Another dice game for infinitely many people

Consider:

• Case 1: There are two countably infinite sets, A and B, of strangers. The people are all alike in morally relevant ways. I get to choose which set of people gets a lifetime supply of healthy and tasty food.

Clearly, it doesn't matter how I choose. And if someone offers me a cookie to choose set A, no harm in taking it and choosing set A, it seems.

Next:

• Case 2: Countably infinitely many strangers have each rolled a die, whose outcome I do not see. Set S6 is the set of people who rolled a six and set S12345 is the set of people who rolled something other than a six. The people are all alike in morally relevant ways. I get to choose which set of people gets a lifetime supply of healthy and tasty food.

Almost surely, S6 and S12345 are two countably infinite sets. So it seems like this is just like Case 1. It makes no difference. And if you offer me a cookie to choose S6 to be the winners, no harm done if I take it.

But now suppose I focus in on one particular person, say you. If I choose S6, you have a 1/6 chance of getting a significant good. If I choose S12345, you have a 5/6 chance. Clearly, just thinking about you alone, I should disregard any cookie offered to me and go for S12345. But the same goes when I focus on anybody else. So it seems that Case 2 differs from Case 1. If Case 1 is the whole story--i.e., if there is no backstory about how the two sets are chosen--then it really doesn't matter what I choose. But in Case 2, it does. The backstory matters, because when I focus in on one individual, I am choosing what that individual's chance of a good is.

But now finally:

• Case 3: Just like Case 2, except that you get to see who rolled what number, and hence you know which people are in which set.

In this case, I can't mentally focus in on one individual and figure out what is to be done. For if I focus in on someone who rolled six, I am inclined to choose S6 and if I focus in on someone who rolled non-six, I am inclined to choose S12345, and the numbers of people in both sets are equal. So I don't know what to do in this case?

Maybe, though, even in Case 3, I should go for S12345. For maybe instead of deciding on the basis of the particular situation, I should decide on the basis of the right rule. And a rule of favoring the non-six rollers in circumstances like this is better for everyone as a rule, because every individual will have had a better chance at the good outcome then?

Or maybe we just shouldn't worry about the case where you see all the dice, because that's an impossible case according to causal finitism? Interestingly, though Cases 1 and 2 only require an infinite future, something that's clearly possible.