In order to reverse the house edge — one must be able to keep track of — what the advantage is at all times. Assumptions or predictions are less useful — as the fable below points out.

The Hare and the Tortoise is a fable attributed to Aesop. The story concerns a hare that ridicules a slow-moving tortoise and is challenged by him to a race. The hare soon leaves the tortoise behind and, confident of winning, decides to take a nap midway through the course. When he awakes, however, he finds that his competitor, crawling slowly but steadily, has arrived before him.

I will return to the importance of this tale and racetrack analogy after I outline simple and powerful concepts which help make it possible to develop a house edge — without using assumptions about who will win, mathematical predictions or probabilities.

Anomaly Detection

Anomalies are typically considered unexpected events and/or outcomes — such as the winner of the race in the above fable. Hence, anomaly detection consist of detecting patterns that do not conform to an established norm. For example, one of the jobs of casino pit bosses is to detect blackjack card counters — who are reversing the house edge — then halting their game play.

In a previous article I described how reversing the house edge requires the ability to track the advantage as events unfold. Most people who play against the casinos leave with losses proportionate to the time spent and amount wagered. This is because a house edge consists of structuring a mathematical edge in a way that compounds money at attractive rates of returns.

While there are anomalies that present negative expectations for the house and positive expectations for players — these can not be exploited without a process that uncovers when the edge is in your favor. Given the huge potential of structuring an edge in environments such as markets — there’s no reason to select more difficult environments that present limited potential or prohibitive oversight. That’s because trading markets offer many more opportunities to structure a house edge.

Advantage Programming Solution

In this article I present new methods to detect the mathematical advantage within the framework of an anomaly detection solution. Detection of anomalies have diverse applications in a variety of games of skills, in resource driven enterprises and trading markets where the outcomes of unfolding events are summarized in time series data. My solution radically reduces market information available in the clouds into information footprints so that anomalies of interest can easily be detected.

Described below are the mathematical foundations, which are components of a concept I have call advantage programming. My blog contains additional details, which one can use to gain deeper insight into each component.

Backwards Induction

Backwards induction is a form of mathematical optimization using concepts such as dynamical programming. Game theory, the second major component, is more frequently used in problems involving multi-player optimization. Advantage programming uses advantage tables as a related rates solution. Information is transformed into 6 advantage classes instead of a specific variable rate of return. View the 2nd column of the table in Diagram 1 to observe those numbers or this page to review how I reduce a larger set of numbers into this limited set of numbers which determines the controls for variable rate compounding.

The mathematical advantage will always be higher — when money is compounding at a higher rates of return. This simple truth means that only anomaly cycles which present an edge that is compounding within the acceptable range are considered as useful solution spaces to participate. Therefore, structuring when to participate requires defining both starting and ending points in time.

Markets have cycles in which the unfolding events can move from highly favorable to unfavorable dynamics in both upwards and downwards price dynamics. The mean value theorem (MVT) — offers a simple and powerful method which makes it possible to describe the peaks and valleys based on curves which are also located between two points. This features make MVT useful for mapping the advantage to a curve.

Optimal Stopping Solution

The areas labeled a to d on the curve in Diagram 1 defines the two points which illustrate the partitioning of our entry and exit boundaries. Our game strategy involves repeatedly using partition boundaries to decide when to participate or not. How do we know the information footprints within the partition are sufficient to help us generate attractive performance or not? This requires understanding the concept called optimal stopping theory.

Diagram 1

The simplest way to illustrate optimal stopping using the mean value theorem is to understand how drivers receive traffic tickets for speeding. Assume that the area between points a to d exists on a highway with a 55 miles per hour speed limit that is being monitored with radar. After communicating with the traffic officer at a the officer at d pulls you over and gives you a traffic ticket for driving 70 miles per hour sighting the mean value theorem. How did the officer know your car was speeding?

The mean value theorem says that you can not average a certain velocity — without actually having reached that velocity at some point in time. A search on the combined key words “mean value theorem’ and ‘speeding tickets” will provide numerous examples how this major theorem of calculus relates values of a function to a value of its derivative to accurately determine average velocity between two points. The point is — the officer does not have to estimate the probability that you are speeding because he knows you are over the speed limit.

Anomaly Cycle Detection

Here’s how I use Diagram 1 with the same mathematical process — to help reverse the house edge. Observe that the curve has 3 colors which are green, yellow and red in which each segment can be labeled with letters a-c, c-d, d-b. This results in three classification considered as — the good, bad and ugly respectively. As in the above speeding ticket example, assume the area between same two points a and d, as in the speeding ticket example, represents data described as advantage classes which are derived from market prices.

Instead of using the mean value theorem to identify cars that exceed the speed limit — we use the same process to identify when the advantage meets our optimal control thresholds. This partitions the cycle of three anomalies into two classifications consisting of 1′s for those that meet the control and 0′s for those that do not. Let’s look at both examples when 1′s define the solution space of the partitioned area.

In the example with the speeding ticket, velocity is measured in miles per hour. In the one where we are structuring a house edge, velocity is measured in the advantage relative to a specific time interval — which is a related rate associated with variable rate compounding. In both cases, the measures are derived by calculating the mean value theorem of a velocity vector. Velocity is speed with a direction and can be correctly calculated with a variety of measures.

An important aspect, and also the purpose of this process, is to define partitions in which the solution space is highly favorable — with a simple counting system. The benefit of using an advantage class instead of an actual return for the period is that a limited set of numbers can be used to define an entire universe of market dynamics. Also, do not assume that we are buying at point a then selling at point d. Trade execution strategy is another issue — as opposed to a simple buy and hold approach.

The idea of a house edge is to systematically compound money without taking a lot of risk — per risk taking event. This requires the ability to partition risk taking events so that individual risks are small relative to total risk capital. In a purely mathematical model — it’s possible to operate on a variety of different scales — so it’s not necessary to have casino resources to operate a house edge.

In trading markets — the high level of variability in price dynamics requires a way to transform information into the curve described by Diagram 1 — without introducing time lags. Here’s how I do it.

Edwards Transform

The Edwards Transform consist of several components which automatically navigates through a time series of market prices deriving the mathematical advantage — including information footprints outlined above which are required to implement it. The full details of this unique tool are outside the scope of this article. However, I will summarize three of the important concepts it uses and provide references to models, which share similar purposes or features.

• When I solved the drunkard’s walk problem — I realized the need for 2-d transform model to detect curves in market data via parameter space evaluation. In Diagram 2 is an image with 2 ellipses, which represents the output of my model. While the Hough Transform is a 1-d model — it detects objects such as a (e.g. line, circle, etc.) and arbitrary shapes including curves.
• Finding favorable anomaly cycles requires a specialized algorithm with the ability to sequentially uncover cycles with specific properties using pointers or other methods. Cycle detection algorithms like the tortoise and hare algorithm are also a form of cycle finding algorithms. Both Floyd’s and Brent’s algorithms are designed to detect cycles in a list of numbers.
• The race track principle is a theorem of calculus, which says that if horse A always runs faster than horse B, and if they start a race at the same place and time, horse A is bound to win. That simple statement is from this url which also explains its relationship to the mean value theorem.

Diagram 2

Markets typically have huge trading activity, readily available data and few restrictions on entry and exit times. The ability to enter and exit markets any time they are open — is equivalent to having the ability to do in-play betting. In-play betting means that you can place bets after a race has started. Before a race starts you can only predict or guess. However, after a race has started — you no longer have to predict or guess as you have other alternatives including the race track principle.

The race track principle implies that if one horse has a strong lead — and keeps that lead — it will win. Waiting until you actually have an edge — before betting — then exiting if your edge no longer exist is the simplest way to structure an edge. Why? If we can limit our in-play subset to a time where our horse has a stable lead, we have a sufficient edge to make money without being concerned about what happens over the course of the entire race.

Unfortunately, you’re unlikely to find betting opportunities that allow you to use this simple principle at racetracks. Fortunately, in trading markets — it’s possible to structure a house edge using the same conceptual strategy. However, the challenge is no less difficult than solving the drunkard’s walk. Why? Structuring such a solution — involving market dynamics requires a way to decipher noisy information on the fly. I have merged the concepts on this page into a self organized model which achieves that goal.

Self Organizing Model

The key feature of Self Organizing Market Entities (SOME) is, it is a self organizing model. The model automatically searches time series on a row by row basis, creating partitions — coupled with information footprints from the Edwards Transformer that contains the pertinent data such as the velocity vector, velocity direction (up or down), mathematical advantage, in-play race and other performance details.

Forget for the moment that our race analogy is a proxy for market dynamics. Assume that the race is evolving on a patch of land in which the two competitors are being tracked with the race track principle from a starting point labeled A in Diagram 3. The finish line in the same diagram is labeled point B. However, point B is unknown at the start of the race. The entire racetrack path on each patch can now be described by adding the 4 labels in Diagram 1 — which gives us the following set of 6 labels: A, a, c, d, b, B.

Earlier I illustrated how the mean value theorem was used in our optimal stopping method to determined when 1′s would be assigned to the area on the Diagram 1 curve labeled a to d and zeros elsewhere. Those optimal points of the anomaly cycles are equivalent to the in-play subset. The advantage is derived on each row and will be higher in the in-play subset than elsewhere due to our optimal stopping method. Still, we need a second optimal stopping method for point d. Why?

After point c in Diagram 1, temporary periods of negative compounding which typically follow periods of positive compounding will occur. It’s very tricky to distinguish between periods which might be temporary (a bad anomaly) and those which might be permanent (an ugly anomaly). That’s because market dynamics can be highly variable which makes it difficult to represent information so that it can be determined whether the mathematical edge is still be used in a stable environment.

I’ve found the best way is to use the contrasting positive and negative factors as role playing characters in a self organizing solution that includes optimal stopping method which uses the racetrack principle to determine point d. In Diagram 2, two ellipses serve as pointers for these role playing characters (RPC) using the key attributes — proximity, velocity and size in a variant of racetrack principle.

In keeping with our focus on compounding and the first image in this article we used the Hare to represents the black ellipse which implies positive compounding and the Tortoise as the red ellipse for negative compounding. The ellipse boundaries and position dynamics are based on a mathematical expression of whether the edge is increasing, stable or diminishing.

This means that, whether market dynamics are moving upwards or downwards, negative compounding can be expressed as an unacceptable level of diminishing returns including uncertainties. During the in-play period — point d is triggered via a second optimal stopping method designed to limit the in-play subset to stable periods.

The mathematical advantage can used to trigger points a and d, because it’s numeric properties are very powerful. However, as humans, we typically need visual models to boost our perception of model dynamics to higher levels. That’s why I run self organizing models where my two entities appear over market dynamics. They automatically self adjust to upward and downward trends and define the in-play subsets. The information footprints of each visual snapshot are reduced to a numeric, then stored adjacent to the advantage variable.

This makes it possible to playback information streams, like movies — consisting of millions of snapshots in which my role play characters compete for domination — with the advantage being displayed across a wide variety of markets and time frames. Casinos have a stable game environment — while market environments can vary enough that an advantage in an unstable environment will diminish returns. What I’ve learned from watching my information streams — is that knowing whether the advantage is occurring in a stable environment, is important to structure a house edge.

Racetrack Principle

This brings us back to the racetrack principle which expresses the same relationship — but which is conceptually easier to understand using Diagrams 1 and 3. The points a to d in Diagram 1 represent a in-play subset where the Hare is being tracked relative to the Tortoise. This subset represented by the horizontal time line which connected to the two middle pointing arrows in Diagram 3. Assume that, at the time the in-play race starts — the Tortoise is at the point labeled T and Hare at the point label H.

Diagram 3

While the Hare and Tortoise start the race at the same time at point A shown in Diagram 3. However, by the time predetermined thresh-hold has been met at point a the Hare has a significant lead on the Tortoise which is illustrated as the difference in the first two arrow pointers. Again, the beauty of using this approach is the fact that all we have to do to make money in the long haul is to be able determine points a to d which represents the in-play subset as the races unfolds.

Frequently, there are partitions in which A to B are represented entirely by zeros — because when the advantage class is too low — the optimal stopping criteria will not trigger an in-play race. Also point d is typically triggered by how the distance between to two competitors diminishes which is most efficient method for limiting the in-play subset. This occurs because discontinuities (sudden, erratic and unusual sharp dynamic) in Rolle’s Theorem, which is a proof of the mean value theorem, are considered a violation of it. Therefore, such dynamics will accelerate the exit of the in-play race.

Role Playing Characters

Self Organizing Market Entities (SOME) uses role playing characters as pointers to detect the anomaly cycles described — by coupling two optimal stopping criteria. The first is the mathematical advantage. The second is a visual representation that implies a mathematical advantage via the racetrack principle.

Furthermore, it would make little difference whether the roles the two characters are defined as are 1) positive and negative compounding or 2) reward and risk; because the two entities function as pointers which are called subroutines that input the exact same information footprints in the in-play registers that are used for performance evaluation.

The key insight in partitioning in-play subsets — is that it’s a bit like distinguishing the walking patterns of a drunkard who has both stable and erratic footprints. The best question to model the solution is: How do you represent contrasting patterns in the presence of noise — so the start and end of the stable pattern can be detected?

In this blog I have answered that question using a solution that means — the collective forces of market participants is still supporting the same direction as your entry position. That support, which is implied by the continual lead of the Hare — will typically be more than sufficient to enable you to exit the in-play race with attractive profits.

Let me point out that it’s possible to use the same approach to develop an almost unlimited numbers of role playing characters and betting games using the market environment. This means the potential exist to use role playing characters in simple and intuitive ways to develop a house edge — in which each market is a stand alone profit center.

Here’s why. Typically, the public is offered very easy ways to lose money. For example, spread betting theme has minimum margin requirements — but participation is at a disadvantage if you consider that it’s a lot more complex to win when you have to select a specific point spread — than with simple directional trading. It’s also a lot more complex to select binary trading bracket that must be over or under a specific target point to win — than it would be without such rules.

When so many market games are packaged in ways that make winning more difficult for market participants, I believe there is a huge potential in showing people exciting and fun ways to reverse the house edge in their favor. Following are a few examples of how I will use role playing characters in resource management games that enable users to monetize market information.

Massive On-line Role Playing Market Games

One way is to transform the two ellipses into actual role play game characters such as, a Hare and Tortoise. Another is empowering role play characters to engage in more visually stimulating environments such as a race track. The ability to design visual models that accelerate learning can attract and retain users in diverse game worlds that range from fantasy environments involving virtual goods — into popular social games. Two examples are outlined below.

• Rate my Edge — This game would be a twist of Rate my Face — the original Facebook theme that helped mushroom the social media industry into what it is today. My design here is for a fun, intuitive, and easy-to-use as market games will help a broad audience learn to monetize information streams by rating their market edge in a team setting.
• Gem Farmer — Our goal is to create an addictive interactive social drawing game which challenges players to take turns drawing pictures that represent the key factors required to develop a house edge. So players actually gain the opportunity to increase their skills in how to monetizing market information — by working on competitive teams that attempt generate the best return performance.

One inspiration for my Gem Farmer design was Draw Something , an interactive social drawing game challenges players to take turns drawing pictures and guessing the words they represent. I noticed that Zynga recently bought the OMGPOP for over $200 million due to an astounding surge in downloads for their Draw Something mobile app game.

My role playing characters and racetrack analogy offer examples of how introducing radically different visual dynamics that improves the recognition of the optimal solution space. Using a similar interactive and collaboration framework, such as popular social media games, because of user interface familiarity — can make the transition from addictive social to serious games easier.

The beautiful thing about a casino style house edge is that the focus on replicating a strong edge over and over again in a process where each game is it’s own profit center. While it’s really possible to create a house edge in the market environment — there is no simple algorithm to do it with. It’s not the size of available risk capital — but your ability to efficiently monitor and control your exposure to risk — as you systematically take risk that are small proportionately to your available risk capital.

I believed that interactive resource management games can boost perception by transforming murky information into clear and concise information. Information has been described as a reduction in uncertainty. However, in the financial field, such reductions have never been pushed as far as they need to go — then forced even further — so that one can see how to develop a house edge.

While this article includes discussions related to partitioning the in-play subset — which represents the optimal solution space — how to efficiently use that space is a different subject. In a future blog post, I’ll discuss that issue along with the financial management aspects required to structure the house edge in your favor.

Reversing the house edge requires turning disadvantages into advantages. Aesop’s tale about the crow and pitcher offers us a simple idea on how we might solve that problem.

A thirsty crow found a Pitcher with some water in it, but so little was there that, try as she might, she could not reach it with her beak, and it seemed as if she would die within sight of the remedy. At last she hit upon a clever plan. She began dropping pebbles into the Pitcher, and with each pebble, the water rose a little higher until at last it reached the brim, and the knowing bird was able to quench her thirst.

Summarizing Information

In fields where we need to evaluate information such as trading/investing, casino games and games of skill — you can compound money more effectively by understanding why and how you should use a simple numeric variable called the mathematical advantage.

The advantage is a single numeric that implies the magnitude of mathematical expectation whether it is positive or negative. As risk taking situations unfold the advantage concisely summarizes your edge — given the current dynamics. Hence, you can benefit by acting on it reliable powers — both as as a profitability measure and as an indispensable tool in creating a house edge.

Now imagine that the crow in the above image is using a pebble that expands two to three times or more as it hits the water. Of course the water would reach the crows beak faster. The advantage provides a similar benefit because when it is higher — using it enables equity curves to grow faster over the long haul.

Using the Advantage with Counting Systems

Let’s look at an example of how the advantage works with card counting in the casino game of blackjack. The above table is using what is called a Hi_Low count introduced — by Harvey Dunbar in 1963. Card Counting was identified in the 60′s as a way to gain the advantage of the house edge.

The benefits of a simple 1 0 -1 count is that keeping track of cumulative score of the advantage as the cards unfold is so simple that almost anyone can do it accurately. Each card that is dealt is assigned the point value number (1 0 -1) that is adjacent to the column entitled rank. As the triangle shows these three numbers map to a positive, neutral or negative contribution by the individual cards as they are dealt.

Adding the individual counts reflects the cumulative total which in turn represents the player’s current edge. Teams that use this simple count do not have to use MIT students as card-counters. Instead, they can train any number of players in this card counting method who could play just as many card hands an hour as those with a higher mathematical background — because the simplicity makes the task is prone to fewer errors than more complex counting systems.

Increasing Performance and Reducing Cost

This benefit has enormous potential outside of the casino environment where team play is not forbidden. The potential is partially due to the cost savings and ease with which one can put together larger talent pools to run operations. Suppose the efficiency is further increased by using computers. This would reduce most task to overseeing game dynamics and/or operations. While it’s not permissible to do this with online casino games — it is with trading markets.

Assume that talent required to run a trading process that generates one million can be done for less than 1/2 the current personnel cost while improving performance. How is this possible? The magnitude of the pay scales between casino and Wall Street workers is different because of the tasks and environments. Using the advantage to run trading operations — not only changes the operational task — but improves control which makes it possible to significantly improvement performance.

Performance Control System

If you increase the temperature controls on a control thermostat upward above the level of the current room temperature — the heat will go up and vice versa. Likewise, when the advantage is higher it means money is compounding money at a higher rate. Almost everything else written about the advantage besides this is dependent on how it is derived and the dynamics that occurs as the game situation unfolds.

In almost any game of skill that unfolds dynamically including trading/investing — the advantage can be derived from information without repeatedly sorting combinations or estimating probabilities. Once the relationships between favorable game play and the advantage is known — it’s possible to develop a function table similar to a Hash Table to proof it.

The blackjack card counting system discussed above has not seen significant improvements in over 50 years. This feature is due to reducing the advantage into a related rates solution. This is similar to the relationship between Celsius on Fahrenheit scales where both provide temperature reading — but we tend to prefer the scale we are accustomed to. How would a related approach work in trading markets? Given the high level of variability — a comparable degree of granularity as used in blackjack is sufficient to reverse the house edge.

Converting the advantage into a counting system that consist of a half dozen whole numbers makes it possible to quantify the trading edge across the universe of markets. Our counting system is summarized to the right of the image in Diagram 2. In the table (x) is the advantage and f(x) our count called advantage classes. How it is derived from the components of the advantage is summarized on this page.

The number on the face of the black dice provide the positive — and that of the red dice the negative components. Therefore, the number of the black dice minus that of the red equals the advantage class (for example 6 – 3 = 3). As events unfold the current advantage is always reflected in the last number. The ellipse diagram above the dice offers an equivalent visual explanation. How to understand it and other visuals that will help to reverse the house edge in our favor will be the subject of an upcoming discussion.

by Harry Edwards

Hundreds of millions of people helped the casino and financial industries generate over a $100 billion in the USA last year alone. With the global array of online gaming, trading markets, lotteries — the money lost taking risk on negative expectation situations — while huge is continuing to grow. The intent of this article is to outline how start-ups can make money by reversing the house edge in favor of customers looking for increased performance. Who isn’t?

To Lionize means to treat one with great interest or importance. The idea here is that a huge potential exist to increase the benefits of risk takers by giving them improved performance and quality services. The benefit to you of giving customers the lion’s share is it attracts and retains customers by providing them with better monetary results.

While tokens, rewards and recognition, games and similar treats might be a real turn on for social media and game audiences — the so-called gamification approach might be a sufficient motivator to increase customer retention. However, such features will fall short with a bottom line orientated audience looking to generate — real money.

Lion’s Share

The lion’s share is an expression which develops from a number of fables ascribed to Aesop Fables with the basic situation of an animal dividing up a prey in such a way that it gains the greater part of it. A fox joins the lion and donkey in hunting. When the donkey divides their catch into three equal portions, the angry lion kills the donkey and eats him. Then the fox put everything into one pile, leaving just a tiny bit for herself, and told the lion to choose. When the lion asked her how she learned to share things this way, the fox replied, “From the donkey’s misfortune”. The source of the above story variation and art below is wikipedia.

Why?

Setting up a start up firm that helps investors, traders and risk takers make money gives you an opportunity to outperform the existing process used by current participants. While numerous inefficiencies and inequalities currently exist — few significant remedies are being offered to financial customers. Conflicts of interest exist that are similar to the donkey taking food out of the lion’s mouth. However, the lion is the customer putting up the money — while financial firms with the exception of casinos are offering to increase or maintain it.

If your start up designs a way to increase the lion’s share — you can attract and retain customers who are interested in increasing their return performance. And the best part is the existing risk taking fields are 1) very lucrative as demonstrated by hedge funds fees and 2) the increase you are going to use to deliver customers greater performance is the house advantage. Hence, you can increase the Lion’s share — out of pockets of your competitors — who are burdened with the belief that the best way to boost their own bottom line is cutting it out of the lion’s share.

How?

The idea behind Lionization is to create a really big edge — by boosting monetary performance. For example, a start up can do this by creating transparent remedies instead of tolerating customer dis-satisfactions with the financial industry. It does not matter whether the competition feels it is their job or not. Your job is to increase the Lion’s share.

Here’s how a football coach introduced a new remedy in the life insurance industry that turned into billions with the theme buy term and and invest the difference. There are plenty of opportunities left to introduce concepts that improve customer benefits that could have an even greater impact in the financial fields. Below are three concepts that can help to reverse the house edge in favor of the customer.

• Private sector insurance to provide safety of all investment / trading funds that extends beyond the limit’s of government insurance such as FDIC.

• Execution service — which lowers transaction cost, eliminates misuse of funds, restricts disclosure of positions, and uses deposits only for the customer’s interest.

• Introduce mechanisms that reverse the house edge in favor of the customer — using the advantage in a process similar to a casino to improve performance.

Maybe this combination of task is not currently in the job description of firms in the industry. Ask yourself — if you were an employer forced to choose between which of two employees to let go — which would it be; a) the employee that just told you — it’s not my job or b) the employee that did the job — he saw needed to be done. Just as employers are attracted to employees that do the jobs they recognize need to be done — customers are attracted to entrepreneurs who remove obstacles hurting their bottom line.

Lionization is based on the concept that increasing customer profitability will attract and retain customer loyalty faster than anything else. In a lucrative financial industry dis-satisfaction is at record level. The opportunity to benefit from from the donkey’s misfortune is ripe.

Lionization is a disruption tactic that trumps other game strategies because it offers more significant benefits to customers. Just as the lion — is at the top of the food chain — monetary issues are the #1 concern for customers.

This blog is part of a series that will outline the concept of lionization so that followers can understand how to create start ups that use it to increase market share. Details on how you can collaborate and use this concepts including mechanisms to deliver a house edge will follow.

The advantage is a ratio that can be dynamically used as a control measure to limit participation to the most optimal situation or environment. It’s highly favorable properties are described in this blog here. The purpose of this article is to explain how mapping the advantage to a particular environment called a patch — can give you a powerful performance edge — which will compound money faster than alternative approaches.

The normal curve and the two diagrams below have in common a single peak that is labeled as point c below. The adjacent theorems explain the features that will occur when such peaks or valleys exist. A generalized measure of performance that can be mapped to almost any situation or environment by assuming that favorable performance occurs before c and unfavorable after it.

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To do this we need to be able to extract the information that will enable us to determine when assets will accumulate faster (same as compounding) in the specific environment of interest. Here extract means to reduce those factors into a concise formula suitable for determining whether we do or do not have an advantage. This process becomes simple after we are able to repeatedly use the same measure to give us a clear advantage.

Mapping Wealth Distribution to a Curve

In reward to risk related situations — when the advantage is higher the reward will also be higher while the risk will be lower. This recurrent theme is easily applicable to physical models where the ratio and magnitude of wins and losses are measurable between two intervals such as a and b described above. What makes this model attractive is the simplicity with which information between the interval points can be dynamically measured.

Much of the power in the model has to do with the volume of evidence related to human conflict to capture and secure the most favorable land masses to grow their societies. In short, military conflicts have typically been a key factor in determining how societies obtain and/or keep various land patches. We now turn to wealth building within societies which can also be defined as patches — typically protected by military powers — as proved by historical evidence.

Human competition to gather wealth is different from — animal foraging as discussed in Marginal Value Theorem. As our societies have evolved — those focused on risk taking situations have sequentially dominated both local and world economic wealth. What is known as the Pareto principle is often used to imply that approximately 80% of wealth as defined by land ownership and/or income growth is controlled by just 20% of the population. Partitioning the 80/20 relationship with the same points as labeled in Diagram 1 — gives us a similar curve that we will use to illustrate concepts related to the advantage and patch dynamics.

Assume points a to c represents the top 20% as shown in Diagram 2 which is called Optimal Accumulation Theorem (OAT). The curve is the same as that of the Marginal Value Theorem — but you can not wander freely due to what is explained above — about how such patches are protected within our human societies.

You don’t get to pick the street you are born on — which could determine your initial place on the wealth distribution curve. However, after birth what you learn about risk taking — combined with your focus on taking smart risk — will typically be the determining factor where you end up on the curve. Most people never accumulate the interest or skill sets — which is part of the reason for the disparity. This can be remedied by increasing risk taking skills and using a credible process that works no matter what part of the curve you are born on — or are on now.

Let’s say you are at point b on the OAT patch. Here’s our big idea. We show you a risk taking process in which you can learn how to use the advantage to trade a wide variety of markets. Obviously, a serious effort would be needed to accumulate and convert your knowledge into cash — but you would have a huge edge — with the capacity to do that. Your challenge would be to understand the math behind the physical model, how to properly use it — and to develop a team to make money using the advantage in trading markets.

What’s the logic behind the math?

Liquid market assets typically have highly fluctuating values. The nature of the fluctuations create such visual problems that most existing mathematical models and/or traders do not know how to calculate or use an actual advantage. Most have to estimate it — or use other means. Both these attempts will distort points a, b and c. The missing link is in the logic not the math. Same reason brilliant mathematicians failed to solve blackjack over the centuries until the 1960′s. This presents limitless potential — because it’s like being in a world where the game of blackjack exist — but card counting as the solution has not been discovered yet.

Sure, it possible to make money in the markets without using an actual advantage, but the performance would be less attractive than if it were precisely calculated. Additionally, because of how market information fluctuates — defining and using the advantage on a similar basis as casinos requires reducing the level of non-redundant factors so that the outcomes can be dynamically controlled.

Map Extraction is a way to dynamically value information streams so that money can be extracted via a compounding process without complex assumptions. Information is partitioned into equivalent sets like a deck of cards. Hence, higher levels of disorder and randomness in markets — are physical dynamics which appear in the same region after c in Diagram 1.

Point d which exist if point c does and arrives after it — can be used as an optimal control point to maximize positive and minimize negative compounding. If you learn how to repeatedly use it to profit and to exploit enough favorable opportunities — to move toward the top 20% of the curve as shown in Diagram 2. What follows in subsequent articles will be more details on how you can use knowledge of these concepts to navigate that journey.

The advantage is ratio of mathematical expectation that can be dynamically used as a control measure to limit participation to the most optimal situation or environment. This makes it a crucial variable for summarizing all sorts of risk taking situations especially in military and business environments.

• The higher the magnitude of the advantage — the more favorable will be the outcome and the lower the risk of loss.
• The reverse is also true — which means that the advantage can be used as both a profit and loss function.

The following animation depicts this relationship with the variation around the normal curve — which reflects on the magnitude of risk as shown by the vertical bar adjacent to it.

Figure 1

In business situations — when the advantage is higher money is compounding at a faster rate and with lower variability. This means that if you know the advantage — and how to use it to dynamically value information — you would be able to make make money over the long haul with fewer assumptions than is otherwise possible.

Additionally, the advantage can be used across all asset classes, values and time frames — typically with only dozen or so advantage values. The benefit in having this level of simplicity is that more people can easily evaluate and use the measure to make smarter decisions with markets, business ventures and/or reward to risk situations.

One of the key purposes of this blog is to explain and demonstrate why and how the advantage can typically be generalized to help you capture the competitive advantage in almost any situation and environment more efficiently than other decision making factors.

The causes of the drunkard’s walk are market noise, randomness and murky market dynamics. But how would you define it mathematically? Take a look at the diagram below. It’s not typically obvious which points peak — then start a decline or bottom and then start and advance with market prices. Smoothing markets introduces time lags — while traditional representations leaves the points labeled as a, b and c camouflaged. In this article — I’m going to show you the solution and the limitless potential of it.

The above diagram illustration of Rolle’s Theorem was offered by Michel Rolle in 1691. At the peak, the first derivative between the two distinct points A and B is zero. But the peaks and valleys in market prices are confusing. Can’t see point c. You can’t repeatedly determine points a, b and c without distorting those points — which smoothing does by introducing a time lag. Life with the drunkard’s walk means attempting to determine point c — which is useful for optimal stopping — is an unsolved problem. Given the high variability nature of market dynamics — it’s no wonder most people have difficulty finding a simple market theory that works consistently enough for them. The simplest and most powerful solution has remained hidden due to the drunkard’s walk.

Time Value of Money Theorem (TVM)

The Time Value of Money dates at least to Martín de Azpilcueta (1491–1586) and is the central concept in finance theory. The concept allows the valuation of a likely stream of income and/or cash flows — both even and variable in nature between specific points in time. Variable sources can also be considered such as interest, projects cash flows and so forth.

Liquid market assets have fluctuating values. The key is to be able to dynamically value information streams so that money can be extracted via a compounding process without complex assumptions. This requires a unique solution that determines when the time lines should start, stop and when a shift of position should occur. This is the case because to know whether money is compounding for — rather than against you — requires a timeline so that the two points defined as a and b in Diagram 1 exist. Point b always unfolds sequentially in time — and positive compounding occurs naturally between points a and c. I will summarize a theorem and process that makes it possible to optimize TVM via the identification of the crucial points on timelines including market information streams.

Optimal Accumulation Theorem (OAT)

After point c in Diagram 1 dimensioning returns will occur — followed by negative returns. The challenge is to be able to classify system dynamics so that as little time as possible is spent attempting to accumulate resources after point c. Our theorem states: “In system dynamics which vary from favorable to unfavorable as defined by point a to b — there is some point called d — beyond c which presents an unacceptable risk.”

In order to optimize the rate of asset accumulation — the identification of point d is required to sequentially convert market information into variable returns streams. While the returns will contain both positive or negative results — classification for the information also enables strategy to limit the negative return streams. With fixed rate compounding — what is called a periodic “accumulator factor” is static and so is the conversion frequency of the compounding period.

The optimal accumulation theorem is an umbrella theorem which covers risk /reward conflicts in human and animal domains. While the scope of this article does not permit its discussion in more detail — readers will grasp the details in the examples that follow using Marginal Value Theorem and Information Foraging which are related concepts. MVT says a marginal rate forager should leave the current path once the marginal rate decreases pass point c in the diagram 1.

A typical illustration is competitive apple picking by humans. On each new apple tree, the number of apples picked per minute is high but decreases fast with time. Continuing to pick apples until the last few apples can be shown to be quantitatively suboptimal by the MVT. In OAT, the competition can take place on protected patches involving human conflicts that can have an extended range of position or negative outcome. It’s a completely general framework applicable where system dynamics as sequential patches can be mapped by partitioning as shown in Diagram 1.

Accumulation Rate Optimization (ARO)

Instead of a fixed accumulation factor — Accumulation Rate Optimization (ARO) uses a variable accumulation factor in an optimal compounding process. Point d as well as the classification of points between a to b are used to maximize performance by decreasing the time spent after the accumulator factor passes point c. Of course point c remains unknown until after it has occurred. An exit in the area of d is practical without prediction or probability estimates. The solution to drunkard’s walk makes discovering c and d simple classification problem. Optimizing positive and negatives returns is therefore a matter of maximizing time in partitions with a positive accumlation factor and minimizing time in those where it is negative.

The MVT implies that a forager should leave the current patch once the marginal rate decreases pass point c in the diagram 1 (which is similar to an MTV diagram). In ORA, optimizing the rate asset accumulation — is an optimal compounding process in which the patches resemble Diagram 1 — where a to b represent the timeline. The best accumulation factor for optimal compounding is the same advantage formula used in blackjack — as it defines mathematical expectation.

Hence, the advantage is able to confirm the correct mapping from a to b. How? Positive and negative return streams appear in their appropriate location in each patch is shaped as redundant curve. Each point exist within partition that makes it easier to determine point d. Additionally, each market patch is self-organized so that both the timeline and time spent in each is optimized by an actual — rather than estimated advantage.

What would life — be like — without the drunkard’s walk?

Imagine your financial life changed by a solution that enables you to use an optimal compounding process. Instead of debating or protesting about the inequalities in the financial industry — you could level the playing field. What makes our solution potential limitless is the ease which those without finance or math background — can do exactly that. How? Perceive how the concept works — then as our affiliate — learn to use it to control your financial destiny by helping a world full of people looking to do the same.