Discrete Distributions (Alatissa expert in probability theory)

I think Alatissa thought she was being used as a calculator and not valued as a person. They insulted the mouse.
Friend, please allow me to say that every Ukrainian needs qualified psychotherapy right now. Because of the two-year-long military invasion of Russia, everyone here is extremely tense and completely intolerant.

We are conducting an experiment with a coin, we make 1000 tosses.
We do expect it to be about 50/50% heads and tails.
Halfway through the experiment, a clear bias in the results is visible: 60% heads and 40% tails.
But it may turn out that this is the thousand that was caught.
Take and calculate the relative deviation.
And keep increasing the throws. 10,000... 50,000... 100,000
If the relative deviation does not tend to zero,
then most likely it is a curvature or a changed center of gravity.

DLK wrote: In its simplest form, the theory goes something like this: If you toss a coin 100 times, it will land on heads about 50 times. If it lands on tails 20 times in the first 20 tosses—theoretically—then there's a good chance it will "correct" and land on heads the next time.

This is really not a straightforward question.

We conduct an experiment with a coin, making 1000 tosses.
We do expect it to be about 50/50% heads and tails.
Halfway through the experiment, a clear bias in the results is visible: 60% heads and 40% tails.

1) Is the EXPECTATION of TRIM to the calculated value (return to normal) for the remaining time of the experiment correct?
2) Where is the boundary of DEVIATION from the norm so that we can immediately start looking for curvature in the coin or a changed center of gravity?
3) Doesn't it mean in such cases that if there is a CLEAR SKILL, then its further increase is precisely what is expected? It would seem that the trend will continue to strengthen, since we don't know the reasons for the resulting skew.

DLK wrote: A man is asked:
- What is the probability that you will meet a dinosaur when you go outside?
Man:
- One trillionth.
A woman is asked:
- What is the probability that you will meet a dinosaur when you go outside?
Woman:
- One half.
- How so? - they ask.
“Well then,” she replies, “either I meet you or I don’t.”

I'll comment on this joke for now.
As for questions for me, don’t rush into life, everything has its time.
But first I would like to thank those who at least somehow understand and feel me.
...
Now let's pay attention to this story.
If I were asked this question, do you know what my reaction would be?
I wouldn't answer.
I'll tell you why.
The problem is stated incorrectly.
To talk about probability, we need a clear probability space, which is very fuzzy here. Even the image of a dinosaur is unclear.

For example, I can formulate the problem differently, in which we can already talk about a random process.

First, you need to decide on the image.
Let the dinosaur be a theater (film) actor who gets into the role of this creature on stage.
There are three streets in the city between his house and the theater. To avoid boredom, he randomly (using a dice, for example) chooses one of the streets and stops at a café for half an hour. A passerby (male or female) also has a chance of finding themselves on the same street and entering the café for a certain amount of time.
And now that the random processes and the image itself are understood, something can be said about assessing the probability of such a meeting...

Roulette can give a gambler the strong impression that character and intelligence will yield positive results if they can be used to create a suitable system. Typically, any system involves developing a model. In its simplest form, the theory goes something like this: if you toss a coin 100 times, it will land on heads approximately 50 times. If it lands on tails 20 times in the first 20 tosses—theoretically—there's a good chance it will "correct" and land on heads the next time. And the roulette table has its greedy observers, trying to spot a "trend"—for example, black numbers appearing repeatedly—in order to bet against it. Players sometimes call this the "law of equilibrium" or the "doctrine of the maturity of odds."

In reality, there is no such law. A more accurate term for this phenomenon would be the "Monte Carlo illusion." The odd numbers remain the same in each round, regardless of the previous one.

The truth is that it is impossible to break the bank legally for several reasons.
Firstly, the house edge is built in. All bets are placed on one or more of 36 numbers or multiple combinations of them – odd or even, black or red, high or low. Payouts are calculated as if the ball had a 1:35 chance of landing on each number.

The thing is, 1,000 throws is already a long enough period for the law of large numbers to kick in. If you wantyou can take a much longer one.

And so no more throws are needed.