Don't 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 outcome of the first spin is red', and B as the event 'the outcome of the second spin is red'
What the authors calculate is the the probability that events A and B occur, which is wrong.
What the authors should calculate is the the probaility that the event B occurs, knowing that event A has occured.
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 fundation 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).
