It seems there are multiple versions of the paradox. It does seem reasonable that you can find someone to take the bet for <$999K if it is known that The Predictor is "very likely to be correct". Any bet amount <$999K is qualitatively the same as my original $500K suggestion, you increase your guaranteed minimum by decreasing your potential maximum without having to resolve the paradox.
I think any version of the paradox that defines the predictor as infallible misses the whole point of the paradox. That's just defining the outcome of the game as the will of God. "Has always been observed to be correct" is the appropriate construction.
However, I think someone could resuscitate the original intent of the paradox by having the Predictor's actions also hinge on whether or not it predicts that you would make such a bet, and leave box B empty if it does predict that. Essentially defining itself to be correct in the situation where, without this addendum, it would have been incorrect and you would have won the bet.
I think you are intent upon maintaining the paradox, whereas I was just pointing out a loophole that allows a better outcome without resolving it. Gordian knot and all.
The paradox is supposed to be maintained. It is supposed to illustrate the incommensurability of the two decision methods that it illustrates. It's not supposed to be "solved" or "cut."
The paradox exists. I did not solve it., I worked within the confines of it to find a potentially better outcome.
You have changed the definition of the paradox. Both can be valuable avenues of thought. I tend to view paradoxes as learning opportunities or a way to practice critical and logical thinking skills. Both of us have achieved that, so yay, but there's definitely not a single way to approach a paradox when presented with one.
As the sibling/nephew posts indicate, the bet is a good deal for anyone who has faith in The Predictor's ability to predict actions.
We also have a huge range for our bet to cover varying levels of certainty.
Again, this is not win-optimizing, but risk-averting. I am pretty sure I am being generous with the technical definition of risk aversion, but that is not material to my suggestion.
The paradox exists because there is no clear best strategy. The best you can guarantee (without resolving the paradox) is $1000, if you always take A and B you will net at least $1K, with the potential (depending on paradox resolution)for $1.001M. My suggestion aims to increase the guaranteed minimum essentially by purchasing it with the decreased maximum. $500K is really just a Schelling point, but unnecessary.
A bet of $999K is the breakeven point - any bet less than this amount increases your guaranteed minimum such that this guaranteed minimum is always greater than the $1000 which is the guaranteed minimum of taking A and B. Since The Predictor is (depending on version of the paradox) either infallible or nearly so, it seems reasonable to me that you can find someone to take a bet at <$999K.
