Algorithms of Physical Wheels and Geometries of Computer RNGs

After clearly demonstrating on computer random-number-generated (RNG) roulette spins that a method yielded no better than expected results, the author of the method protested that the test results were not applicable because the spins were computer generated from algorithms, and thus, less “geometric” than spins from live, physical roulette wheels.

However, what is a physical roulette wheel but a mechanical, spinning algorithm, and what is a computer but a collection of geometrical objects?

Algorithms of Physical Wheels

A physical roulette wheel is simply an algorithm based on physical, mechanical variables: angular acceleration, angular velocity, friction, collisions, and gravity.  Newton’s Laws.  Input all the variables into the equations of motion, and you will get a precise answer.

The only reason why the results appears random to us is because we don’t know all the values of the variables precisely enough and are not able to calculate with them fast enough.   But if we did, we could predict the outcomes with 100% accuracy.  Indeed, Shannon, Thorpe, and the Eudaemonic Pie Team tried to calculate fair approximations on the spot in casinos, and they were able to beat “random” enough to win some money in the process.

Moreover, a basic demonstration in physics is to calculate a very fair prediction of where a ball will land in a roulette wheel.  It a standard lab exercise in angular dynamics.  Roulette spin results are completely deterministic, and to insist otherwise betrays a lack of understanding of basic physics.

So, to argue that a physical roulette wheel is somehow a source of more “geometric” random numbers than a computer algorithm is not consistent, because a physical wheel is but an algorithm that generates only apparent randomness.  The apparent randomness is entirely due to our lack of complete information. In fact, from a physical perspective, the live spin results of a physical roulette wheel are entirely deterministic.

Likewise, the order of cards in a deck or shoe is entirely deterministic, and they only appear random to us due to our lack of knowledge.  If someone had x-ray vision which enables him to see through the backs of the cards, the sequence of card values would not be random to him at all.

(Where a physical wheel may yield non-random results is if it has defects and tilts toward a particular region.  Or, if the dealer uses release tricks to manipulate the ball into the desired regions.  Or if the wheel is not completely balanced on its mounting.  Or the table on which it is resting is not perfectly level.  Etc.  In those cases, the results will show a clear trend and tendency, and the results won’t be characteristic of randomness.  Indeed, one can analyze results from live wheels to try to extract useful information about tendencies which arise from the physical imperfections of the wheels.)

Geometries of Computer RNGs

Likewise, computer RNGs have physical geometries. What is a computer, after all, but a collection of matter?  Silicon, copper, gold, iron, titanium, etc., all crafted together into components which have very definite and precise geometries.  The only difference is that these microprocessors consisting of  registers, transistor, resistors, capacitors, switches, traces, and a host of other electrical parts are of a scale that you can’t see with your naked eye.  But they have geometries as natural and physical as any larger-sized object such as roulette wheels.  Indeed, they have even more symmetry and balance than any large-sized object.  Even though an algorithm is generating a string of random numbers, what is executing the algorithm but beautifully geometric, micro-sized objects?

So, to argue that a computer RNG is somehow any less legitimate a source of “geometric” random numbers compared to physical roulette wheels is not consistent, because computers are composed of very real, physical objects composed of elements with definite geometries and symmetries.

Simulating Physical Nature

If, for the sake of argument, we admit the point that computer RNG cannot adequately simulate a simple, straightforward game such as roulette, then we have absolutely no hope of using RNG to simulate the incredibly more complex aspects of physical nature, such as nuclear decay rates, astrophysical collision rates, economic dynamics, climate studies, manufacturing failure rates, population mortality rates, enzyme kinetics rates, etc., etc.  Yet, in all of these areas, computer simulations have quite successfully used RNG to model the random aspects of their physical counterparts.

Perform Buffon’s Needle Experiment with physical needles or simulated ones, and the same value for pi will emerge, the more trials, the better.  Then why should physical roulette wheels yield different answers from simulated ones?

The fact is, from a mathematical perspective, it doesn’t matter where the string of numbers comes from, whether baguettes, needles, physical wheels, decks of cards, ping pong balls, many-sided die, drawn sticks, cosmic rays, electronic noise, thermal vibrations, switches in mechanical relays, transistors in computers, or registers in computer microchips: If the sequence of numbers satisfies the main characteristics of randomness, such as unpredictability, equal chance frequencies of all outcomes and between outcomes, and Gaussian distribution of event frequencies, then the results from any and all of them are mathematically equivalent on a practical level.