This almost always
bogus law refers to the
belief that, given a set of
possible alternative
outcomes, the
distribution of said outcomes will tend to be even, or "
average out", with repetition over time.
Belief in The Law of Averages is particularly prevalent in games of chance, lotteries, and most other forms of gambling*, in all of which cases it is entirely false, owing to the fact that the outcome of previous games has no bearing on the next game. (Assuming a straight game.)
Intuition will suggest that, because double six has not been thrown in the last 200 throws of the dice, it must therefore have a high probability of coming up next. This is false. In reality, it has the same probability as at any other throw, namely 1 in 36. There is no causal link between previous throws and the next. History does not come into it.
The Law of Averages is a fine example of the immense gulf that may exist between intuition or common sense, and reality. Just because something seems right, it does not necessarily follow that it is right.
* An exception is horse racing, in which prior races obviously play a role in determining outcome, and which is considered by the cognoscenti as a science rather than a game. But punters have numerous ways of turning even horse racing into a game of chance, in order that they may apply The Law of Averages -- e.g. by always betting on number 2.
Well, pardon me, Azure Monk, but I think you are taking The Law of Averages in a different sense to that which I intended. To take your example as illustration:
If a person flips a coin ten times and it comes up heads ten times, then that person's intuition might lead him to say, "OK, by the law of averages, tails should come up next". In other words, it feels like it should be tails' turn. But as we both know, the chance of tails coming up next is precisely 1 in 2.
So my point is that, taken as a basis for predicting the next outcome, The Law of Averages is completely bogus.