Roulette Open letter to Snowman

Hello, I find one article about a different way to explore a biased wheel using a short cut method.
But the internet is full of information and material that don't reflect reality.

So this is a question for you!

I quote:

The easiest way to do this is by finding section bias. If you find that the wheel favors half of a side, you can gain a long-term edge.

Here’s an example:

• You record 500 roulette spins.
• You put all of the results into a spreadsheet.
• You find that a section of 19 numbers running between 0 and 5 is biased.

The best thing about looking for section bias is that you only need several hundred spins to find this with confidence. The wheel is favoring a large group of numbers,meaning you need less data to spot the bias.

Compare this to looking for favored pockets, which requires far more data and analysis. You’re searching for a bias in one or more pockets out of a possible 37 (European wheel) or 38 numbers (American wheel).

Finding single favored pockets can be more lucrative, because you’re narrowing down where the bias(es) occur. But it also takes 4,000 to 5,000 spins to find a single biased number with any confidence.

The problem with individual pocket biases is that you’ll waste an incredible amount of time if/when your search turns up nothing.

The article is from
https://www.gamblingsites.net/blog/3-ways-that-casinos-prevent-roulette-wheel-bias-today/

My notes ...

Why would someone look between 0/5 that is opposite of each other that the text suggests?
Any half of the wheel could be biased, not just between the numbers 0/5

Cheers Patrik

 

""You find that a section of 19 numbers running between 0 and 5 is biased""
What does it mean?

 

0/32/15/19/4/21/2/25/17/34/6/27/13/36/11/30/8/23/10/5/ is a half...and just an example.

 

Hello Sharptracker, but, they did not said which frequency is the one that confirm a biased wheel/sector.
in any 500-trial-sample you can find 19 numbers hitting better than the other 18/19

 

I think that know every serious player - you simply look at the chance that results is random. And that chance each can choose for himself accordingly his skill - the weaker player needs less chance that result is random...

 

benas, I cannot understand what you meant.

 

Maybe Dr.Sir Anyone aka Snowman will join the discussion and offer his relevant opinion .



ND

 

If you know such words as a standard deviation - must understand, that deviation has some expectation that it is random. If that expectation is small - means that are some forces which create that deviation and we can exploit that. If the deviation is more similar to random in future it can be or not be random - so we exploit that cant. That is all and you must such things to know...
Degree how big must be chance that deviation is not a random player can choose for himself - for example, I know good wheel observe 25 spins and see that one half of wheel fall 15/10 against another. For me, because I know wheel, that is enough. But for somebody other, that is not enough because of that 15/10 can be a simply random result. So all depends on player - that who good know all not need many spins, but who not know - need much....

 

in 500 trials you may find a sector of 19 numbers hitting better than 19/36 easily.
Standard deviation count could mislead you when your data set is scarse(500 1000 5000 and more)
What I do not understand is the sentence I quoted in my first post.

 

I not see any sentence which you quoted ?

 

This ?

 

yes

 

So what is here not clear ? that who wrote that article, only maybe heard by half ear what is bias ...
Ok, he maybe looks for which 19 number sector have most hits and name it biased - that is all...

 

That article is very loose with the facts.

1. Billy Walters and The Computer Group were involved with sports betting, not bias wheel play.
2. Billy Walters did play biased wheels, but without the computer group and with a group of other people. He was merely the front man.

Regarding tracking for a section bias. I suppose you could track for a half wheel bias, but it's rare that an entire half of a wheel would be biased enough to overcome the house edge. Over the years I have found half wheel biases, but have always narrowed down the betting width to no more than 12 numbers. Most section biases are three to five wide.

In order to find a section bias, if you haven't predicted which section will be bias in advance, then you want to look for a section that's at least five standard deviations above normal. If after X number of spins the section isn't above five, then keep tracking until it is. As the spin sample grows, so should the standard deviation. The model and make of wheel will also determine section widths.

 

""In order to find a section bias, if you haven't predicted which section will be bias in advance, then you want to look for a section that's at least five standard deviations above normal. If after X number of spins the section isn't above five, then keep tracking until it is. As the spin sample grows, so should the standard deviation. The model and make of wheel will also determine section widths.""

After predicting a section in advance you should break at least 2 standard deviations(I would wait for at least 2,5 sd) to be closer to a accurate prediction.
It often happens you predict for instance a section of 6 numbers, you take new data and some of these 6 numbers perform at very well frequency but section seemed to be close to the one we predicted. It could be because we have predicted with lack of info or regular fluctuations made some noise. You miss a number or two in a prediction of a 6-number-section , it matters. You mus recalculate.
The other item is the proper size of data set to look for our goal(+2,5sd)
I remember have read a way to calculate it, a former master biased wheel player used a formula when you predict a sector in advance.

Ybot

 

There are no different ways how to calculate - must use the standard formula for counting STD and multiplay it by how many STD you want to have. But all that is simply a mathematical way - much better to notice reasons why some sector is different from others and here are absolutely different calculations...

 

Benas, what is the only way to calculate it? could you give us an example?

 

Standart formula of STD . I am benediktus in all forums and you have me in skype if you want to know ask in skype

 

https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/z-score/

 

ybot, no need to go begging to Benas via skype.

Here is a simple explanation of z-score calculations for standard deviation. It was posted on VLS forum many years ago by Tangram who shared knowledge openly, and never made people follow him off to a secret page or place or site...sheesh!


Introducing the "z-score"

The calculation generates a number called the "z-score", which tells you how far away your actual results are from what you would expect to get (on average) if you were simply betting randomly for the same number of decisions. The higher the score is, the lower the chance that your results are due to random variability, or "luck".

In the statistical literature, there are 3 z-score values which are commonly quoted. For our purposes they can be expressed as the following:

z-score of 1.0 - there is a 16% chance that your results are due to luck.
z-score of 2.0 - there is a 2.3% chance that your results are due to luck.
z-score of 3.0 - there is a 0.13% chance that your results are due to luck.

Scores higher than 3.0 mean that it's highly unlikely that luck is involved at all. If you have a true advantage the score will (and must) continue to rise as you get more results.

To calculate the z-score for your system you need 3 pieces of data:

• The number of placed bets. It's important that these are actual bets - you don't count any "virtual" bets.
• The number of wins (or hits).
• The probability of a win on a single outcome. e.g. if you're betting 5 numbers, the probability is 5/37, if dozens it's 12/37, two columns is 24/37 etc.

Note that this measurement is only valid for bet selections - it doesn't apply to systems using a progression.

This isn't really a problem because you can still get the z-score by just counting the number of wins without taking account of the actual profit (In fact you could argue that finding the z-score is more important for those systems which do use a progression, precisely because a progression can easily give the illusion that a method has merit, whereas in all probability you have no advantage at all, and are surviving on borrowed time...). For example, if you were using a 4 step grand martingale of 1,3,6,12 on R/B then after a series of wins and losses like this:

LLLWLLWLWLLLWLLLWLWLLWWW

You would have made +16u, but the number of wins is 9 and the number of placed bets is 24.

Similarly if you were betting on 2 numbers you might get a series like this:

LLLLLLLLLLLLLLLLLLLLLLLWLLLLLLLLLLLLLLLLLWLLL

If using a progression you may well be in profit at this point by an amount depending on the progression, but for the purpose of calculating the z-score all you need to know is that the number of wins is 2, and the number of placed bets is 45.

As such, the z-score can be regarded as a "figure of merit" for bet selections. Mathematically, there is no way to win consistently using a progression alone. The bet selection is what's important. If you can win flat betting, then you can boost profits with progressions, but you can't use a progression to paper over the cracks of a poor bet selection. This happens to also be my opinion, but not everyone will agree. Regardless though, even the most hardened progression players are looking to shorten those losing runs, so it makes sense to pay at least some attention to bet selection.

Note that the score can come out negative. What does this mean? Well, it depends, because if the score is between -3.0 and +3.0 then you are within the accepted interval governed by chance. In other words, if your score is consistently between these two numbers, you can't assume that your strategy is giving you any advantage. The vast majority of systems and methods will give scores which fluctuate between these values - that's just randomness at work. It's only when your score moves outside these values (and continues to move away from one or the other of them) that you know you're on to something.

In general, a negative score means you're doing worse than average (a score of zero means your strategy is right about where it should be, according to chance). But note that a score of -5 means you're doing much worse than you should be, and this is just as significant as a score of +5. If you you're getting scores which are increasingly negative, logic suggests you should (if possible) bet the opposite strategy.


[box title=Z]----- -4 ------> -3 ------ Interval of Chance (Luck) ------ +3 <------ +4 -----[/box]


It's important to realize that your score needs to keep increasing as you make more bets, to be sure that you're operating "outside" randomness. Fluctuations will still occur even if you have a real edge, so it doesn't matter if the score climbs to 3.0, then drops back to 2.5 over the next session, as long as the overall trend is upwards.

Here is the formula for z:


z= (w - np)/sqrt(np(1 - p))Note: "sqrt" is the square-root function


Don't panic, I'll go through some examples.

There are 3 variables in the formula:

• w - the number of wins in the sequence
• n - the number of placed bets (wins + losses)
• p - the probability of winning a single bet

example 1

Let's take the first sequence of W/L above (betting R/B) -

LLLWLLWLWLLLWLLLWLWLLWWW

There are 9 wins, so w = 9
The total number of placed bets is 24 (9 wins, 15 losses), so n = 24
The probability of a winning a single outcome is 18/37, so p = 18/37 = 0.4865

Plug these numbers into the formula:

z = (9 - 24*0.4865)/sqrt(24*0.4865*(1-0.4865)) = -1.093

Notice that even though the score is fairly poor, a profit of 16u was made in this sequence. The danger with progressions is they can lead you into a false sense of security, making you think you have an advantage (you're making money right?) , but the "advantage" is often illusory.


example 2

Ok, we'll take the 2nd sequence above -

LLLLLLLLLLLLLLLLLLLLLLLWLLLLLLLLLLLLLLLLLWLLL

Here there are 2 wins - w = 2
There are 45 bets, so n = 45
If the sequence comes from betting 2 numbers, then p = 2/37 = 0.0541

So z = (2 - 45*0.0541)/sqrt(45*0.0541*(1-0.0541)) = -0.286

So for this sequence, the bet selection was running a little below average.


example 3

Here is a sequence of W/L playing 2 dozens -

LWWWWWLWWLLWWWWWWLLWWWWWWWWWWWWWWWLWLLWLLWWWLWWW

There are 36 wins, so w = 36
There are 48 bets in total, n = 48
The probability is 24/37, p = 0.6486

And z = (36 - 48*0.6486)/sqrt(48*0.6486*(1-0.6486)) = 1.472

Not bad, more testing needed...

Ok, that's enough examples. One question though, what about if you're not betting on the same group (size) of numbers? suppose your method calls for a number of bets on a dozen, then maybe a couple on streets, or perhaps you start off on 24 numbers and gradually work you way down to a single number (as in the so-called "parachute" strategies), is there a way of calculating the z-score for that kind of system?

The answer is yes, but it can get a little tedious working it out, so a spreadsheet is highly recommended. Actually, it's not a bad idea to use one anyway, then you can update the z-score quickly every bet or few bets as you do the testing. By doing this you might be able to spot more easily any weaknesses in the strategy as they occur.

Suppose you make a series of 20 bets:

5 on double streets (p = 6/37 = 0.162),
5 on singles streets (p = 3/37 = 0.081),
3 on dozens (p = 12/37 = 0.324),
7 on an EC (p = 18/37 = 0.486)

To use the z-score formula, you need an average value for p, so you have to multiply each separate p by the number of bets, add up the total, and divide by the total number of bets made (20).

So,

5 x 0.162 = 0.81
5 x 0.081 = 0.405
3 x 0.324 = 0.972
7 x 0.486 = 3.402

Add them up - which gives 5.589, and 5.589/20 = 0.279. This is the average p which you use in the formula for z.

You can find more information on statistical testing here: http://www.fourmilab.ch/rpkp/experiments/statistics.html

Note:

There are actually 2 interpretations of the z-score. In both cases it measures outcomes, but in one case the outcome represents a win/loss result and in the other it represents what the wheel actually produced. There's no conflict - for example, if you were betting Red, and the wheel generated a sequence of 10 Reds in a row, then the z-score would be the same for both your wins vs losses (10 consecutive wins), and for the outcomes generated for the wheel (10 reds in a row). This is simply a consequence of the probabilities being the same for an individual outcome - ie; the probability of a win betting on Red is the same probability of a Red occurring.

Alternatively, you might be using a bet selection which bets on Red for 5 spins, then switches to Black for 5 spins, alternating this way. So if you start a session and the first 10 outcomes generated by the wheel are:

RRRRRBBBBB

Then your z-score would be more than 3.0, but the z-score with respect to Red would be zero, because there are as many Blacks as Reds in the sequence.

It might be more helpful to think about what the z-score actually measures; it measures the difference between actual results, and what the results should be, on average, according to the normal distribution. Whether they are your results (from a particular bet selection), or results "from the wheel" is irrelevant. In that sense the z-score is a relative measure.

Another way to think about it (which might be a little less confusing) is to interpret the z-score in only one way - that of what your results would be if you were betting on the outcomes that the wheel actually produced. So an increasing z-score would mean that the outcomes generated by the wheel coincide with what you are choosing to bet on.