Escaping as Mr. Jack
Notice that on an even turn, you know which characters will be available next, and you get first pick next turn. Therefore, if on an odd turn you manage to put Mr. Jack in range of escape and in the dark, you win next turn.
Otherwise, the basic strategy is to keep as many suspects as possible in the light or in the dark, and Mr. Jack always in the larger group.
Playing as a detective
Try to split suspects as much as possible between light and dark. On odd turns, prefer to put suspects that are playable this turn in the dark, and other suspects in the light. That way Jack can't escape on the next turn.