There may be countless lucky dips to go through This is done until a suitable match is found. One can use one's own random number generator. This is impractical with Camelot's terminals. It is also possible to obtain random numbers without computers. Mostly, however, this is subject to human nature.
Human nature is difficult to avoid.
The first set of digits of the serial number might be examined. Assume one person does this only. Any note could have been picked. There are millions of notes in circulation. Any serial number could be on it.