Discrete Distributions (Alatissa expert in probability theory)

I promised to comment on the second option.

Alta's post #810 is very cool, it echoes the first page a little, but it's deeper here.
It's good that he wrote "it is not necessary that the distances from 1 to 25 should be
70%''
Yes, of course, it is not necessary.
We just get different options that lead to this advantage.

Our topics are very related to "roulette mathematics"
I will continue what I started, because once you give your word, you keep it.
Initially, I was very eager to describe it in detail... but the atmosphere was already the same.
If any of the readers are interested. You have to respect your listeners.

I disputed the 70% advantage after straightening and with specifics.
But 70% or half as much is still very high.
So I'll be brief.
This is a standard type of gr from 1-25 make up 50%


this is when the distances from 1-25 make up 70%

Alatissa please don't leave continue your calculations

There are 2 fundamentally different options:
a) when the probability of the entire sequence of events or elements of the system influences the outcome;
b) when what happened before the next event is not important at all.

A)
What is the probability of getting "heads" 2 times in a row? That's right, 0.5*0.5=0.25. That is, 2 times less than the probability of getting "heads" in a single attempt.

b)
You flip a coin 10 times, and all ten times it came up "tails." Let's flip it for the 11th time. Question: What is the probability that it will come up "tails" again?
The correct answer is 0.5! Although I really want to say (1/2)^11 = 0.00049.

The probabilistic nature of most events results in a fundamental difference between the so-called a priori and a posteriori assessment, i.e. assessment before and after the event.
There is a big psychological difference!

The most important processes in our lives are fundamentally uncertain, due to their exceptional complexity and multifactorial nature. As a result, our most significant decisions are always made under conditions of insufficient information, when the probability of success is not as great as we would like to think. And we have no choice but to try to learn to take this calmly and be effective enough in any conditions.

In a game, when you try to evaluate something, you can incorrectly take into account a nuance and get a result that is far from the correct answer by several orders of magnitude. Like the probability that tails will fall again on the 11th try.

I would like to throw in various roulette problems with solutions. Alatissa will look through them and correct errors.

The probability of any number coming up on European roulette is P=1/37.

No one has any problems with this. But dig deeper and the answers become completely different.