Playing Replays on Casino Roulette

alt2005

In half the cases, a dozen on roulette is repeated after 2 spins. The standard maximum of not falling out is 18-20 spins. Very rarely - after 36-40 spins, these are probably already outliers, going beyond 3 sigma. For progressions this matters, for flat - no.

On the graph there are ~20K spins, dozens are repeated every 2 spins in 10628 cases.



On the Y axis: on which spin from the dozen drop does it repeat.
On the X axis there are just dots for repetitions
- immediately (on the 1st spin after falling out),
- on the 2nd back after falling out,
- on the 3rd, etc.
Well, in short - for each dozen it is calculated when it will repeat again. We get a set of such "distances." / Then we simply sort them, this is the X axis. This is more convenient for me.
Example: there is a horizontal line at the Y=2 level. This corresponds to the fact that the distance to the repeat is 2. You see, this line on the graph is from point 6343 to point 10628. This means that the number of repeats of a dozen on the 2nd spin after the fallout (it doesn't matter which dozen) was 10628 - 6343 + 1 = 4286. Let's say that dozen 1 fell on the 11th spin and repeated on the 13th, and dozen 3 fell on the 23rd spin and repeated on the 25th. These repeats are included in the set of distances 2.
Distance 1 (i.e. if the repetition was immediately on the next spin) corresponds to 6342 points, which means that this is how many such distances were in this sample. By the way, there are most repetitions immediately, slightly fewer repetitions only after a spin, even fewer repetitions after 2 spins, etc.
For each dozen, you can consider the repetitions separately, simply sorting them as needed.
You can't show everything in a picture. But I hope you get the idea.

A dozen may not appear 20 times in a row, but that doesn't mean that the 21st time the probability of it appearing is higher. The same.
Take Russian roulette. If you don't spin the drum before each shot, the probability of a non-blank shot increases and by the 6th time it will be 100%. But if you spin it before each shot, the probability of a non-blank shot is always only 1/6. Roulette is when the drum is actually spun.
The probability of guessing does not increase with progressions. But the turnover does increase - this is your hard-earned money. It is one thing to lose 1 euro with the same probability of 25/37 (or 2/3), and another thing to lose 50 euros. Why am I in favor of flat? Because I have seriously studied progressions. There, it is not so much the negative MO that rules, but the dispersion, and it is generally unpredictable. But there is still a clear pattern: you will regularly run into long series of failure to get something. And you will regularly not have time to win back these drains. Either you will run into the limit, or the bank will not be enough.

40 spins is nothing. The law of large numbers doesn't have time to operate there. This means that the patterns are very weak. But you wouldn't stop after playing 40 spins and then not play at all, would you? And if you play 100 sessions of 40 spins, that's 4000 spins, and the patterns will rule. Roulette doesn't care how you view the sessions - 40 spins or even 20.
Why cover the entire universe? I have 20K spins, if 300 spins a day, then 2 months of play. And even less on pneumatic. And if I find a pattern that allows me to make 6000 chips on these 20K, when betting on the number. What else do you need? What works stably on 20K will work on 100K.

Olynes

You know, even when you don't look at the physical side of the roulette wheel at all, you're still looking for exactly the same thing that I'm looking for. But on the physical wheel, there's something simpler.
The same repetitions - I have the same thing - if the distance - fell out - it can fall out again. And here I make the assumption that what fell out has a greater chance of being repeated than the distance that did not fall out - to appear. And such an assumption is generally correct. Simply because if it were not correct, the Gauss hat would not work...

alt2005

Where would I get the Gaussian hat? This thing exists for the normal distribution. And I'm dealing with a geometric one. Where would I put this hat?
I also studied the repetitions of the distances. They are distributed in exactly the same way as the repetitions of the numbers themselves. Not according to Gauss. According to GR, and this is the problem.
Although some of what you are talking about is also true. There is a certain maximum balance (it doesn't matter if it is negative or positive), which depends on the initial entry point into the game. To the right or left of this point, the balance is already less.



Yes, there is a rubbish, in terms of balance, what I said. There are many points on which the strategy allows betting. At the same time, inside this set, there is a set of central points from which it is most profitable to bet. In the sense that the maximum balance is achieved, but the ROI is smaller. And where the maximum ROI is, there are few bets, and the balance is small.

The statement is true precisely because of the GRD (whatever you call it). The GRD, and the 2/3 property, and the 25 property (about half of the numbers come up in 25 throws) - all this is one and the same consequence of the probability of 1/37. Just like on Russian roulette with one cartridge, the probability of a non-blank shot is always 1/6, if you spin the drum. Just imagine that there is one live cartridge in the drum, and the other 5 are loaded blanks, but each blank can have its own characteristics. For example, instead of a bullet, a stream of gas of different colors flies out. And when you load, these colors are chosen randomly. For simplicity, let's assume that the gas of a live cartridge also has a color - for example, black, and blanks are not black. Then in 6 shots you will get about 4 different colors. But which ones - you can not know. The same thing with roulette.

The statement about 12 cartridges is true. About the infinity of blanks - no. Theoretically, a number can not fall out for an indefinite time. Just like blank cartridges. But in practice - 24-25 different numbers, yes. But what good does it do you if you don't know which ones? The real probability of one number for a specific spin is always 1/37.
I have already spoken about my definition of probability. But there, not one spin is considered, but a set. On which a certain average probability is taken. This set is not just a stupid addition of individual spins, they must be considered in the aggregate. Then the quantity turns into quality. On cgm, I gave an analogy. If you take an atom of uranium-235, then by itself it is nothing. But a certain set of such atoms (critical mass) - gives an explosion.