☄ alt2005 reveals the math behind roulette and answers questions

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.

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).

alt2005 wrote: Let me give you my definition of probability. Taken from CGM.

P = 1 - 1/[ 2^(1/k) ]
where k is the number of distances before the event is repeated, which is half the total number of all distances.

Example.
Half of all distances to the number repetition lie from one to 25 spins. This is a property of geometric distribution. This fact is derived elementarily: (36/37)^25 = 0.504103 ~ 0.5 ~ 1 - (36/37)^25
Then P = 1 - (2 ^ 1/25) = 0.027345 ~ 1/37

I want to add. This definition of probability may cause confusion (to put it mildly). In order not to get into confusion, I will try to explain. It does not apply to one spin, but rather as an average probability on a set of spins.
I repeat. In itself, it will not help in finding the grail. But it gives at least some justification that it makes sense to look for it at all. Because the distance curve can in principle be changed, and then the probability in the sense of this definition will also change. Namely, ver-t, not frequency.

InquisitorEA wrote:

alt2005 wrote: I can post an xlsm file with routine operations.

Please post it, I want to see it.

OK, I'll post it. But not today.
First I'll prepare the file, it takes a little time. Throw out the unnecessary, put it in order, make instructions. If you're going to post it, then post it properly ))

InquisitorEA wrote:

alt2005 wrote: I can post an xlsm file with routine operations.

Please post it, I want to see it.

I'm posting it as promised.
Be sure to enable macros, otherwise nothing will work. It is advisable to rename the file to "samples.xlsm" (files with this extension cannot be attached here, apparently)
Basic operations:
- calculation of distances to repetitions (future and past)
- temperature calculation
- finding a room with a given temperature
- calculation of the frequency of occurrence of a number in a given interval
- string operations

alt2005 wrote:
It is advisable to rename the file to "samples.xlsm" (files with this extension cannot be attached here, apparently)

In Windows it is not easy to rename the extension. I had to install Total Commander.

It worked when I enabled macros and reopened the file.