☄ alt2005 reveals the math behind roulette and answers questions

DLK wrote: I suggest going from the general to the specific. For simplicity, you can start looking for patterns at the level of dozens: 1-2-3. Then move on to sixlines, streets, splits, arbitrary blocks of numbers and specifically to single numbers.

It's easier for me to work with numbers. On odds, sixlines, etc., zero is deliberately not taken into account, which already distorts the overall picture. And guessing the numbers is more difficult. And I count on maximum difficulty. But the winnings are also maximum.

DLK wrote: The concept of "number repeat" is a special case.
I propose to move on to the more general case of "any guessed number".

In theory, all alt2005 calculations are also applicable to any guessed number. In its sample, alt2005 started counting between pairs of identical numbers, and in the general case, counting can be started from the moment the forecast is formed.

Mathematics tells us that we can guess any number from 0-37 with absolutely equal chances of success, because the numbers that came up in the past do not affect the numbers that came up in the future.

But experience, the son of difficult mistakes, tells us that a lot depends on the ability to GUESS numbers. It is very stupid to take numbers out of thin air. There are models that allow you to "be in trend", "catch collisions", "ignore the cold", "take into account adaptive responses", etc., which allows you to increase your efficiency.

If "17" hasn't appeared in the last 50 spins, what's the point of betting on it?

I would like to understand the factors and markers that, despite dry mathematics, will allow us to be harmonious in understanding the generation of spins.

I won't take on guessing the numbers. How will you guess them?
But the rest is true. In general, we should not care about the specific number, they are all equivalent. The number is just a sticker on the wheel, it does not carry any physical meaning. But the distances between the repetitions of these stickers are already subject to probability laws. For convenience, it is easier to take the distances between the same numbers. That is why I say "repetitions".

And here's another thing. About the lack of influence of the past. Yes, the numbers themselves do not influence the future. But let's take the so-called temperatures. Everyone knows that there are cold numbers and hot numbers. At one time, I formalized these concepts. The temperature of a number is the number of different numbers between adjacent occurrences of this number. For example, 0, 2,15, 15, 3, 4 3, 0. The last bold 0 has a temperature of 4, because that is how many different numbers fell between the last zero and its previous occurrence. What's interesting is that the temperatures have exactly the same range 0...36. If you take their falling temperatures instead of numbers, you won't see any differences in the statistics. But the nature of numbers and temperatures is different. If we change some numbers in the past, the future numbers will remain the same, but the temperatures will change. Another question is whether this can be used...

I'm looking. In order to get around, you need to find a section where the distances between the numbers (not necessarily adjacent) cluster around some value. It doesn't matter what, as long as it's some kind of constant. If mathematically, then starting from some point it should be like this: the next 25 distances should occupy more than 50% of all the remaining distances. Otherwise, we get a standard geometric distribution, and that's a drain.
Once again. For example, we start betting from spin 100 from the previous number drop, we look for the next drop of this number starting from this spin. If the distances 101...125 are significantly more than half the distances 126...infinity, then this is a plus.

I am definitely not ready for such a definition of probabilities.
"the number of distances before the event is repeated, which is half the total number of all distances"
How to calculate the probability that 5-5-10 will come up on the roulette wheel right now?
In the classics it's just (1/37)^3

I can use Google for Monty Hall and I've read all the explanations. But in fact we have 3 doors, only one has a prize.

FACT
We guess a door (the probability is 1/3 that we guessed it right away), when the host opens one empty door, nothing happens, except that we see that now there are only 2 options left and the probability of guessing is 50/50 = 1/2.

All these stories are about how MENTALLY we imagine that we immediately chose 1 door (car 1/3) and there are 2 other doors left (the probability that the car is there is 2/3) and one of them (empty) was opened for us by the leader, so we go to that group and choose the "second" door, as if exchanging our 1/3 for a probability of 2/3. Such nonsense!

Why not IMAGINE that we immediately chose 2 doors? One of ours and the other empty one that the host opened? It turns out that we were immediately in 2/3 and nothing needs to be changed.

If you remove the fantasies that can be twisted as you like, there remains a FACT and the Monty Hall paradox seems to be a hoax and a manipulation of facts. The fact that DLK wrote statistics of those who remained on their opinion and changed their choice can be either a short-term bias in the results, or the host persistently suggested changing the choice when the person pointed to an empty door (host-benefactor).

klick wrote: I am definitely not ready for such a definition of probabilities.
"the number of distances before the event is repeated, which is half the total number of all distances"
How to calculate the probability that 5-5-10 will come up on the roulette wheel right now?
In the classics it's just (1/37)^3

Well, did the classics help you much? From them you learn what everyone already knows - the probability is 1/37, MO = -2.7. That is, the probability for one spin with a random bet. Does this suit you? I don't. A non-standard problem must be solved in a non-standard way, the classics will not help. On the contrary, it denies the very possibility of a solution. Therefore, I created a new definition, first of all for myself. To justify the meaning of searching for this solution.
And readiness or unreadiness is a personal matter for everyone.

FACT
We guess a door (1/3 probability that you guessed it right away), when the host opens one empty door nothing happens, except that we see that now there are only 2 options left and the probability of guessing is 50/50 = 1/2.

It's like - nothing happens if he shows you an empty door, after which you only have two doors left? Or for you the probability of 1/2 ((at least) is equal to 1/3?
The FACT is that you simply didn't understand the explanation. Just say so.

All these stories are about how MENTALLY we imagine that we immediately chose 1 door (car 1/3) and there are 2 other doors left (the probability that the car is there is 2/3) and one of them (empty) was opened for us by the leader, so we go to that group and choose the "second" door, as if exchanging our 1/3 for a probability of 2/3. Such nonsense!
Why not IMAGINE that we immediately chose 2 doors? One of ours and the other empty one that the host opened? It turns out that we were immediately in 2/3 and nothing needs to be changed.

What mentally. You are shown an empty door in reality, not mentally. And no one changes anything, no need to talk nonsense. If you initially chose the door change strategy, no change actually happens. You simply tell the presenter: show me what door I need to change to. And there is no need to "imagine" anything here and complicate simple things.

If you remove the fantasies that can be twisted as you like, there remains a FACT and the Monty Hall paradox seems to be a hoax and a manipulation of facts. The fact that DLK wrote statistics of those who remained on their opinion and changed their choice may be either a short-term bias in the results, or the host persistently suggested changing the choice when the person pointed to the empty door (host-benefactor).

It seems, it doesn't seem... there is no such concept in the theory of faith. But there is understanding and not understanding.
In short. Here is a file illustrating the Monty Hall paradox. I did not make macros there on purpose. Everything is extremely simple.
At the top in cells A1, B1, C1 the values are 0, 0, 1. 0 is empty, 1 is a car.
Column A - initial door selection (1...3) You can insert the formula RANDBETWEEN(1;3) there, starting from the 3rd row and further down. Right now there are just random values from 1 to 3.
Column C contains the number of the empty door that the presenter will open. It is clear that
Everything is in line with the theory. If you change the door, you win in 2/3 of cases, if not - only in 1/3 of cases.
If you want, you'll figure it out.

Here is the same file, but in xls format (Excel 2003), in case anyone doesn't have Excel 2016

P.S. I accidentally duplicated the previous message. I don't know how to delete it.