Law of Truly Large Numbers

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

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.

In pseudoscience
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.

Criticisms
Critics of this law deny its application to supernatural events on the basis that they are by definition "above nature". That is, a supernatural event is one in which the physical laws of nature (as we currently understand them) are violated. The concept makes a distinction between the natural universe and another dimension that is separate from our natural universe. A common analogy is to think of the universe as a fishbowl and the supernatural as a person outside the fishbowl. The person outside the fishbowl can interact with the fish inside the fishbowl, but not the other way around.

Therefore supernatural events are very different from highly improbable events, such as rolling 8 sixes in a row on a 6-sided die (which has a probability of less than 1 in 1 million). By definition then, a supernatural event has a zero probability of occurring at any random time, no matter how large the sample size. This way, the law is still valid as an explanation for the occurrence of highly improbable or coincident events, implying that there is no super-natural cause to be suspected in those occurrences.

On the other hand, if one adheres to the philosophy of naturalism, all events are considered natural. Any supposed "supernatural" events are then interpreted as a result of physical laws that we are currently unaware of or do not understand properly, so the Law of Truly Large Numbers should apply to them as well. Criticisms of this philosophy are included in the article on Naturalism,