When a new student enters a class of twelve, the assumption is that s/he is the thirteenth student. But perhaps they are now the first student, the one the instructor is most cognizant of, and all the other students are pushed back by one, with former number twelve losing any luck to become the new number thirteen. Is the thirteen indicative of all now having bad luck, or is it centered on a single individual, with the other twelve in the clear? One of the odd things about the way it’s never said “unlucky thirteenth”, but always “unlucky thirteen”, but many times what is meant is unlucky thirteenth.
Is the one doing the counting to be counted—i.e., what about the instructor? Is not there now actually a change from 13 to 14 students. A lucky change, then, when a new one comes and disorders the order.
*In economic/food transactions, getting 13 of something probably means you paid for a dozen and got the 13th free, so that is definitely a valuable 13th!