### Author Topic: Are there any limits?  (Read 3004 times)

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#### BlueAngel

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##### Are there any limits?
« on: March 26, 2016, 09:47:00 PM »

Many gamblers have experienced abnormal levels of gambling performance volatility during various periods of the results' cycle.
While volatility may be greater than anticipated during certain periods of time, a case can also be made that the manner in which volatility is typically measured contributes to the problem of unexpected volatility.
The purpose of this topic is to discuss the issues associated with the traditional measure of volatility, and to explain a more intuitive approach that can be used by gamblers in order to help them evaluate the magnitude of their investment risks.

Most gamblers should be aware that standard deviation is the typical statistic used to measure volatility. Standard deviation is simply defined as the square root of the average squared deviation of the data from its mean.
While this statistic is relatively easy to calculate, the assumptions behind its interpretation are more complex, which in turn raises concern about its accuracy.
As a result, there is a certain level of skepticism surrounding its validity as an accurate measure of risk.

To explain, in order for standard deviation to be an accurate measure of risk, an assumption has to be made that investment performance data follows a normal distribution.
In graphical terms, a normal distribution of data will plot on a chart in a manner that looks like a bell shaped curve.
If this standard holds true, then approximately 68% of the expected outcomes should lie between ±1 standard deviations from the investment's expected return, 95% should lie between ±2 standard deviations, and 99% should lie between ±3 standard deviations.

For example, during the period of June 1, 2015 through September 1, 2015, the three-month rolling quartered average performance of the EC Red was 9.5%, and its standard deviation was 10%.
Given these baseline parameters of performance, one would expect that 68% of the time the expected performance of the EC Red would fall within a range of -0.5% and 19.5% (9.5% ±10%).

Unfortunately, there are three main reasons why investment performance data may not be normally distributed.

First, gambling performance is typically skewed, which means that return distributions are typically asymmetrical.
As a result, gamblers tend to experience abnormally high and low periods of performance.

Second, gambling performance typically exhibits a property known as kurtosis, which means that gambling performance exhibits an abnormally large number of positive and/or negative periods of performance.
Taken together, these problems warp the look of the bell shaped curve, and distort the accuracy of standard deviation as a measure of risk.

In addition to skewness and kurtosis, a problem known as heteroskedasticity is also a cause for concern. Heteroskedasticity simply means that the variance of the sample investment performance data is not constant over time.
As a result, standard deviation tends to fluctuate based on the length of the time period used to make the calculation, or the period of time selected to make the calculation.

Like skewness and kurtosis, the ramifications of heteroskedasticity will cause standard deviation to be an unreliable measure of risk.
Taken collectively, these three problems can cause gamblers to misunderstand the potential volatility of their investments, and cause them to potentially take much more risk than anticipated.

A Simplified Measure of Volatility

Fortunately, there is a much easier and more accurate way to measure and examine risk.
Through a process known as the historical method, risk can be captured and analyzed in a more informative manner than through the use of standard deviation.
To utilize this method, gamblers simply need to graph the historical performance of their systems, by generating a chart known as a histogram.

A histogram is a chart that plots the proportion of observations that fall within a host of category ranges.
For example, the three-month rolling quartered average performance of the EC Red for the period of June 1, 2015 through September 1, 2015 has been constructed.
The vertical axis represents the magnitude of the performance of the EC Red, and the horizontal axis represents the frequency in which the EC Red experienced such performance.

The use of a histogram allows gamblers to determine the percent of time in which the performance of a system is within, above, or below a given range.
For example, 16% of the EC Red performance observations achieved a return between 9% and 11.7%.
In terms of performance below or above a threshold, it can also be determined that the EC Red experienced a loss greater than or equal to 1.1%, 16% of the time, and performance above 24.8%, 7.7% of the time.

Comparing the Methods

The use of the historical method via a histogram has three main advantages over the use of standard deviation.

First, the historical method does not require that investment performance be normally distributed.

Second, the impact of skewness and kurtosis is explicitly captured in the histogram chart, which provides investors with the necessary information to mitigate unexpected volatility surprise.

Third, gamblers can examine the magnitude of gains and losses experienced.

The only drawback to the historical method is that the histogram, like the use of standard deviation, suffers from the potential impact of heteroskedasticity.
However, this should not be a surprise, as gamblers should understand that past performance is not indicative of future returns.
In any event, even with this one caveat, the historical method still serves as an excellent baseline measure of investment risk, and should be used by gamblers for evaluating the magnitude and frequency of their potential gains and losses associated with their method opportunities.

Application of the Methodology

Now that gamblers understand that the historical method can be used as an informative way to measure and analyze risk, the question then becomes:
How do gamblers generate a histogram in order to help them examine the risk attributes of their methods?

After performance information has been gathered, or manually calculated, a histogram can be constructed by importing the data into a software package, such as Microsoft Excel, and using the software's data analysis add-on feature.
By utilizing this methodology, investors should be able to easily generate a histogram, which in turn should help them gauge the true volatility of their investment opportunities.

Conclusion

In practical terms, the utilization of a histogram should allow gamblers to examine the risk of their investments in a manner that will help them gauge the amount of money they stand to make or lose on an annual basis. Given this type of real-world applicability, gamblers should be less surprised when results fluctuate dramatically, and therefore they should feel much more content with their system's exposure regardless the deviation degree.

#### kav

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##### Re: Are there any limits?
« Reply #1 on: March 27, 2016, 04:38:04 AM »
This sound so scientific I'm a bit intimidated.
not sure I understand what is being said.
I just want to remind however this excellent topic : Can volatility be reduced?
« Last Edit: March 27, 2016, 10:58:14 PM by kav »

#### BlueAngel

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##### Re: Are there any limits?
« Reply #2 on: March 27, 2016, 12:10:03 PM »
This sound so scientific I'm a bit intimidated.
not sure I understand what is being said.
I just want to remind however this excellent topic : Can volatility be reduced?

Don't be discouraged by the terminology, the main principle is simple, it's all about distribution here.

Perhaps Harry J. could add a thing or two because he is familiar with risk management statistics due to his extensive experience in insurance policies.

« Last Edit: March 27, 2016, 10:58:56 PM by kav »

#### scepticus

##### Re: Are there any limits?
« Reply #3 on: March 27, 2016, 10:54:02 PM »
Interesting post BA.
My take on this is, I suppose, "Gut Feeling".
I now use  a "Total Betting Bank" of £500 with which I make 4x£1 bets. Should my bank fall to , say
£250 I shall halve my bets until, hopefully, this is increased back up to £ 500.
My risk profile is low as my main aim is Not To Lose  !

#### BlueAngel

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##### Re: Are there any limits?
« Reply #4 on: March 28, 2016, 01:52:48 PM »
In other words some sort of kelly criterion MM, that's sensible.

Following your "guts" isn't sane and don't recommended it.
« Last Edit: March 20, 2017, 10:42:03 PM by kav »

#### scepticus

##### Re: Are there any limits?
« Reply #5 on: March 28, 2016, 02:35:51 PM »

In other words some sort of kelly criterion MM, that's sensible.

Following your "guts" isn't sane and don't recommended it.

Sane or insane BA I profit. Anyway my "Gut Feeling " will not be  needed  until I reach halfway point. Which, hopefully, will never be reached !
« Last Edit: March 20, 2017, 10:42:13 PM by kav »

#### Harryj

##### Re: Are there any limits?
« Reply #6 on: March 31, 2016, 07:22:18 PM »
Hi BA,
I congratulate you on a very erudite post. There were a couple of words there that I haven't come across, but I assume they are stock exchange terms. I am also a little adrift with those percentages for Red. I know they cannot mean that Red only came up 9.5% of the time for a 3 month period. So I am going to assume that red only missed its expected TARGET by that figure. Please correct me if I am wrong.

Your figures for the SD were pretty much on target, but you missed the emphasis ! eg

68.3% of the time  V (the variation) will be within 1 SD either side of THE MATHEMATICALLY EXPECTED RESULT.
95%    of the time  V ...................... will be within  2 SD either side of the math expected result.
99.7% of the time  V........................ will be within 3 SD either side of the  math expected result.

I emphasis THE MATHEMATICALLY EXPECTED RESULT, because this really ONLY pertains to that elusive term THE LONG RUN. As Dobbelsteen, Pales and I have pointed out on many occasions. There is a very big difference between small and large samples !

Another small point the extra 0.7% for 3 SD is very important because it makes quite a large difference. It means that ONLY 0.003% of the time the math expectancy will be more than 3SD.

The rest seems to boil down to a method that Pales and I have often advised.

A large number of previous results, obtained under similar conditions, should be analysed and a bell graph can be formed. This will indicate what we call "The winning range". Bets placed in this area are far more likely to win.

The method used was a simple pattern break comparing the 1st to the 6th result. As each game (BET) is completed the previous results form the trigger for the next game.

There were 143 Betting opportunities (BOP) in 330 spins. As each game averaged 2-3 spins there was very little waiting time.
Sipn 1 won 75 times
Spin 2 .......33
Spin 3........20       From these figures the "winning range" is obvious. Just those four spins can be bet with profit,
Spin 4 .......11       or you can do as I have often done. Bet the discarded spins with a heavily "insured" marty. at
Spin 5 .......2         Least you will recover part of your bank on the losing numbers.
Spin 6 .......1
Spin 8........1

For the record I have nothing to do with the insurance industry. However as the problems facing actuaries are exactly the same as those facing gamblers. It is worth taking a look at how they work.

Harry

#### BlueAngel

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##### Re: Are there any limits?
« Reply #7 on: March 31, 2016, 09:06:36 PM »
Quote
I am also a little adrift with those percentages for Red. I know they cannot mean that Red only came up 9.5% of the time for a 3 month period. So I am going to assume that red only missed its expected TARGET by that figure. Please correct me if I am wrong.

I meant that 9.5% of the total results were above expectation, above the mean.

Quote
Your figures for the SD were pretty much on target, but you missed the emphasis ! eg
68.3% of the time  V (the variation) will be within 1 SD either side of THE MATHEMATICALLY EXPECTED RESULT.
95%    of the time  V ...................... will be within  2 SD either side of the math expected result.
99.7% of the time  V........................ will be within 3 SD either side of the  math expected result.

I emphasis THE MATHEMATICALLY EXPECTED RESULT, because this really ONLY pertains to that elusive term THE LONG RUN. As Dobbelsteen, Pales and I have pointed out on many occasions. There is a very big difference between small and large samples !
Another small point the extra 0.7% for 3 SD is very important because it makes quite a large difference. It means that ONLY 0.003% of the time the math expectancy will be more than 3SD.

What you said is true but not the only one non the less...
Another reality is that also 99.7% of all times results are deviating from the mean, from what probability theory dictates as average.
So let's say that number 0 is the mean, a deviation towards on side is -1 -2 -3 -4...etc and towards the opposite side is +1 +2 +3 +4...etc
No matter which direction a deviation could follow, one could be winner as long the deviation exists, it doesn't have to grow, just to exist.
For example after 6 spins of the wheel, Red hit 4 times and black 2 times, in this small sample of results there is 16.66% deviation, should this deviation grows, so could our profit.
Should the deviation declines towards the mean, we would lose but from experience I can confirm with certainty that the longer the total of results the longer could grow the deviation and this where the opportunity lies.
In samples such as 10 results it might seem that are evenly balanced, but as our total increases, so does the deviations.
I'm challenging everyone to find a sample of 100 plus outcomes which has a distribution of exactly 50%/50%.
Don't bother because you won't find such.
By establishing regular, short intervals between spins we could follow deviations along the whole way towards one direction or the other.
Anything could be profitable as long as what probability theory determines as mean is never quite there.

Quote
Spin 1 won 75 times
Spin 2 .......33
Spin 3........20
Spin 4 .......11
From these figures the "winning range" is obvious. Just those four spins can be bet with profit,   or you can do as I have often done.

What if we reduced this range just to the first spin in order not to double up?
You would have won 75 out of 143 bets with a net of 7 units, not bad hah?

I'd like to finish with a parable;

There were 3 blind men who were guiding each other inside a jungle...
Along the way they find an elephant, the first one touches the rough part of elephant's legs and announces: ''it's the trunk of a tree'', the second one touches elephant's proboscis and says: ''it's a brunch of a tree'', the third blind man touches elephant's genitalia and says: ''it's a snake''!
« Last Edit: March 31, 2016, 09:11:59 PM by BlueAngel »

#### Harryj

##### Re: Are there any limits?
« Reply #8 on: April 01, 2016, 06:14:08 PM »
BA, no one denies the importance of variation when compiling systems and progressions. It is the fact that variation alters with every spin, and that alteration is often in both size and direction. Almost all non physical methods make use of that fact.

In your example, 6 spins being 4-2. You fail to note that the variation of nearly 17%, is in fact less than 1 SD. Therefor in no way out of the ordinary.

I am well aware that in the range I posted the 1st spin won more than 50%. This is not always the case, but not important. I have posted on a number of occasions that for some time I successfully used a 7 step Marty that only won on the 1st bet. The next 2 spins broke even and the last four all lost. The whole point was to "insure" that 1st successful bet.
Another point I don't consider 7 units in 330 spins and 143 bets "not bad". I call it, 'Very Bad". If you take a look at the 4 step Marty I laid out for Godfrey. You will see that it would have won 72 units. That's not bad !

Your point about 100 spins is well taken. That is not only a "small" sample(mathematically),but is very close to the average session for many players. The important thing is that variations that DO NOT challenge the the 3 SD level can be very lucrative. I believe that the percentage within the 'cycle" of the proposed bet is much more important.  Eg. Had your example been 5-2, it would still have been within 1 SD , but would have offered a viable trigger. There are some that even say that 4-2 could be a trigger.

Believe me BA I am not trying to find fault or put you down. I liked your post. I just felt that it doesn't help to get philosophical with us poor mortals. Say what you mean don't wrap it up in verbiage.

Harry

#### BlueAngel

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##### Re: Are there any limits?
« Reply #9 on: April 01, 2016, 08:04:11 PM »
@ Harry

My point was to follow the difference between any EC pair as soon as possible!

If you let this difference to grow, for example +5 points for one side or the other, then it could be late because by the time you start betting it could move towards the opposite side.
Therefore we need a small amount of spins which is even number in order to allow the possibility of draw between an EC pair.
In such case as a tie we don't bet, with 6 spins sample we can bet soon enough in order to catch the trends on their beginnings, it could also be 4 spins.

Should the trend reverse its direction, we also change the direction of our bets in order to profit both ways.
My aim is to have more correct predictions than wrong, 7 units might seem small but if the unit value was 100 Euros wouldn't be so small, right?
By Martingaling you are increasing the win ratio but comes with a cost by the rare but possible bust.
That's why your unit value should be small in order to accommodate a 4,5,6,7,8...steps of doubling up, also you should play longer in order to reach my level of profits.
For you 10 Euros unit value need 70 wins to be equal with my 7 wins of 100 Euros, additionally  with what I'm suggesting, the ups and downs will be much smoother than with a steep and aggressive progression such as the Martingale.

That's the importance of bet selection, every session is unique and contains different characteristics, in choppy, tough sessions I'm quitting with even 1 unit profit, but tough sessions for Martingale is a disaster...!