The phrasing of the question can be taken to fight the hypothetical pretty hard.
If the mechanism is that “machine looks at you and boots 1000 new instances with your structure” then one approach is to say that those newly booted instances are not you, so the probability of getting a lollipop is 0. “If it comes up heads… before flipping the coin” also makes for weird retrocausality.
If you are supposed to be uncertain who you are then “machine creates 1000 instances of the source code” will not happen for each instance (you would get 1000*1000 except the new instances would also get the trigger so 1000*1000*1000 and it would just keep recursing. The answer would be 1 except a set of measure 0 (that is “almost surely”. Getting to be the original root is infinidesimally lucky).)
If it is not your instances coin then the procedure on which coin the machine reads is a bit murky. If only one coin is ever read it will slightly break the situations symmetry (which might be undetecable). The coin reading is not in the same timestream as the instances experience it.
The phrasing of the question can be taken to fight the hypothetical pretty hard.
If the mechanism is that “machine looks at you and boots 1000 new instances with your structure” then one approach is to say that those newly booted instances are not you, so the probability of getting a lollipop is 0. “If it comes up heads… before flipping the coin” also makes for weird retrocausality.
If you are supposed to be uncertain who you are then “machine creates 1000 instances of the source code” will not happen for each instance (you would get 1000*1000 except the new instances would also get the trigger so 1000*1000*1000 and it would just keep recursing. The answer would be 1 except a set of measure 0 (that is “almost surely”. Getting to be the original root is infinidesimally lucky).)
If it is not your instances coin then the procedure on which coin the machine reads is a bit murky. If only one coin is ever read it will slightly break the situations symmetry (which might be undetecable). The coin reading is not in the same timestream as the instances experience it.