Measure of Standard deviations

[Toby]

Hi, I want to know how do you calculate a probability and SD for certain events.

Fo example, what is the difference between a measure of SD over a sample when you have picked a section beforehand or not?

The probabily to find a 6-number-section on any group of 6 numbers that has 4 stendard deviations is easier than picking a double street and get 4 standard deviations.

The former searchs for ANY group of numbers that have 4SD(such as dozens, columns, any of the 3), the latter place the eye on a DETERMINED section and try to get 4SD.

So, when we see a sample of 1000 trials where a double street hit 209 or a dozen hit 383 we have 4 standard deviatons but it is not the same as to determine the range beforehand.

How can we know the difference using math?

Best regards.

[Bayes]

Hi Toby,

I think I understand what you're saying, but there isn't any difference . It's true that it's more likely you'll find a sequence of ANY 6 numbers which exceed 4 SD than a particular double street you have pre-determined, but there is no difference in the meaning of the SD or how it's measured.

Actually, you raise an interesting point. There is always SOME combination of numbers (because there are so many combinations) which will be at a very high SD, it's just that you don't ordinarily notice them because you generally confine your attention to the "standard" combinations on the layout (or maybe sectors on the wheel). If you go searching for the big sleepers, you will always find them, or they'll find you. 

As an example, think about the "law of the third". This says that after 37 spins, there will be 12 or 13 numbers left which haven't hit. Now you don't know beforehand what those numbers will be, but this means that there is SOME group of at least 12 numbers which has slept for 37 spins. However, if you look at the stats for dozens you see that the longest sleep for a dozen is around 30-35 and this is supposed to be a 'rare' event. Yet it happens for some group of numbers every 37 spins. There is no contradiction here, it's just a basic fact of probability that a predetermined event will be less likely to occur than one which isn't predetermined beforehand, because the selection which is predetermined is always a subset of a much larger set. e.g. A double street is only one possible selection of 6 numbers from all the ways of choosing 6 numbers from 37. In fact (believe it or not) the number of ways of choosing 6 from 37 is 2,324,784.

This is why waiting for sleepers is bad idea. Some combination of numbers will sleep for a very very long time (in fact, there is no limit).

[maestro]

i just love your posts Bayes..here is little question then,say we have certain bet selection lets say we map numbers like, if 1 hits we bet 20 lets say,if 2 hits we bet 29 and so on can be any other mappping way by doing our maping this way we virtualy wait untill say in our map we have sector of the wheel of six or eight or say 12 numbers and then we start betting on it...what are the chances exactly this sector to sleep..thanks

[Toby]

So, when you find + or - 4sd on a sample it doesn't mean that you can take advantage of this.
Another fact is when you start playing a double street and hit 209 times on 1000 trials, you actually have 4sd, a very strange event.
Finding ANY double street that hit 209 on 1000 trials is noy easy but it is less than 4sd, it goes by 2.5sd, I guess so.
What I want to know is a way to calculate de difference on the measure.

[Toby]

It isn´t hard to find a 12-number-section that sleeps long on a sample.

Take a dozen/column/12 strait neighbor numbers, is easier to find -4sd looking for any group than picking the 1st dozen and playing for 1000 spins.

I chalenge you to try to lose 4sd picking a dozen and playing 1000 trials. The mean is 324, -4sd means that you hit 265 times, the worst bad luck.

These sutle things about how to calculate a probability are the ones that confuse us.

[kelly]

Bayes, the point toby raises is sort of a very important point in for example bias search.  If a random sector reaches 3 SD with no visible biases, its not as strong an indication as if you with basis in what you see and hear in the wheel expects a certain area to receive donantions from the surrounding "weak holding" areas and it actually DOES perform as a biased sector.  Laurance had done an extensive research in this area, including mail correspondence with good old Thorp, of all people.  I had the entire research on my old computer that unfortunately exploded when my son lend it to play Battlefield, so there is no danger that anything leaks unless laurance does it.  Its an art of probability which is not really covered anywhere in any books but the calculations are still the same. Only, if you put them in a context where the "probability of a specific probability at a specific place..." etc. to occur, you get some very interesting values, which both discards bias search throug simple number tracking and at the same time gives the answer to WHY its so important to visually search for an advantage in the wheel. 


Al Kriegman wouldn`t be able to wrap his mind round it, thats for sure.

[ego]

Bayes, the point toby raises is sort of a very important point in for example bias search.  If a random sector reaches 3 SD with no visible biases, its not as strong an indication as if you with basis in what you see and hear in the wheel expects a certain area to receive donantions from the surrounding "weak holding" areas and it actually DOES perform as a biased sector.  Laurance had done an extensive research in this area, including mail correspondence with good old Thorp, of all people.  I had the entire research on my old computer that unfortunately exploded when my son lend it to play Battlefield, so there is no danger that anything leaks unless laurance does it.  Its an art of probability which is not really covered anywhere in any books but the calculations are still the same. Only, if you put them in a context where the "probability of a specific probability at a specific place..." etc. to occur, you get some very interesting values, which both discards bias search throug simple number tracking and at the same time gives the answer to WHY its so important to visually search for an advantage in the wheel. 


Al Kriegman wouldn`t be able to wrap his mind round it, that's for sure.

Nice reply and i could add that Laurance build a complete playing model upon how to distinct random fluctation towards being a true bias with out deffect spotting.
Its a kind of formula witch you use to determined a valid bias not being due towards random fluctation.
One among other distinction is that you can make a difference between psudo and actualy std.
Also that you make a distinction from actualy collected data to measuring with a new sampel collected data to verify the previos one to confirm a valid situation not being due towards random fluctation.
Just to mention some hints about the subject.

[Bayes]

Interesting stuff, kelly. Just to make sure I understand you here; are you saying that evidence of bias CAN be found by purely statistical means? ie; because the 'donating' regions of the wheel have lower SD and the 'acceptor' regions have a higher SD? That makes sense, but I imagine the analysis gets pretty involved.

[Bayes]

i just love your posts Bayes..here is little question then,say we have certain bet selection lets say we map numbers like, if 1 hits we bet 20 lets say,if 2 hits we bet 29 and so on can be any other mappping way by doing our maping this way we virtualy wait until say in our map we have sector of the wheel of six or eight or say 12 numbers and then we start betting on it...what are the chances exactly this sector to sleep..thanks

Hi maestro,

Unfortunately, no matter how complex your mapping function, that alone won't give any advantage above expectation. Essentially all you're doing here is rearranging the sequence of wins and losses. It's a bit like using 'follow the last' on the ECs, if the outcomes are running streaky, you'll do well, but it's just as likely to run choppy (there are as many chops as streaks) so it again it comes down to having a crystal ball.

[Bayes]

So, when you find + or - 4sd on a sample it doesn't mean that you can take advantage of this.
Another fact is when you start playing a double street and hit 209 times on 1000 trials, you actually have 4sd, a very strange event.
Finding ANY double street that hit 209 on 1000 trials is noy easy but it is less than 4sd, it goes by 2.5sd, I guess so.
What I want to know is a way to calculate de difference on the measure.

See kelly's post above. 

A group of numbers which is hitting way above or below its weight doesn't necessarily indicate a good bet because it could just be a random fluctuation which may disappear when you start betting on it (or against it). However, if you have supporting evidence, such as a correlation between the hot/cold sector and some imperfection on the wheel which you've spotted, then it's more likely to be a real bias, in that case you can be much more confident that it isn't a random blip.

[ego]

See kelly's post above. 

A group of numbers which is hitting way above or below its weight doesn't necessarily indicate a good bet because it could just be a random fluctuation which may disappear when you start betting on it (or against it). However, if you have supporting evidence, such as a correlation between the hot/cold sector and some imperfection on the wheel which you've spotted, then it's more likely to be a real bias, in that case you can be much more confident that it isn't a random blip.

Yes we can learn from that as i remember one player at m y r u l e t post short sample of close to 3 std and got exited for no reason at all - my opinion.
Start to ask all kind of questions and pepole to run he's numbers.

Shold also mention this guy did have some real success or being lucky finding a true bias in the past and made half year of income and behave like that.
True knowledge about bias is nothing some one find on boards on internet - that is for sure.

[Toby]

Suppose you are a sleeper´s player and decide to play on a double street when it gets -3SDs.

When you have 200 trials and a double street hit only 18 times it has reached -3SDs.

But, it may not be true because we waited for any double street to sleep such a time. It is not necesary that a double street sleeps on strait spins. We are waiting for inbalances.

We know that 3sd means 99,7% that it happens but the correct way to have the 99,7% is to choose the double street beforehand and we positively have the 99,7% of difficulty to happen.

Waiting for any of the 6 double streets to loose has less than 99,7%. How much less? How do you get the number?

Is this a question for math guys o can be answer for other experienced player?

[Bayes]

Toby,

I know what you're getting at but there is no difference in the measurement whether you've decided beforehand or not. Supposing there were 6 players who all chose a different double-street to bet on, and decided to wait until -3sd before doing so. Of course each of them has an equal chance that their chosen DS will hit -3sd first, so the only conclusion is that each DS always has an equal chance regardless of whether it has been selected.

Waiting for any of the 6 double streets to lose has less than 99,7%. How much less? How do you get the number?

Each double street on its own has the same chance, there isn't a different measurement. Thinking about a lottery may help. Where I am the odds of getting the winning ticket is 14 million to 1, which is a very low probability, and it's the same chance for anyone who buys a lottery ticket. But the odds that someone will get the winning ticket is much higher (not 100% on any given week, but much higher than 14 million to 1). If you take a group of individuals, then as a group, the odds are much higher to win than they are for any one individual. The larger the group, the higher the probability. Of course, it also depends on how you define an 'individual'. An individual could define a number of people, in which case the probability of this 'individual' winning is greater than for a single person.

So it's the size of the group relative to the total number of possible groups of equal size which determines the probability, and that's all. That's the very definition of probability:

Probability = number of "looked for" events / total number of equally likely events

Obviously, the "looked for" event can be anything you choose, but then you have to be careful to get the right number of equally likely events, otherwise it isn't a valid probability measure.

[Toby]

Bayes, even though being 6 players on each DS the chance that the one you choose was the one that looses is not the same as to cver the 6


The -3SD must be taken when you choose 1 of the 6 


To confirm the -3sd covering the 6 DS you should tke more data to see if it goes further 


I guess the -3sd weakens between the 6 options of 6 DS 

[Bayes]

Ok, I think I know what you mean now. You're asking what is the probability that ANY DS gets to -3SD as opposed to a particular one you've preselected, right?

In that case, you have to add up the probabilities for each DS. The chance that a particular DS will hit -3SD is 0.001349 (see here, and scroll down to "calculate probability Q from z")

So the probability that any DS gets to -3SD is 6 × 0.001349 = 0.008094 or 0.81%

Using the same calculator at the site, this corresponds to a z-score of 2.4, so you weren't far off.