Martingale Roulette Strategy: Full Outcome Analysis with Charts

 Martingale Roulette Strategy - Full Outcome Analysis with charts

Can the Martingale Strategy be used for Roulette? That depends on your definition of work. Which one will you win? How much? When? How much? How much? When? I asked myself these questions and wrote a little Python code to help me find the answers using Monte Carlo Simulation.

Martingale systems have a high win rate in the short term but a strong chance of losing all your money over the long term. The table maximum not only reduces the chance of total loss but also increases the odds of winning overall.

So how did I figure this all out? How does one find these statements in the first instance? I'll tell you all about it below. I'll also show you a few cool charts and detail overview tables to help you understand how the Martingale System works in Roulette.

You should read my simulation disclaimerOpens new tab..

What is the Martingale Strategy exactly?

The Martingale strategyOpens up a new window In general, the Martingale strategy refers to the following idea. When someone bets on a game outcome with nearly equal probabilities, one uses this betting systemOpens a new tab :

Start with a fixed amount, such as 10$, and bet that amount in your first round.

You can lose this round if you are unsuccessful. Now, if you've just lost 10 dollars, you can bet 20.

Double the amount if you lose the second round. As an example, let's say you lost 20$ and now you are betting 40$.

You win and the amount for the next round resets back to the base, which in this case is 10$.

This system is also known as a "progression".

Each win will give you back the entire amount you have lost from the base up to the winning amount. It doesn't sound convincing, does it?

The catch is that if you lose enough times in a row all your money will be gone quickly. Because of this, the betting amount goes up exponentially with each loss. This sounds complicated. You might find it a little confusing.

Probabilities for a Single Step in the Martingale System

Before I begin putting the puzzle together, there is an interesting piece to the Martingale puzzle. It's the probabilitiesOpens a new tab. for having subsequent losses over a number of rounds.

Let's say that there is a 50/50 chance of winning. While this may not be true for Roulette application, which we will discuss below, it is not crucial for our argument. Also, see below for my discussion about the house edgeOpens up in a new window. ).

Therefore, the chance of losing one bet or round is 50%.

p1=1/2

Because the rounds' outcomes are totally independent, multiplication is used to combine the probabilities of the subsequent rows. This is how we arrive at

p2=1/21/2=1/4=122

We can just generalize this for more than two rounds (because this formula is accurate)

pn=12n

As you play more rounds, it becomes less likely that you will lose all your money. However, the likelihood of a total loss from the beginning in the first progression (and in such a situation only) is never zero. You can lose all your money while using this system with a small but possible probability. Which time is it most likely? Let me show you. This was a lot theory.

Overview Table of Amounts, Simple Probabilities and a Martingale Doubling up Strategy

The table below shows the progression details for the double-up of wagers. These are equal to the potential win in each round and collective losses. There is also a possibility for a losing all-streak for several steps up. Start with 10 $.

So what does this all mean? It can be interpreted as a variety of things:

Once you win, the base amount you receive is equal to what you lost, in this example, 10 $. It is easy to see this by looking at the columns 2 and 3. Why?

Double your bet after a loss to make the odds of winning an even greater. But that doesn't account for all the other lower bets placed and lost before you finally win.

It all depends on how much you have to spend. You will quickly be able see how many steps this scheme can take you through. You can double your money if you have 1270$ to start, or step seven if you have 1270$.

If you lose enough consecutively from the beginning, it's game over.

It is less likely that you will lose a series of n consecutive times. But, we will be keeping an eye on the lower numbers of N, as we'll find that it is impossible to go up arbitrarily high in this progression in practice (and not because you have run out of money).

Example: Let's suppose 100 gamblers show-up with 150 $ each. This means they could move on to step 4 in their first progression. On average, 6 out 100 people can return home empty handed after four rounds.

Let's take another example. 1000 gamblers turn up with a staggering 10000$ each (plus some money, actually). This means that they could move up to step 10, if necessary. However, after 10 rounds, the average player will have lost all of his or her money.

The losses will outweigh any wins. We'll show you how much money one can win after how many rounds, and with what probability. It is obvious that you can lose your entire money in a matter of minutes. What amount could you win over the same number rounds in an ideal situation where you win every single time? The base amount divided by the number you have played.

That's 40 $ after four rounds or 100 $ after ten rounds in our example. This unlikely win can be offset by a loss of up to 1270 $ and 10230$, respectively.

This doesn't sound all that promising. Let's get in depth and learn more. the martingale system explained