Various ROI tables are available to participants, and you can even design your own ones. If you are conservative, you can choose one offering a maximum return of 10% (for finding the exact value of a winning number), a 54% chance of winning on any transaction, and a maximum potential loss of 4%. This table is safe enough that we will allow you to "trade" on margin. Another interesting ROI table offers a maximum return of 330%, and the same 54% chance of winning on any transaction, with a maximum potential loss of 4%. Keep in mind that this return is what you can make (or lose) in one day, on one sequence. New winning numbers are issued every day for each life sequence, so your return (negative or positive) gets compounded if you play frequently.
If you are a risk taker, you may like a table offering a maximum return of 500%, a 68% chance of winning on any transaction, and a maximum potential loss of 60%. Or another table with a maximum return of 600%, a 80% chance of winning, but a maximum potential loss of 100%. To download all the sample ROI tables discussed in this presentation, click here.
All the sequences currently offered on the market consist of 8-bit numbers: each winning number (a new one per day per sequence) is an integer between 0 and 255. We will soon offer 16-bit numbers. By design, all ROI tables (even if you use a customized one) offer an average return of 0%. This is true regardless of the sequence you are playing with: sequences and ROI tables are independent.
Below, we explain how this works, using a real-life example.
How it Works: the Secret Sauce Here is an example of a sequence being tested in our lab. It shows how the winning numbers are computed, for the sequence in question. The purpose is to illustrate the mechanics, applied to one of our 8-bit systems. The 32-bit version offers more flexibility, as well as potential returns that can beat those of a state lottery jackpot. Our sample 8-bit sequence is defined by the public algorithm below.
Start with initial values x(0) and y(0) that are positive integers, called seeds.
Then for t = 0, 1, 2, and so on, compute x(t+1) and y(t+1) iteratively as follows:
If 4x(t) + 1 < 2y(t) ThenThe Winning Numbers
y(t+1) = 4y(t) - 8x(t) - 2
x(t+1) = 2x(t) + 1
x(t+1) = 2x(t)
y(t+1) = 4y(t).
The winning numbers for a particular sequence, start at a specific machine-generated iteration T that no one knows, not even the platform operators or software engineers. Typically, T > 30,000,000 and can be chosen randomly. The iterations represent the time. The future winning numbers are always integers between 0 and 255, and they occur only at iterations t = T, T + 8, T + 16, T + 24, and so on. Their value at iteration t is x(t) - 256 x(t-8).
Past winning numbers are those occurring at iterations t = T - 8, T - 16, T - 24, and so on. The last 2,000 of them are published before the sequence is available (life) on the platform, allowing participants to predict future winning numbers, using the public algorithm or by other means, and make (or lose) money. For our above test sequence, the 2,000 past winning numbers in question are available in this text file.
For each sequence, one new winning number is published each day. So, the time unit used here is 3 hours since one day is 8 x 3 hours. To win the maximum amount, one must correctly predict the winning number attached to a future day. Good and fair approximations also result in a gain, albeit lower. These gains and losses are explicitly specified beforehand, in very precise ROI tables, see below. Finally, by design, the winning numbers are not auto-correlated; they appear to be independently and uniformly distributed (more so than many software-generated pseudo-random numbers), and do not exhibit any known or visible pattern. In short, they look totally arbitrary, yet generated using a rudimentary formula.
Using Seeds to Find the Winning Numbers
Most participants are likely to do random trials to find or approximate winning numbers. The few who want to use the public algorithm need extra information to compute winning numbers, and even then, their chance of finding such numbers is virtually zero, due to the tremendous amount of computations required. In short, you need to know the seeds, and when to stop your computations. The stopping rule is simple: you stop when you have found numbers that match the past winning numbers publicly available. Then you known for sure that your next number will be a winning one.
We offer information about the seeds in two different ways:
We guarantee the following:
Of course, you could be a mathematical genius, and somehow figure out what the private algorithm is, to make your computations far more efficiently. This is highly unlikely to happen. There is a considerable amount of very advanced, unpublished mathematical research that has been done to make our systems robust. Also, we regularly change the type of sequences that we use in our system, every few months or so. And we work with white hat hackers (paid to hack our system) in order to identify potential vulnerabilities.
Finally, seeds that lead to unpredictable winning numbers (simulating an efficient market) are known as good seeds. Of course, all the sequences that we offer are based on seeds highly believed to be good ones, and that have been run through a battery of statistical tests. Using sequences based on bad seeds would not hurt the players, quite the contrary, but it would make our system easier to crack and cause problems with the ROI tables, thus hurting us.
Proving that specific seeds are good or bad, is one of the most challenging, unsolved mathematical problems of all times. If solved, we would know for sure whether the digits of a number such as Pi, are evenly distributed or not. These mathematical concepts have been studied for some time, see recent material on this topic, here and here.
The ROI tables tell you how much money you will make or lose when submitting a number. Your ROI is a function of the distance between your submitted number z and the actual winning number x. The distance, also called error, is computed as follows: d(x, z) = min(|x - z|, 256 - |x - z|). It is always an integer value between 0 and 128. A pre-determined ROI is attached to each of the 129 potential error values. These ROI's characterize the type of risk that you are willing to take, and can be customized by each user, as long as the theoretical expected return (automatically computed in the ROI spreadsheet) is zero.
You will find these values in the ROI tables, available in spreadsheet format, here. Look at the second row in the spreadsheet, between column K and EI. The spreadsheet also contains 1,000 user-submitted numbers (simulations) with the ROI computed for each submitted number. Other summary statistics of interest are available in the spreadsheet: highest and lowest potential payout, chances of winning, and more.
This short presentation only features the tip of the iceberg. The possibilities are endless, including the implementation of:
Let's now look at how the money flows.
Managing the Money Flow
Managing the money involves subtracting or adding dollars to user accounts after each completed transaction. On a given day, how do we know whether on average, gains and losses will balance out, since we don't control the numbers entered by the participants?
Actually, we don't know. Sometimes the balance is slightly negative, sometimes slightly positive. However, by using fair ROI tables and good seeds, we are guaranteed to be flat on average. You can even compute the daily volatility resulting from the daily winning and losing transactions. Example: with 1,000 transactions in a single day, each one consisting of a $20 bet, the most conservative ROI table introduced in this presentation produces a theoretical standard deviation of $24, over a volume of $20,000. The most aggressive one produces a standard deviation of $314, still entirely manageable. These theoretical numbers have been confirmed by simulations, and are included in each ROI table, for internal use. When offering customized ROI tables, you might want to put a cap on the standard deviation being allowed.
More technical details are available here.
Vincent is a pioneering data scientist, mathematician, entrepreneur, innovator, investor, co-founder of Data Science Central, former VC-funded executive, author and patent owner. Vincent's past experience includes Big Data positions and consulting with Visa (fraud detection), Wells Fargo, eBay, NBCi, Microsoft, CNET, InfoSpace and other Internet startup companies (one acquired by Google), working on web traffic quality scoring, Botnet detection, ad arbitrage and business intelligence. Vincent is also a former post-doctorate research fellow at the University of Cambridge and the National Institute of Statistical Sciences (NISS).
He has published in Journal of Number Theory, Journal of the Royal Statistical Society (Series B) and IEEE Transactions on Pattern Analysis and Machine Intelligence. Vincent currently manages his own, self-funded data science research lab, along with his other corporate responsabilities.