Sometime ago there was a posting about something like “If all you knew was that the past 5 mornings the sun rose, what would you assign the probability the that sun would rise next morning? It came out so something like 5⁄6 or 4⁄5 or so.
But of course that’s not all we know, and so we’d get different numbers.
Now what’s given here is that Omega has been correct on a hundred occasions so far. If that’s all we know, we should estimate the probability of him being right next time at about 99%. So if you’re a one-boxer your expectation would be $990,000 and a two-boxer would have an expectation of $11,000.
But the whole argument seems to be about what extra knowledge you have; in particular, Can causation work in reverse? or Is Omega really superintelligent? or even Are the conditions stated in the problem logically inconsistent (which would justify any answer.)
Perhaps someone who enjoys these kinds of odds calculations could investigate the extent to which we know these things and how it affects the outcome?
Let’s take Bayes seriously.
Sometime ago there was a posting about something like “If all you knew was that the past 5 mornings the sun rose, what would you assign the probability the that sun would rise next morning? It came out so something like 5⁄6 or 4⁄5 or so.
But of course that’s not all we know, and so we’d get different numbers.
Now what’s given here is that Omega has been correct on a hundred occasions so far. If that’s all we know, we should estimate the probability of him being right next time at about 99%. So if you’re a one-boxer your expectation would be $990,000 and a two-boxer would have an expectation of $11,000.
But the whole argument seems to be about what extra knowledge you have; in particular, Can causation work in reverse? or Is Omega really superintelligent? or even Are the conditions stated in the problem logically inconsistent (which would justify any answer.)
Perhaps someone who enjoys these kinds of odds calculations could investigate the extent to which we know these things and how it affects the outcome?