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TobyBartels comments on Probability is in the Mind - Less Wrong
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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:
The bottom line is that you don't know what the next value will be, and that's the only thing that matters.