Even more important, I think, is the realization that, to decide how much you’re willing to bet on a specific outcome, all of the following are essentially the same:
you do have the information to calculate it but haven’t calculated it yet
you don’t have the information to calculate it but know how to obtain such information.
you don’t have the information to calculate it
The bottom line is that you don’t know what the next value will be, and that’s the only thing that matters.
GBM:
Q: What is the probability for a pseudo-random number generator to generate a specific number as his next output?
A: 1 or 0 because you can actually calculate the next number if you have the available information.
Q: What probability do you assign to a specific number as being it’s next output if you don’t have the information to calculate it?
Replace pseudo-random number generator with dice and repeat.
Even more important, I think, is the realization that, to decide how much you’re willing to bet on a specific outcome, all of the following are essentially the same:
you do have the information to calculate it but haven’t calculated it yet
you don’t have the information to calculate it but know how to obtain such information.
you don’t have the information to calculate it
The bottom line is that you don’t know what the next value will be, and that’s the only thing that matters.