Yeah, It wouldn’t be a way to win, since in the original problem you could throw a coin and base your decision on that. Average gain of $500,500 isn’t so bad, but not nearly as good as $1,000,000 from one-boxing. You’re right, it’s not a resolution to the paradox, but if the situation is changed it’s a possible way of winning.
I guess I’m looking for ways to beat Omega, and I’m trying to figure out if this would be one of them. Something like “harnessing the power of random”?
It’s called a mixed strategy Nash equilibrium. It’s a very interesting topic on its own, but it doesn’t have a whole lot to do with the decision theory paradoxes that Omega is used to show off.
That’s a slightly different problem. How would it be a resolution to the original problem?
Yeah, It wouldn’t be a way to win, since in the original problem you could throw a coin and base your decision on that. Average gain of $500,500 isn’t so bad, but not nearly as good as $1,000,000 from one-boxing. You’re right, it’s not a resolution to the paradox, but if the situation is changed it’s a possible way of winning.
I guess I’m looking for ways to beat Omega, and I’m trying to figure out if this would be one of them. Something like “harnessing the power of random”?
It’s called a mixed strategy Nash equilibrium. It’s a very interesting topic on its own, but it doesn’t have a whole lot to do with the decision theory paradoxes that Omega is used to show off.