Omega asking you that question, “What’s the probability that the bead will be red” is itself information about the beads—Omega is more likely to ask that question in cases where the color is relevant.
To do things properly, you could suppose that Omega is inspiring himself from existing bead-color-guessing logic puzzles (there are plenty of examples of those in human history), and you could assign probabilities to each type of guessing games, noting how many types of beads there are etc. You can also collect statistics about which combinations of colors are often used for puzzles (red-and-blue and black-and-white seem common), and from all that, have a probability to assign to each color coming out, knowing that “will the bead be red” is a reasonable question.
That kind of thinking seems like closer to what you can come up with with limited computational resources, and it might give you a probability of 0.5 for red.
Omega asking you that question, “What’s the probability that the bead will be red” is itself information about the beads—Omega is more likely to ask that question in cases where the color is relevant.
I’m not sure what you mean by this. Obviously the color is relevant, in that it’s what he wants you to guess at—but the fact that he asked about red and not about brown is not suggestive in any way. This is Omega we’re talking about, not someone with normal psychology.
Omega asking you that question, “What’s the probability that the bead will be red” is itself information about the beads—Omega is more likely to ask that question in cases where the color is relevant.
To do things properly, you could suppose that Omega is inspiring himself from existing bead-color-guessing logic puzzles (there are plenty of examples of those in human history), and you could assign probabilities to each type of guessing games, noting how many types of beads there are etc. You can also collect statistics about which combinations of colors are often used for puzzles (red-and-blue and black-and-white seem common), and from all that, have a probability to assign to each color coming out, knowing that “will the bead be red” is a reasonable question.
That kind of thinking seems like closer to what you can come up with with limited computational resources, and it might give you a probability of 0.5 for red.
I’m not sure what you mean by this. Obviously the color is relevant, in that it’s what he wants you to guess at—but the fact that he asked about red and not about brown is not suggestive in any way. This is Omega we’re talking about, not someone with normal psychology.