I just thought of something. Given Alice's precog, could she, for instance, guess passwords? Assuming a numeric entry code, could she do something along the lines of 1. decide to press 0 first; 2. if she sees the door opening in her precog set, press 0 and then go to 1; 3. if not, then try 1 with the number 1 instead, etc. (i.e., does her precog give her a set of possibilities based on future decisions, or does it give her only one possibility based on what she has in mind at the time?)

If the latter holds, and hence the above algorithm won't work, then how long a password is it feasible for her to guess by exhaustive mental search of the command space (i.e. resolve to type 0000, then if she sees door opening type it, otherwise go to 0001, etc.) with vampire mental speed? The advantage of this over simply trying each password is 1. that it's likely to be faster, with physical bottlenecks removed, and 2. it doesn't trigger anti-brute-force alarms in the system.