Lionization — imagine a world where customers can reverse the house edge

by Harry Edwards

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.