In the next section, I will present to you the most common strategies and their results on 10,000 simulated rounds of roulette (or as many rounds as it takes for the player to lose all of their chips). All strategies were tested with the same starting deposit of $1000 and a starting bet of $1. To further objectify the results, we ran simulations of five players for each strategy. Each player's financial progress is plotted in graphs.
Author's note: The simulations were run using the standard random number generator provided by the Java programming language. Some fraudulent sites claim that their strategies are based on long-term monitoring of random number generators, in particular those used by casinos. When it comes to roulette, the random number generator is, of course, the roulette itself. Manufacturers of real roulettes test their products with hundreds of thousands of spins to test the probabilities of getting individual numbers. The odds of flawed roulette wheels making it into a real casino are therefore quite slim. With video roulettes, rendered by a computer system, the random number comes is either very similar to that used in our test, or more probably from special hardware which generates numbers from electrical noise. As a software developer for online casinos I can safely say that the chance of predicting the result of these random number generators is zero.
Martingale is the most well-known roulette strategy. It is based on player betting one chip on a chosen colour, even/odd numbers, or low/high numbers. If he loses, he doubles his bet on the same colour. This is repeated until he wins. Subsequently, he will again start betting with one chip. This strategy is justified by the belief that the chosen colour, given enough play, will inevitably appear.
From a theoretical perspective, this reasoning is sound: in an infinite number of plays, the probability of a certain colour not appearing approaches zero. In practise, no one has the funds to continually double their bet. Even if this were the case, casinos impose a maximum bet as discussed before. All that remains of the ideal mathematical model is a huge bet, a very small probability of losing, and a win amount that is proportionally smaller.
In this simulation, all players started with a budget of $1,000 and a first bet of $1. Let's see how they did.
(Simulations of Martingale strategy)
Each of the players lost all their chips within 10,000 rounds. If each player were able to recognize the optimal time to walk away with this strategy, he could have left the casino with a net profit. In fact, this is the danger of the strategy. Initially, the player has the feeling that he is winning, that the strategy is invincible, and the winnings can continue forever. Of course, the opposite is true.
By playing the strategy in the long term, you inevitably lose more than you managed to win beforehand, if for some reason you don't stop playing at the appropriate time. Additionally, there is no guarantee that you won't lose the whole budget in the first round of bets (even though the probability of this happening is quite small).