Random number generators and what the word random is doing
Posted 5 April 2007 at 21:02
The word random is doing two jobs at once in most conversations about machine games. One job is mathematical: a sequence is random with respect to a distribution if each draw follows that distribution and no draw carries information about the next. The other job is a feeling, roughly that a sequence looks unpatterned to a person watching it. The two jobs come apart more often than they meet.
A generator of the kind used in machine games is not random in the first sense at all. It is a deterministic recurrence: a starting value is transformed by an arithmetic rule to produce the next value, and that value is transformed again, and so on. Given the starting value and the rule, the entire sequence is fixed for all time. What such a generator provides is a sequence whose statistical properties are difficult to distinguish from a random one over any realistic span of observation.
That distinction sounds like a weakness, and it is worth being precise about why it usually is not one. The properties that matter for a game are properties of the distribution: how often each outcome appears over a long run, and whether the appearance of one outcome shifts the frequency of the next. A well constructed recurrence with a long period satisfies those properties to a tolerance far finer than any sequence of play could test.
Where the word does mislead is in the second sense. People reading a sequence look for structure, and they find it whether or not it is there. A run of six identical outcomes in a long sequence is not merely possible; it is expected to occur, and to occur repeatedly, and its occurrence tells an observer nothing whatsoever about the seventh. The sequence has no memory of the run. The observer does, and that asymmetry is the source of most of the folklore.
So it is useful to keep the two senses labelled. When a rule card says outcomes are determined by a random number generator, it is a statement about the distribution of outcomes. It is not a statement that the sequence will look disordered to a person, and it is certainly not a statement that a stretch of the sequence can be read for what comes next.
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