Law of Truly Large Numbers

Law of Truly Large Numbers
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The Law of Truly Large Numbers seeks, among other things, to debunk one element of supposed supernatural phenomenology. It states that with a sample size large enough, any outrageous thing is likely to happen.

Here is a simplified example of the law:
A given event might be 0.1% likely to happen in one occurrence. However, for this never to happen in, say, a sample of 1000, would require a probability of 0.999 to the power of 1000. This in fact comes out as a chance of 36.8%. Thus it is more likely that this individually unlikely event will happen at some stage than for it never to happen at all. In other words, events may be unlikely - but the likely opposite event always occurring is even more unlikely.

Because we never find it notable when the likely thing happens, we highlight coincidences and notice them more. But in fact they are happening, as you would expect, some of the time, but amongst all the possibilities in the world, not that regularly.

The law comes up in pseudoscience and is sometimes called the Jeane Dixon effect (see also Jeane Dixon). It holds that the more predictions a psychic makes, the better the odds that one of them will "hit." Thus, if one comes true, the psychic expects us to forget the vast majority which did not happen.
Humans can be susceptible to this fallacy. A similar manifestation can be found in gambling, where gamblers tend to remember their wins and forget their losses and thus hold an inflated view of their real winnings.