Human beings tend to be just terrible at predicting things like this. The first step is to admit we really do not know then we can start guessing realizing they are just guesses.
I've written an expression down that represents a number between 0 and 1,000,000. If you can guess it then I'll give you a prize. I'll give you a hint; it isn't an integer. Anyone that thinks they can predict the number is fooling themselves but it can be fun guessing and rationalizing the guess. Also, note the prize is variable; if the exchange rate between today's Bitcoin and today's US dollar goes to $0 then you can have all of my Bitcoins leftover at the moment it dies. If the rate does top $1,000,000 then the prize will be 1 BTC.
Your challenge is not applicable: market is governed by society, society is composed by humans, and human behavior is far from random.
In fact, it is quite predictable if you have the accurate variables and models.
Using your example: It is not about arbitrarily setting a number, but having a set of obscure and complex rules for the generation of this number between 0 and a million. If you give me enough time with this black box I will be able to approximate very closely and predict the next numbers.
Maybe not exact, but good enough.
That's how social sciences work, and the black box is our human mind.
We have enough empirical information about human behavior to estimate a possible outcome under certain variables.
Alright, but, it isn't just one human mind; it is billions of them. In my experience human minds work differently enough that sometimes in a few words I can convey a concept and inspire rapid action vs. a strong negative reaction to the same concepts to the point of risking relationship or even life and limb.
So, I will give another hint; the most significant digit (MSD) is 9 narrowing the field down by a factor of 9 (the MSD couldn't have been 0). There; all human minds operate similarly enough because they are constrained to the physics of the brain
http://en.wikipedia.org/wiki/Human_brain. My expression is very very far from random
http://en.wikipedia.org/wiki/Statistical_randomness; it is in fact stunningly ordered as compared to something truly random. No one has written a computer program attempting to predict the exchange rate, right?
Make no mistake; no one here is remotely close to estimating any possible outcome at all based on any variables. We are strictly guessing for the fun of it. Anyone that thinks they are predicting anything in this space is categorically delusional but that can be a delightful source of fun too.
Heck, the environment alone can wreck havoc with any and all predictions. When the comet strikes and takes out the planet, unless we've escaped to safety elsewhere, the exchange rate won't matter. If so then I will declare a push and not payout.
Social psychology, sociology and economy take care of the masses.
There isn't a general model that encompasses from neuropsychology to psychology of masses, in the same way that there isn't still a Theory of Everything in physics (that means, a theory that explains quantum to relativity which are by themselves incompatible to each other).
That's why your example is inapplicable again, you can't talk about physics, neurology or theories of mind to explain social behavior, we are talking of different scales and different specialties.
But it is just all a matter of time, our behavior is definitely deterministic, we just haven't uncovered the whole picture yet.
But what we have is good enough to have a very important impact, and its practical application in our daily lives are scary, especially when you see how heavily -and effectively- exploited it is in advertising.
In any case, while I consider to be impossible for now to predict exact prices, I am more than satisfied with my pretty accurate predictions of trends. Not exact but good enough to be profiting quite handsomely.
One advice: everything seems impossible if you ignore the answers. Never consider something to be random or impossible from ignorance, that mentality itself is very unscientific.
One problem: humans hate to be cataloged or to be considered predictable, because that undermines their illusion of free will.