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.
