How do you interpret the "dice problem"?

[arcimede$]

So it's okay to count the same die twice? And to assign different values to that same die?

Yes, you are assigning different values on different throws. Think VP. You aren't limited in the number or types of aces you will get on future deals because you got one on the current deal.

I guess probability is different from elections where you can only vote once.

That's right.