Rates of return can often be misrepresented due to irrational thinking about the given situation.  In gambling situations, this could include anthropomorphizing the gambling machine (e.g. statements like "This machine hates me", caressing the machine when winning, or swearing at the machine when losing), superstitious beliefs (e.g. lucky charms, or behavioural superstitions), or an illusion of control (i.e. believing a chance situation is determined by skill).  Since anthropomorphism and superstitious beliefs are fairly self explanatory, in this section I will be discussing the illusion of control.

        Henslin (1967) was one of the first to note this illusion of control in gambling behaviour.  In his study of craps players (a dice game), he found that the gamblers attributed winning to skill; the players were more likely to bet with someone they considered to be a 'skillful' player.  As well, the gamblers tended to think that there was skill involved with the actual tossing of the dice.  That is, a hard throw would be 'more likely' to produce a high number whereas a soft throw would be used when a low number was needed.

            Since Henslin's (1967) study, many psychologists have begun to examine the irrational thoughts and illusions of control in gamblers.  Griffiths (1994) compared regular gamblers with non-regular gamblers.  He found that despite the fact that there was no difference in the number of wins, there was a difference in the estimation of skill that was involved.  Specifically, the regular gamblers believed that the game involved a higher degree of skill and they were more skillful at the game (the game was, in fact, a chance game that did not involve skill). Other findings have supported this conclusion by demonstrating that there is no relationship between the frequency of wins and irrational thinking (Landouceur et al, 1988).

            Similarly, Langer & Roth (1975) found that judgements about the amount of skill involved depended not on the frequency of wins, but on the order in which those wins took place.  In this study, subjects were asked to guess whether a coin toss would result in heads or tails.  After each toss, the experimenter informed the subject whether they had 'won' or 'lost' the coin toss.  In actuality, the result of the coin toss had nothing to do with the report of 'win' or 'lose'; the experimenter was simply following a predetermined script of wins and losses.  The subjects were randomly assigned to one of three conditions: ascending condition (in which they were told they lost the first few tosses, then gradually increased so they won many tosses at the end), descending condition (they won the first tosses, and lost many at the end), or a 'random' condition (they lost and won equally at beginning and end).  Langer & Roth found that subjects in the descending attributed the most skill to situation.  The distinction between the other two conditions was not statistically significant, but seemed to indicate that subjects in the ascending condition said the situation was mostly based on chance, and the random condition was somewhere in the middle.  

        A six-part study by Langer (1975) also demonstrated the illusion of control in a number of different facets.  In experiment one, Langer placed subjects against a confident or awkward “opponent” (a confederate in the study) in a chance task.  The subjects (and opponent) were told to bet on who could turn over a higher card from a deck.  They could bet anywhere between 0 and 25 cents.  It was found that the subjects against the confident opponent bet less than the subjects against the awkward opponent.  Thus, it seems that the subjects believed they would have a better chance of winning against the awkward (or perhaps less skillful) opponent even though the task was entirely based on chance.

            The second two experiments involved lotteries.  In both cases, the subjects were either given a choice of their lottery ticket or not; the dependent measure was how willing (and how much) the subject was to sell their ticket before the draw.  Subjects who were given a choice in choosing their ticket were much more reluctant to sell, and asked for a much higher price.  The third experiment also compared the subjects’ familiarity with the tickets.  In one case, the subjects were given letters of the alphabet as tickets and, in the other case they were given novel symbols. The subjects with the familiar tickets were less likely to sell their ticket.

            Experiment four investigated both familiarity and involvement on an “Illusion of Control Apparatus”.  The subjects were required to choose the ‘correct’ path out of three on the apparatus (the ‘correct’ path changed randomly each trial).  Subjects were more confident in the task when they had a chance to practice first, or when they were the one to choose the path (high involvement) rather than simply telling the experiment which path to choose (low involvement).

            The fifth experiment involved a lottery at a racetrack.  Confidence measures were taken throughout the night; it was found that subjects tended to become more confident as time passed that their ticket was the winning ticket.

            The last experiment also examined involvement.  In another lottery study, subjects were either given a three-digit lottery ticket all at once, or were given the three-digits in “installments”.  That is, the subjects were given one number of their lottery ticket each day (high involvement condition).  Afterwards, the subjects were given the opportunity to keep their ticket, or exchange it for a ticket in lottery with better odds.  The subjects in the high involvement condition were less likely to exchange their ticket.

            In each of the six experiments, subjects responded as though the tasks were skill-oriented. The results of the six experiments are summarized in Table 1.

 Table 1.  Summary of  Data, Studies 1-6.

(redrawn from Langer, 1975)

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