There are few popular roulette strategies out there. Most of them are based on the idea of adjusting your stake as you keep playing so when you finally win, it will cover all your past loses and make some profit.
Most known is the Martingale strategy. You bet on red or black and double your bet after a loss. Sooner or later, you will win and make a profit equal to your initial bet. Makes sense, let’s see how it will look like if you decide to make it your full-time job. We will simulate a 1000s of games and see how much you can make.

Setup

At GitHub you will find a code for a roulette simulation I wrote and notebook for all strategies I will test in this post. You can easily adapt it and write your own strategy.
To define a strategy, we need three elements:
Initial bet - How we pick the very first bet. That is a selection and size of the bet.
Placing bets - How we pick follow-up bets.
Exit - When do we cash out

For “Exit”, we will always use double or nothing. If we start with X amount of cash, we will exit when either:

• we can’t afford next bet
• we have 2X or more of cash.

For cash, we will use the term “unit”. One unit is equal to the minimum bet.

All-in:

Initial bet - we can use any of the 1:1 selections, I will use red with 1 unit.

Placing bets - there will be just one bet so no need for anything fancy here.

We do 10 000 simulations.

A 4849 of out of 10 000 is within expectations for 48.65% chance.

Martingale Strategy:

Initial bet - we need to pick either red or black, or any other 50/50 selection. I will go with red and 1 unit.

Placing bets - we will always bet the same selection. After each loss we double the last stake, after each win, we go back to the initial stake, that is 1 unit.

Let’s see for 10 000 simulations how many times we doubled up and how many times we lost:

As you can see, we would win only in around 27% cases. Relatively low compared to 48.65% you have by just betting all-in on red or black. At least you can play a few more rounds.

Gustek strategy:

Here is the strategy I like to play when I go to a casino and play roulette.

In this strategy, we bet on an outright number.
We will double stake after every 17th round lost, that is:

Let’s simulate it:

This time we managed to double our money in 44% of plays. Still not better than all-in bet on red but there is another reason I like that strategy more. It allows for a longer play.
Compared to martingale, with 1024 min bets you can play for 102 rounds instead of just 10. Assuming 1 min per round in the worst-case scenario, you can enjoy play for over 1.5h instead of 10minutes. We are less likely to hit table limits as well.

Gamblers fallacy:

One common belief is that after you see long streak of red, black must come soon. Or that a cold number, one that has not been winning for a long time, must come soon and placing a bet on it is a good idea.
Let’s test it. I will adjust our strategies a bit:
For All-in, I will place a bet on red after ten not-red numbers win.
For Martingale I will start placing bets on red only after there were five black numbers or zeros in a row.
For Gustek strategy, I will take a cold number after 200 rounds.

All-In

Martingale

Gustek

If you heard about gambler’s fallacy before or know some math, the result should not surprise you. That is the crux of betting on independent events. It does not matter how you pick your bet selection and how many times you placed a bet; your chance of winning is always the same.

The winning strategy:

Don’t play. You may have heard it before. The casino always has the edge. Each time you make a profit in a casino, this is pure luck. Long term game with any strategy will result with your pockets empty and casinos happy.
If you plan to make money in a casino, you lost already. I find it enjoyable to gamble with small amounts and try my luck. It is not a sustainable way to make money unless you are the casino.