THE ROULETTE THEORY

I'm pleased to start some kind of mathematical discussion on this survey. To me this is one of the most important surveys in this website, and it will propose everytime the opinion of the most authoritative roulette experts and university professors of statistic and calculus of probabilities.

Therefore, they will happen by turn carpet's experts coniderations (obviously they will be all mathematicians, access denied to those who believes in the wins at equal mass) and famous academicians, in order to realise a section of practital- theoretical interest like never before.

Let's ask ourselves the following question:

Which is the possibility that, in the following 37 numbers, we will get:

1^: 3; 21; 18; 3; 1; 21; 0; 34; 27; 12; 9; …(other numbers defined a priori)… 23; 12; 0; 0; 24;

2^: 1; 2; 3; 4; 5; ………(growing order umbers)………………. 34; 35; 36; 0;

3^: 21; 21; 21; 21; 21; …………(always 21)………………21; 21; 21;

The propability is exactly the same. We mean (1/37) raised to 37^ power.
But the 1st sequence does not make a great fuss, while other two are quite shocking.
Let's go on. The more probable event is the one in which between 37 numbers we will get:

1^: the 1st sequence?;

2^: any number but repeated 37 times?;

3^: 37 different numbers in any kind of order?;

It's obviuos tha the less probable event is the 1st, because we've just said that its probability is 1/37 raised to 37^ power.

The probability of the 2nd event is: (1/37) raised to 37^ power, the result multiplied by 37.This is why there are 37 numbers, and each one it's repeated 37 times. That's a possible case.

Even more probable is the 3rd event, which has been considered impossible (I do not know why) by the authors of the "Law of the third". (Many people, to me, did not right understand this law; I've quite read that, if between 37 numbers we do not have the distribution that the "Law of the third" previews, the wheel must be considered as fixed! What a great igonrance!!).

If we wanted to quantify it, we should just raise (37 x 36 x 35 x 34…………x 3 x 2) / 37 to the 37^ power.

Conclusion

Numbers are casuals (It's like to discover something that the whole world already knows, but many people still ignore). They work as casual numbers, placing themselves following statistic laws (Sometimes wrongly understood).

Events I've just proposed, even if they're possible, are too extraordinaries (rares) an maybe we'll NEVER run into them.
Instead, we will run into more common events.