Discrete Distributions (Alatissa expert in probability theory)

I will now show the table in full, as it turned out in Excel calculations



Here we paid attention to the exponential notations and the fact that the calculations are up to nine decimal places.
That is, rounding occurs, and small errors result.
It's actually a bit early to get a value of one at step seven.

I think many people have noticed the type of function:
integral or weight.





i.e. when you choose "false" - these will be the values of the probability density,
when you select "true" - the values of the integral distribution function.

For some reason, no one asks what these meanings are.
Even Shpilevoy became quiet.
Although he was perplexed when I showed the distribution function in the topic
"Calculate three numbers in series of thirty spins"

Shpilevoy writes:


"Ten times 1, what does that mean?" he asked.
....
Since I have already taken a segment of 10 spins, I will continue according to this example,
and 30 spins will be similar.

I hope he paid attention to the Y axis.
In the density plot of the distribution p(r)
in the graph of the distribution function f(r)

I'll continue a little later,
Please do not comment for now.

Alatissa wrote:
What kind of coordinate system does Olynes have, where does he see thousands and millions of sigmas, I have no idea.

But I'll explain a little - you've probably heard such expressions, for example - "as high as a mountain" or - "as many as there are stars in the sky"... or the most common - "so... high".

Or something like this - when I was studying, there was some kind of assignment and the teacher explained what needed to be calculated and said "And take the data from the reference book of Vasily Potolkov (I'm trying to translate the last name)... well, there was one who went to look for such a reference book in the library.
I have a suspicion that you would be a match for this seeker

The fact that I wrote millions means... ...well, I didn't count how many there are, and what difference does it make, it's the same as with the data from Vasya Potolkov's encyclopedias... how could you do that...?

And finally, in the game I play, sigmas are not counted in order to find some rare coincidence - they are counted to make sure that what is constantly happening is not a coincidence.
Read again - "happens all the time" and since I'm talking about that, I mean that 10 out of 10 or close to that is always guessed.

You understand - I'm not interested in rarities because it's impossible to use them. I'm interested in certain constancies because my game is built on the fact that what was - will be in the future, because this is the shortest path to victory... again in the game I play.

klick wrote: Alt, is it necessary to say anything about your linguistics if D. London never wrote novels about casinos and roulette.
For the fact that you went to Google to look for De Steil's reference book, that's a credit! It's immediately obvious that you're far from the Ukrainian language, as well as from foreign literature.

I apologize in advance to the Admin and all other forum members. But I'll still answer Klick. Read, klick, about Smoke Bellew, how he won at the dried-up roulette, and then judge who wrote about what and who is far from what. Of course, I don't know Ukrainian to such an extent that I can immediately understand the joke about Steil, but the humor itself is somehow dubious ))

Now on to the topic. I don't actually count sigmas. Whether the graph is negative or not can be seen from the distribution of distances. But since we're talking about sigmas, I'll express some thoughts.

10 spins in my opinion is not enough to calculate sigma. But let's take 370 spins. The average number of number drops or, what is the same, the average number of guesses on this segment = 10. We calculate sigma:
1/37 * 36/37 * 370 = 9.73
Sigma = SQRT(9.73) = 3.12 so 3 sigma = 9.36
Then if guessing on 370 spins consistently occurs more than 20 times (10+9.36), then there is reason to consider this not a random guess, but a positive strategy.
But if you regularly guess less than 1-2 times (10 - 9.36) - then there is reason to suspect a casino setup. In any case, such numbers are no longer (most likely) random.

Alatissa wrote:
I will write my answers both for distances and for the 10-spin interval in a normal environment,

thanks for the detailed description
there are some things that I stubbornly can't get my head around... but with your help I'll definitely get my head around them )))