A quick google found me this explanation (from a problem gambling site, surprisingly enough).
People will often judge the coin-tossing sequence of H, H, H, H, H, H as being less random than H, T, H, H, T, H, even though the probability of obtaining each of these given sequences is identical: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.015625. Note that this is the probability of getting a specific sequence compared to the probability of getting a second specific sequence. Kahneman and Tversky (1982) call this tendency the representativeness heuristic. People who make this error are often computing the probability of getting 6 consecutive heads compared to every other possible sequence. Most random sequences of heads and tails do not have an easily recognizable pattern. This tends to reinforce the belief that a sequence of all heads is less likely. However, any one specific arbitrary combination of heads and tails has exactly the same chance of occurring as any other specific combination. Another factor that contributes to this error is that there is only one possible way of getting 6 heads and only one possible way of getting 6 tails, while there are a total of 64 possible ways of tossing six coins, 20 of which produce exactly 50% heads (e.g., H, T, T, T, H, H or H, T, H, H, T, T). This gives the illusion that combinations that “look random,” are more likely, but in fact each one of those specific combinations (e.g., H, T, T, T, H, H) has the same chance of occurring as H, H, H, H, H, H.
Another reason for errors in our understanding of randomness may be confusion between the way the word random is used in everyday speech and the way it is used in statistics and mathematics. According to the Merriam-Webster Online Dictionary, the most common meaning of the adjective random is “lacking a definite plan, purpose, or pattern.” It also lists “haphazard” as a synonym (www.m-w.com). Judging solely by its appearance, a sequence of 6 heads in a row might appear to have a pattern. Probability theory, however, is concerned with how the events in a sequence are produced, not in how they appear after the fact.
A third reason is the tendency of the human brain toward “selective reporting”—the habit of seizing on certain events as significant, while ignoring the other neighbouring events that would give the chosen events context and help to evaluate how likely or unlikely the perceived pattern really is. Big or salient events will be recalled better. We recall plane crashes because they are highly publicized. Uneventful flights are ignored. Because of the occasional well-publicized plane crash many people are afraid to fly, even though plane crashes are much rarer than car crashes. Kahneman and Tversky (1982) call this tendency the availability heuristic.
A closely related tendency is for people to underestimate the likelihood of repeated numbers, sequences, or rare events occurring by pure chance. The basic problem is that we do not take into account the number of opportunities for something to occur, so we are often surprised when random chance produces coincidences. As an example, in a class of 35 students, we assume that the chance of 2 people sharing a birthday is very small, say 1 in 365, or maybe 35 in 365 (Arnold, 1978). The actual probability that at least two people will share the same birthday is close to 100% because there are actually (35 x 34) / 2 = 595 possible combinations of people in the class. Because the possible combinations of people (595) exceed the number of days in the year (365), the chance that at least 1 pair of people will share a birthday is surprisingly high.
Our minds are predisposed to find patterns, not to discount them. It is argued that we have evolved the ability to detect patterns because to do so was often essential for survival. For example, if a person was walking in the jungle and saw a pattern of light and dark stripes in the shadows, it would be prudent to assume that the pattern was a tiger and act accordingly. The consequences of incorrectly assuming that the pattern is not a tiger far outweigh those of incorrectly assuming that it is. But when applied to random events, this survival “skill” leads to errors.
That is a very nice novel.
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Topic: Why does luck in Dominion feel streaky? (Read 10005 times)