Fallacy decision making is based on the idea that humans, and indeed other animals, quickly identify patterns from very small samples. We like to be able to categorize things and if something does not fit neatly into a category we know, we fit it into a similar category. We've all seen this in action when somebody is introduced to something new and they say 'Oh yes, it's just like...'
Overall, the mistake is the assumption that similarity in one respect means similarity in other respects. This is called 'representativeness heuristic'.
Gambler's fallacy is one of the major illusions of fallacy decision making that we get caught with. First written about in 1796, this is the mistaken idea that the chances of something occurring increases or decreases depending on recent occurrences, despite the fact that the probability of occurrence is fixed.
An example. If somebody tosses a coin, and it comes up heads five times in a row, would you choose heads or tails on the next toss? Most people will choose tails because chance would seem to indicate this. But the odds of tails is still 50-50. The probability is fixed and it could just as easily be heads.
This kind of fallacy decision making, gambler's fallacy, means that casino owners and those who run lotteries stay in business!
Hot-hand fallacy is another major illusion of fallacy decision making. In 1985 Gilovich, Vallone, and Tversky noticed that people involved in basketball believed that a player who scores several times in a row is very likely to score the next time, because he is 'hot'. Various studies have shown that no such correlation exists. If anything, such players may be less likely to score again.
However, it's not quite so clear cut. Winning streaks have been noted in golf putting, dart throwing, 10 pin bowling, and other sports. Humans are not static systems, they are dynamic. And when you introduce them into any system, they don't always follow simple rules! So belief in the hot-hand fallacy may not always lead to fallacy decision making.
These two kinds of fallacy decision making are not exactly opposites. Gambler's fallacy suggests that the events will not continue. Hot-hand fallacy suggests that the events will actually continue. But gambler's fallacy concerns beliefs about outcomes of the random process. Hot-hand fallacy has to do with outcomes of the individual.
The opposite of gambler's fallacy is actually the hot outcome, that the next flip of the coin will be the same as the preceding ones. The opposite of hot-hand fallacy is sometimes called 'stock of luck' and once the stock of luck has run out, the winning stops.
It's also possible to have these two kinds of fallacy decision making running together. "The last three were heads so the next one must be tails and I guessed the last three correctly so I just know I can guess the next one as well."
Many theories have been suggested as to why these fallacy decision making things occur. One interesting idea is the consideration of whether somebody is operating from an internal or external locus of control. Whether they consider themselves responsible for themselves or not.
People who are internally referenced consider their outcomes are a result of their personal decisions and efforts. Externally referenced people believe they are outcomes are a result of chance and other external factors. If the latter folks have a winning streak and believe their luck is going to run out, they exhibit stock of luck behavior and bet less. An internally referenced person who wins and thinks it's because of his skill, will bet more, exhibiting hot-hand behavior.
How does the internal/external reference affect fallacy decision-making in relation to random processes? The person with the external locus of control after three heads in a row should believe that the external luck will continue and that another head will appear. So they exhibit stock of luck and hot outcome traits.
The people with internal locus of control will reject randomness because that doesn't fit with the idea of their own skill. A win confirms this skill and builds confidence so they bet more (hot-hand). Representativeness explains the supposed pattern detection skill so they bet with gambler's fallacy. So the internal bias leads to hot-hand and gambler's fallacy traits.
Other effects of representativeness include base rate fallacy where people tend to discount the actual rate that an event occurs. For example, fear of flying is very common but the actual incidence of air crashes is incredibly low.
The law of small numbers is where people assume that a small sample somehow represents a much larger group. If two salesmen from a company are very pushy, it does not necessarily follow that everyone in the company is this way.
It's possible to use the representativeness heuristic for influence and persuasion. In order to make something more attractive for somebody else, you simply have to associate it with something they actually like, preferably by finding some way in which they are similar.
And, of course, be aware of this occurring for you!!
So learn how to make your own decisions...