The player’s fallacy is a topic that has been debated since Ancient Greece, in the days of Aristotle. It is based on the idea that on the one hand, no matter how long you make an event not happen, we will not be closer to this event happening again, or seen from the other side, even if a fact has just happened, it does not mean that don’t repeat again soon.
There is still a belief among many players that they analyze the latest roulette balls and find that some number has not dropped for a long time; they go crazy betting on those numbers. For example, if double zero has not fallen in a long time, it does not mean that it will fall soon.
In the long run, an American roulette wheel that is not tricked will tend to have all numbers having the same chance of falling. That is 1/38 (since there are 36 numbers from 1 to 36, in addition to 0 and 00).
That all the numbers have the same probability of falling does not mean that see the last results, some numbers have more probabilities of falling in the following balls because this probability is fulfilled when we have infinity and this must be taken into account if we want to understand how to win at the casino.
Let’s give an example to better understand the gambler’s fallacy.
We note the result of the last 100 balls and note that most numbers have dropped three times, but there are some numbers that have dropped two times or four times. And we also observe that there is some number that has fallen only one time and 31 that has fallen five times. While the number 17 has not fallen in all that last streak of 100 balls.
The player’s fallacy tells us that as much as we bet on 17, that number will not come out sooner. In the same way, although 35 is falling more than the other numbers, it is not going to stop falling either.
Therefore, let’s not be fooled by the player’s fallacy because each ball is a world of its own, and it doesn’t matter what has happened before in that roulette.
There are some manuals that show strategies that do recognize the player’s fallacy as correct, so be very careful, because we should reject these strategies that will not work for us in American roulette.
On the Law of Large Numbers
The Law of Large Numbers was developed by numerous mathematicians, among which we highlight Bernouilli and Poisson. This law says that the expected value of a random variable is equivalent to the long-term average when doing repetitive sampling, and it was used to understand the issue of predicting roulette and analyzing its best strategic forms from a theoretical point of view.
For simple luck, in American roulette, we will be talking about 16/38 for any of these simple luck: red, black, even, odd, miss, and check.