In complex situations, people often rely on certain shortcuts to reach a conclusion or decision.  However, if the shortcut does not represent the situation adequately, it can lead to misrepresentation of probability, statistics and the nature of chance situations.  These shortcuts can include the representativeness heuristic (Kahneman & Tversky, 1972), availability heuristic (Kahneman & Tversky, 1973), belief in the 'law of small numbers' (Tversky & Kahneman, 1971) and the gamblers' fallacy.

Representativeness Heuristic

The representativeness heuristic, introduced by Kahneman & Tversky (1972), describes the tendency for people to think something is more likely if it reflects their beliefs of a situation.  This is comparable to reliance on stereotypes – people will believe that something is likely because it seems to be true.  Representativeness, then, is characterized by the similarity of a sample to its parent population.

            However, this can be very misleading.  Kahneman & Tversky (1972) give the following example:

"All the families of six children in a city were surveyed.  In 72 families, the exact order of births of boys and girls was G B G B B G.

What is your estimate of the number of families surveyed in which the exact order of births was B G B B B B?" (p.432)

Statistically, both birth orders are about equally likely.  However, the ratio of boys to girls in the second sequence (5:1) is clearly not representative of the population.  Thus, most subjects judged the sequence to be less likely than the first sequence. 

            Similarly, when the same subjects were asked to "estimate the frequency of the sequence B B B G G G, they viewed it as significantly less likely than G B B G B G".  In this case, although the ratio of boys to girls seems representative, the first sequence seems too orderly or less random.  Thus, the second sequence is more representative of the population.

Availability Heuristic

            The availability heuristic (Tversky & Kahneman, 1973) is very similar to the representativeness heuristic.  The availability heuristic, however, is characterized by the tendency to believe that what first 'comes to mind' is more likely.  A common example is the judgement of word frequency (Kahneman & Tversky, 1973):

"Suppose you sample a word at random from an English test.  Is it more likely that the word starts with a K, or that K is its third letter?  According to our thesis, people answer such a question by comparing the availability of the two categories, i.e., by assessing the ease with which instances of the two categories come to mind." (p.211)

It is generally easier to think of words that start with the letter K, so most people will judge that this is more likely.  However, words with K as the third letter actually occur far more frequently than words that start with the letter K.

            Casinos commonly take advantage of the previous two heuristics by setting up slot machines such that when someone wins, there are  many lights, bells and whistles.  As well, since the machines are situated very close together, you can often hear/see 'winning' slot machines.  This situation supports the representativeness heuristic by making winning very represented in the population, so that it will seem more likely.  As well, the availability heuristic is supported since wins will easily come to mind.

            Conversely, if the machines were spread out or did not have lights and whistles to announce wins, the gambler would probably only notice their own performance – which would probably include more losses than wins.  In this situation, losses would become more representative and available.

Belief in the "Law of Small Numbers"

            Tversky & Kahneman's (1971) 'Law of Small Numbers' is an aspect of the representativeness heuristic.  Their law describes the tendency for people to believe that rules that apply to large samples will apply also to small samples.  For example, in the case of flipping a coin you know that after a large number of flips, you should end up with 50% heads and 50% tails.  However, these proportions do not necessarily apply to small samples.  In a sample of 10 flips, you could just as easily end up with 70% heads and 30% tails.

            This comes into effect in gambling on VLTs since people are aware of the payout rate.  On Alberta, for example, the payout is 92% (taken from http://www.telusplanet.net/public/gibson/odds.htm ).  According to the law of small numbers, people mistakenly believe that this rate of returns means for every $100 they put into a machine, they should get $92 back.  However, the 92% rate of return is a number for a large sample and does not necessarily apply to a small sample such as $100.

Gamblers' Fallacy

            The gamblers' fallacy is a misinterpretation of probability.  Specifically, it is "mistaken notion that the odds for something with a fixed probability increase or decrease depending upon recent occurrences" (Carroll, http://www.skepdic.com/gambling.html ).  Again, taking the coin flip as an example, the probability that the coin will land on heads is 0.5 (or 50%) for each flip.  Since there are only two possible outcomes, this probability is constant.  The gamblers' fallacy suggests that after a streak of 'tails', a person will believe that the probability of the coin landing on heads on the next toss is greater than 0.5 even though this belief is probabilistically incorrect.

            In a gambling situation, this becomes apparent when a person believes that they are "due" for a win after a long string of losses.  The probability of an outcome does not change based on the previous outcomes.  This is similar to the belief in the law of small numbers since they are both concerned with the idea that the proportions of long-term outcomes should be preserved in short segments.

            These heuristics may all play a role in 'near win' situations (Johnson, 1987).  Know that the win was "right there" make winning seem more available.  As well, according to the gamblers' fallacy and the law of small numbers, the loss may make a win seem more probable.

            Ganzach (1994) found that a 'deviation representation' of feedback (i.e. knowing how much you missed by) could cause more extreme predictions.  Interpreted in a near win situation, knowing how close they were to winning could cause the gambler to predict an upcoming win (even if the probability is quite low).  

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