If each prisoner has their own ordering, it's exceedingly likely that one of those orderings will have a 51-cycle.
This strategy only works with one common dictionary. You have the same individual odds, but you've linked each person: each member of a cycle succeeds or fails together.
If it wasn't decided beforehand, you could just make up the ordering as you go. This gives exactly the same odds as random selection.
This strategy only works with one common dictionary. You have the same individual odds, but you've linked each person: each member of a cycle succeeds or fails together.
If it wasn't decided beforehand, you could just make up the ordering as you go. This gives exactly the same odds as random selection.