Is Human Probability Intuition Actually ‘Biased’?

[Scott Laing]

I realize this is not your main argument, but re ‘gambler’s fallacy’ — streaks of random individual outcomes do end.  It is not fallacy to expect so.  It is only ‘fallacy’ to incorrectly predict when.

The Monte Carlo example is not mere unusual frequency, but instead an example of the highest intensity or concentration of frequency, the term for which is ‘streak’.  Gambler’s fallacy is not commonly used to describe mere heightened frequency of a particular result, but rather streaks of a result.

Commonsense (intuition gained from knowledge about how the world works) about the nature of streaks of random outcomes does tell us that truly random, non-biased events – like coin flipping or roulette wheels – which happen with unusual frequency (streaks) will ‘wear out’ the likelihood of maintaining that streak without interruption.   On its own, the potential outcome of each spin is as random and unpredictable as the previous.  But, any collection or streak of random outcomes, by definition, takes on the properties or nature of streaks, the chief of which is they eventually end.

The ‘fallacy’ is in guessing incorrectly when a streak will end, combined with a common tendency of exhaustible funds.

I suppose one could claim there are no such things as streaks, just a random outcome happening over and over again. Until it doesn’t.

Ancient Greek philosophers observed a tendency of things to prefer the mean.  Balance was observed to be characteristic of the natural order.  It would seem streaks interrupt balance and so are, predictably, rare and short-lived.  However, balance would seem to imply that a streak of 25 black in a row must be countered eventually by a streak of 25 red.  Though it is impossible to ever know if this is true it seems reasonable to expect it is.  Since the conditions that produce such streaks remain constant it holds theoretically that streaks of one colour, given enough time, are matched by identical streaks of the other.

 

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