Randomness, Part I - "Random" dice

This is a three part series about randomness and predictability. For CASTrader, predictability of the stock market equals alpha. Unpredictability of the stock market due to randomness means CASTrader is a wasted effort. Given how crucial the question of the predictability of the stock market is to CASTrader, I thought I’d examine randomness and it’s cousin unpredictability in detail.

Try this thought experiment: a dice throw with non-loaded dice - how predictable is it? Is which face of the die that end up on top truly random? Think about your answer before you read on.

Random Dice

You probably think non-loaded “fair” dice throws are essentially random, and each face has a 1-in-6 chance of coming up. What if, however, you were allowed to bet on the dice before they come to a complete stop and the outcome is certain? At the instant in time where the die is rolling over an edge for the last time before coming to rest, you can be almost 100% sure what face will turn up, with a little knowledge of physics and dice geometry. Given odds that are based on the dice being random, you should be able to clean up. What about when the dice first hit the table? Given the exact rotational and translational speed of the dice and their geometry, the physical properties of the table along the path the dice will roll, a powerful, fast computer, and other such goodies, I’m guessing a good physicist/programmer could probably predict which faces will end up with a better than 1-in-6 probability.

Where is the randomness threshold?

At what point in time then do dice throws magically cross from totally random to partially or fully predictable? What event, exactly, causes this to occur? Is it when they leave the thrower’s hand? Maybe it’s before that - given measurements of the thrower’s arm speed several seconds before release and the exact dice position, and well, maybe you still have an edge because the release is somewhat predictable statistically from there on. Maybe it’s entirely predictable at the point the thrower’s brain fires a signal to throw, given their current body position and the state of electrical impulses in their brain and muscles. Maybe the thrower is so consistent, that simply knowing the geometry of the dice in their hand before their brain fires (or the geometry of the dice when they pick them up) could give you an edge of predictability, however slight. What is the secret magical point of true randomness/unpredictability? Does it exist at all?

Is unpredictability a continuum?

Maybe there is no magical point/event, but rather several points or even a continuum along the way. Maybe if the corner of the die hits the table just right, say nearly balanced right on the sharp corner, then the exact path the die from that point on depends on the nuances of the die and table at a near atomic level. Maybe the path of die bifurcates into an equal chance microscopically left or right depending on the truly unpredictable (quantum?) vagaries of the atoms involved. Maybe this only affects the final die face only 1 time in a million, but it’s enough to throw your predictability off, ever so slightly and randomly. Accumulate enough of these random perturbations along the way, and the degree of unpredictability snowballs as you look back in time in the dice throw. Somehow, this continuum makes more sense to me than having some single point in time where some magical event happens that crosses the dice throw over suddenly from unpredictability to predictability.

Perspective matters

From my perspective, if I was suddenly shoved into a dice game right now, I couldn’t predict the throw of fair dice with any better than 1-in-6 probability at virtually any point prior to the dice achieving complete rest. I simply can’t think/compute fast enough, let alone process such computations in my head. Given, say 3 million USD in research money and several years to develop a fast computer vision/prediction system, and who knows how much better my system might be able to do than 1-in-6? Maybe the threshold between unpredictable randomness and predictableness would extend back at least several seconds before the dice came to rest. This isn’t farfetched when you realize that Ed Thorp and Claude Shannon performed a similar feat to gain an edge on the casino roulette wheel as described in Fortune’s Formula. So how much predictability could be gained with a $3 billion dollar research budget over say, 20 years? What is the theoretical limit of predictability of a dice throw?

Is “randomness” solvable?

What if some crazy science fiction writer’s nightmare came true, and we were visited by an alien race that decided to give us a survival intelligence test. If we pass we survive, and if we fail, we are completely terminated. The test is predicting a single dice throw a split second after the human of our choice is given a signal to throw the die on a table of known properties. They prove they are serious by obliterating, say, North Korea. If they give us ten years to work on the problem, what are our chances of survival if we throw all our best remaining resources at it? Are they no better than random 1-in-6 or something much better? Can we predict something that once seemed random and unpredictable with say 50% certainty? 99%? 100%? If the answer is other than 1-in-6, then what we once thought was random is not wholly so, given some effort at it. We may find it actually had a partial random component as well as a predictable component.

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