $457 and you win $914! Congrats you're now only down $86!
Or maybe you lost and are down $1000.

Or maybe you scrounged up $272 so you could keep playing
Bet 729 and lose. Now you're down $1272.
Or
Bet 729 and you win 1458. Pay back the $272 you borrowed from your buddy, you're still up $186. 
You just bet $729 dollars for a %50 chance of winning $186.

But what are the chances of getting 6 or 7 losses in a row? 1 in 64, or 128 respectively, actually worse because roulette wheels aren’t 50/50, they’re 18/19 (18 wins and 19 losses in 37 plays on average) or worse. So losing 6 times in a row will happen 1 in 54 plays, 7 losses is 1 in 106.

Google says roulette wheels spin 55 times per hour so with your strategy you will lose your bank roll in about one hour assuming your starting bet is 0.1% of your bank roll.

So help me out here, what am I missing?

You’re forgetting that not all outcomes are equal. You’re just comparing the probability of winning vs the probability of losing. But when you lose you lose much bigger. If you calculate the expected outcome you will find that it is negative by design. Intuitively, that means that if you do this strategy, the one time you will lose will cost you more than the money you made all the other times where you won.

I’ll give you a short example so that we can calculate the probabilities relatively easily. We make the following assumptions:

• You have $13, which means you can only make 3 bets: $1, $3, $9
• The roulette has a single 0. This is the best case scenario. So there are 37 numbers and only 18 of them are red This gives red a 18/37 to win. The zero is why the math always works out in the casino’s favor
• You will play until you win once or until you lose all your money.

So how do we calculate the expected outcome? These outcomes are mutually exclusive, so if we can define the (expected gain * probability) of each one, we can sum them together. So let’s see what the outcomes are:

• You win on the first bet. Gain: $1. Probability: 18/37.
• You win on the second bet. Gain: $2. Probability: 19/37 * 18/37 (lose once, then win once).
• You win on the third bet. Gain: $4. Probability: (19/37) ^ 2 * 18/37 (lose twice, then win once).
• You lose all three bets. Gain: -$13. Probability: (19/37) ^ 3 (lose three times).

So the expected outcome for you is:

$1 * (18/37) + 2 * (19/37 * 18/37) + … = -$0.1328…

So you lose a bit more than $0.13 on average. Notice how the probabilities of winning $1 or $2 are much higher than the probability of losing $13, but the amount you lose is much bigger.

Others have mentioned betting limits as a reason you can’t do this. That’s wrong. There is no winning strategy. The casino always wins given enough bets. Betting limits just keep the short-term losses under control, making the business more predictable.