Do not Trust Roulette Systems and Save Your Money

Who never heard about "Easy money with our roulette system", "ultimate roulette system" and other fancy names like "the d'Alembert martingale", etc ...?

With this article I would like to warn you: if you use these systems, you will loose your money most of the time! And apart this "most of the time" time frame, you can win, but it's just pure luck!

Take a few minutes of your precious time to read this article!

So, you want to make some money playing roulette? And as most beginners do, you "google" the net with words like roulette, systems, martingale, money, win, etc ..

And you realize that winning systems exist! Good for you (?) !!

So you decide to take a close look at one of these winning systems. Well, the author claims it's a "winning" one. His explanation makes use of probability theory, and gives a few examples linking the reality (= the stuff you understand) and the (probability) theory (= the fuzzy stuff).

So, the author's first goal is reached: YOU UNDERSTAND what he's talking about. Seems like a clever guy. Let's trust him!

I am not going to review all roulette systems (is a life enough?). My goal is to use a very basic roulette system, ans show you that it is based on STUPID STATEMENTS.

So consider the MOST DANGEROUS ROULETTE STRATEGY: the Martingale System.

Easy to use and to understand: you bet only on red or black. Start to bet $ 1 on red. The wheel is spinning, and a black number is drawn.

Never mind. You lost $ 1. If you bet $ 1 again on red, and if red is drawn, you win $ 2, but your net profit is 0.
Instead of betting $ 1, bet $ 2. Your total bet since you started to play is $ 3. If the red is drawn, you win 2 x $ 2 - $ 3 = $ 1!

If you lose (= black is drawn), you lose $ 3. Now bet $ 4, and so one ...

The idea is to bet twice the amount of the previous bet. If you win, your total net profit is $ 1.

WHY IS THIS SYSTEM DANGEROUS? BECAUSE OF WRONG PROBABLITY CALCULATIONS!

Well, suppose that the black color is drawn 6 times in a row. Your 7th bet amount will be equal to 1 + 2 + 4 + 8 + 16 + 32 = $ 63.

And how much did you win? $ 1 for a $ 63 bet. And I hear you say "ok it may take some time, but the probability of winning is 100% So it's worth it!"

As you have noticed, the amount to bet at every spin grows exponentially. After n spins, the amount of all your bets is equal to 1 + 2 + 4 + ... + 2 ^ n = 2 ^ (n + 1) -1.

After 9 spins, the amount of all your bets is equal to $ 1,023.
After 10 spins, the amount of all your bets is equal to $ 2,047.
After 11 spins, the amount of all your bets is equal to $ 4,095.

But what is the probability that the same color is drawn ten times in a row? And here comes my favorite: "almost 0"!
WRONG !!!!!!!

The question is now: the red color has a probability of 18/37 to be drawn. What is the probability that the red color is drawn twice in a row? The wrong answer is (18/37) * (18/37), which gives 23.67%.

If you trust this "logic", then the probability that the red color is drawn ten times in a row would be equal to 0.07%.

THESE CACULATIONS ARE WRONG !!!
Define A as the event 'the output of the first spin is red', and B as the event 'the output of the second spin is red'
What the authors calculate is the probability that events A and B incidence, which is wrong.

What the authors should calculate is the probability that the event B occurs, knowing that event A has occurred.
Since A and B are independent events, this probability Pr (B | A) equals Pr (B) = 18/37 = 49%.

You can extend this result to '10 times the red color': the probability that the same color is drawn 10 times in a row is equal to 49%.

Imagine the money you could loose just to win $ 1 !!!!!

This miscalculation is the foundation of some roulette systems, based on similar strategies like "wait until the same color is drawn 4 times in a row, and then bet on the opposite color". This is based on a so-called "natural feeling" that the same color will rarely be drawn more that 4 times in a row! Whoever makes such a claim has never played roulette more than a minute.

There are at least two mathematical properties related to the Roulette game that you can trust, an use to develop a winning roulette system (if any exists):

- the law of Large Numbers: for a very large amount of spins, the red color will be drawn as many times as the black color.

- the law of the third: after 37 spins, only about 24 numbers will be drawn (and about 13 numbers will not).

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Source by Patrick R. Meyer