There are multiple consistent answers here, because there are multiple ways to map measures onto events in ways that obey the probability axioms and are consistent with some reasonable meanings of the words in English. There are many points of ambiguity!
Most importantly, what exactly does the term you refer to in every instance where it is used in this scenario description?
Does it always refer to the same entity? For example, if the term “you” always means a physical entity, then the probability is zero because in this scenario no physical entity ever receives a lollipop. (There are some simulated entities that falsely believe they are you, who experience receiving a lollipop, but they’re irrelevant)
Maybe it refers to any entity in an epistemic state immediately prior to flipping the coin in such a scenario? Then there may be 1 of these, 1001, or any other number depending upon how you count and what the rest of the universe or multiverse contains. For example, there are infinitely many Turing machines that simulate an entity in this epistemic state having subsequent experiences. I would expect that most of them by some complexity metric do not simulate the entity subsequently experiencing receipt of a lollipop. Should they be included in the probability calculation?
If the “you” can include entities being simulated, can the term “coin” include simulated coins? How are we to interpret “the coin has an equal probability of coming up heads or tails”? Is this true for simulated coins? Are they independent of one another and of whichever “you” is being discussed (some of which might not have any corresponding coins)?
So in short, what sample space are you using? Does it satisfy any particular symmetry properties that we can use to fill in the blanks “nicely”? Note that you can’t just have all the nice properties, since some are inconsistent with the others.
There are multiple consistent answers here, because there are multiple ways to map measures onto events in ways that obey the probability axioms and are consistent with some reasonable meanings of the words in English. There are many points of ambiguity!
Most importantly, what exactly does the term you refer to in every instance where it is used in this scenario description?
Does it always refer to the same entity? For example, if the term “you” always means a physical entity, then the probability is zero because in this scenario no physical entity ever receives a lollipop. (There are some simulated entities that falsely believe they are you, who experience receiving a lollipop, but they’re irrelevant)
Maybe it refers to any entity in an epistemic state immediately prior to flipping the coin in such a scenario? Then there may be 1 of these, 1001, or any other number depending upon how you count and what the rest of the universe or multiverse contains. For example, there are infinitely many Turing machines that simulate an entity in this epistemic state having subsequent experiences. I would expect that most of them by some complexity metric do not simulate the entity subsequently experiencing receipt of a lollipop. Should they be included in the probability calculation?
If the “you” can include entities being simulated, can the term “coin” include simulated coins? How are we to interpret “the coin has an equal probability of coming up heads or tails”? Is this true for simulated coins? Are they independent of one another and of whichever “you” is being discussed (some of which might not have any corresponding coins)?
So in short, what sample space are you using? Does it satisfy any particular symmetry properties that we can use to fill in the blanks “nicely”? Note that you can’t just have all the nice properties, since some are inconsistent with the others.