[jbay808]

I guess this is a tangent. First of all my point really doesn't hinge on the infinity; it can be finite (but really big) but regardless, whenever you apply minmax you must first crop your decision space to a probability threshold, or else you'll make nonsensical decisions based on what gives the best outcome if the sun should happen to explode.

But secondly, I think (although I'd happily concede if convinced otherwise) that the space of possible scenarios really is infinite, even if the observable universe is not. The space I'm talking about is not the actual state space of the universe, which in some interpretations of physics might be finite or even unitary. It spans the space of hypothetical universes that are all consistent with your information with nonzero probability, which I think is probably infinite, but again, if it's not infinite that's a technicality. If you include the states that have with zero probability (because why not? GGP was advocating that the probability is irrelevant to minmax decisions) then the space is definitely infinite, because even physically impossible states of nature will impact our decision making.

[brownbat]

Another way to conceptualize the "cropping" is to get rid of all future states where planning would have been meaningless anyway.

We are momentary Boltzmann brains? We'll assume not, because if so, nothing really matters.

Trivial difference, but that avoids potentially difficult threshold problems and cousins of the St. Petersburg paradox or even Pascal's mugger, at the risk of being slightly more hand wavy.

Arguably an aesthetic distinction at this point, I generally think your description and approach are right.