Paradoxes of Gambling Behaviour

Willem A. Wagenaar

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781134879366
• Edition: 1
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Why does a large proportion of the population engage in some form of gambling, although they know they are most likely to lose, and that the gambling industry makes huge profits? Do gamblers simply accept their losses as fate, or do they believe that they will be able to overcome the negative odds in some miraculous way? The paradox is complicated by the fact that those habitual gamblers who are most aware that systematic losses cannot be avoided, are the least likely to stop gambling. Detailed analyses of actual gambling behaviour have shown gamblers to be victims of a variety of cognitive illusions, which lead them to believe that the general statistical rules of determining the probability of loss do not apply to them as individuals. The designers of gambling games cleverly exploit these illusions in order to promote a false perception of the situation.

Much of the earlier interest in gambling behaviour has been centred on the traditional theories of human decision-making, where decisions are portrayed as choices among bets. This led to a tradition of studying decision-making in experiments on betting. In this title, originally published in 1988, the author argues that betting behaviour should not be used as a typical example of human decision-making upon which a general psychological theory could be founded, and that these traditional views can in no way account for the gambling behaviour reported in this book.

CHAPTER 1

Theoretical Contexts

Two-hundred-and-fifty years ago, in 1734, the Dutch magazine The Hollandsche Spectator contained the following curious advertisement (Fokker, 1862):

“The publisher is requested, with permission of The Spectator, at the earliest possible moment to make public, that if the owner of ticket no. 1431 in the second draw of the Eleventh State Lottery, would transfer that ticket to the person in whose name this advertisement was placed, he shall receive 50 guilders. The petitioner has the firm impression that a considerable prize will fall on it. He relies upon a calculation, of which he wishes to reveal nothing more than that this number is divisible by nine and that the time letters of his name constitute the same number.” (P. 138)

A heated discussion immediately arose concerning the sanity of the advertiser. Two letters are memorable. In the first, the advertiser disclosed his identity: he was Conradus Leopoldus van Luckwichel (a pseudonym: wichel means divining rod; hence: the luckseeker). He defended his sanity firstly by arguing that the owner of ticket no. 1431, who had paid Dfl. 10 for it, apparently cherished a similar reasoning, because he refused to sell it for a five-fold price. But he also warned the owner that he could never profit from his property: “Because it is clear from the advertisement that only I, and no other person, will according to my reasoning, win anything of value on this lottery ticket.” (P. 139)

His reasoning ran as follows: “If we subtract 1431 from the year 1734, the remainder is 303. The beginning and the end of this number together make six, the first perfect number. They enclose the number zero which, having the shape of a circle, is the greatest and most perfect of all figures…. My age was 303 months, that is 25 1/4 years, on the day I submitted my request to the publisher; a circumstance that cannot be without benefit.” He had not paid attention to lotteries previously, because: “the time had to be right. I have just come of age, and received my capital from my guardians who, in accordance with the laudable customs of these substitute parents, supported me in such slender manner so that I was unable to wager money in lotteries, if you may call it wagering when you acquire lottery tickets the way I do.” (P. 139)

The second letter was from the owner of ticket no. 1431. He claimed that he did not give any credence to the prediction, nor understand its rationale. But he wanted to keep the ticket anyway, even if someone offered a hundred ducats. He explained that he was wealthy enough to afford himself the expense of a ticket, and that he did not need the 50 guilders offered by Mr. Luckwichel. He had acquired the ticket in order to have the chance of winning a fortune. Why would he now deprive himself of this opportunity? Moreover, his wife had told him: “I do not understand all these minute calculations, but this I do understand, that the lottery ticket is as good in your hands as in anyone’s. It is all in the drum; will the ticket change place when you sell your receipt to someone else?” (P. 140)

In her last statement she referred to the practice of mixing all lottery tickets in a large drum, out of which the winning tickets were drawn. Finally, the nephew of the owner commented that he knew two fools: “One who made so much fuss about the numbers. And one who claimed not to believe this infatuation, but proved the contrary by his behaviour.” (P. 140)

The story is an excellent illustration of what I mean by paradoxes of gambling behaviour. Mr. Luckwichel offered to pay for one ticket only, the amount that would have paid for five tickets in the same lottery. Apparently he was convinced that this one particular ticket was worth more than five others, and this conviction was based solely on considerations that were unrelated to the mechanical process of drawing tickets from the drum. It is not clear how the results of his cabbala could have influenced the drawing of tickets, unless it is assumed that mysterious influences, other than the actual shuffling and drawing, affect the outcome. In the following chapters we will see that many gamblers cherish similar beliefs. The discussion seems to concentrate on the question whether the ticket will be lucky, dependent on whom the owner is. Mr. Luckwichel’s cabbala implies a positive answer, because it was based on his personal situation. The ticket would be lucky in his hands, not in somebody else’s. Many gamblers believe that luck is personal, or even that luck is an aspect of personality, and that indeed one person’s luck cannot be transferred to another person. The owner’s wife thought differently. She accepted the possibility that ticket no. 1431 would be a lucky one. Therefore she agreed to keep it. But she refused to believe that luck would depend on the owner’s identity, because “it is all in the drum.” How then, if only physical causation determines the outcome, this ticket could be especially lucky and worth more than five other tickets, remains a puzzle. The owner’s nephew adopted a third position: he did not even believe that ticket no. 1431 would be more lucky than other tickets.

The existence of organised gambling is in itself as much a paradox as the foregoing anecdote. The organisers invariably win, while the players on the whole lose. It is, of course, true that occasionally players may win, but the law of large numbers specifies that, with continued gambling, the gross result will approximate the mean expected outcome as determined by the odds of the game. In organised gambling the expected outcome is always positive for the organiser, and negative for the player. Moreover we will see that a large majority of wagers are placed by habitual gamblers, who play frequently enough to render the likelihood of overcoming the unfavourable odds infinitely small. Why does the gambling industry attract so many clients, when these same clients are certain to lose? Don’t these people know that they are losing? Or do they like to lose? Do they perhaps believe that just once they are going to have a big win, and regain everything they lost before? Do they, like Conradus Leopoldus van Luckwichel, believe that something special will happen, favouring them above other players, which will invalidate the expectancy that in the long run they must lose?

EXPLANATIONS OF GAMBLING

The paradox of prolonged gambling in the face of systematic losses has been explained in many different ways. First it has been argued (cf. Vickrey, 1945; Devereaux, 1968; Hess & Diller, 1969) that gamblers value the money they expect to win more highly than the money they have already lost, and that gambling is rational in this perspective. As will be argued later on, such theories are only tenable if a major part of previous losses is discounted. Second it has been said that gambling is a form of entertainment, for which players are prepared to pay (Devereaux, 1968). Third it has been argued that gambling gives prestige to the gambler. Even the anonymous gambler could be flattered by the plush environment of casinos, the polite treatment by personnel, and all the extras bestowed on players, such as drinks, meals, and shows (cf. Zola, 1963). There is also a suggestion that deep psychological motives play a role. Examples are a need for conflict resolution (Devereaux, 1968), a need for competition and aggression (Thomas, 1901; Zola, 1963), and a need for self-punishment in neurotic people (Bergler, 1957). All these explanations could carry some truth. But none of them provides insight into the reasoning of Mr. Luckwichel and his contemporaries. Their appraisal of how lotteries operate, and how one should bet, tells a story of its own. The strong belief in principles other than statistical expectation constitutes a sufficient explanation of gambling and could, more than other explanations, provide some understanding, not only of why people gamble, but also of how people gamble.

The thesis defended throughout this monograph is that the nature of the gambling paradox is cognitive. Gamblers are motivated by a way of reasoning, not by defects of personality, education or social environment. A hint in this direction can be gained when we look at the vast number of people regularly involved in gambling. In The Netherlands 2 million people out of 14 million take part each month in the State Lottery. An even larger number play in the Giro Lottery, football pools, lotto games, foreign (especially German) lotteries, number games, illegal commercial lotteries, and semi-legal Bingo games. In addition there is betting on horses, there are four state-controlled casinos with an annual total attendance of one-and-a-half million people, and about 200 illegal casinos with a clientele of some 200,000 regular gamblers. In the United States about 60% of the population engage in some sort of gambling (cf. Lesieur & Custer, 1984). Gambling is almost universal. It cannot be explained by a defect in a minority of people.

I will attempt to support my thesis by an experimental investigation of human cognition. Often my subjects will have been observed in casinos or other gambling places. But not always because, again, it is my conviction that the cognitive factors inducing gamblers to gamble can be found in the large majority of people.

If indeed gambling should be understood in the perspective of human cognition, it may be useful to place it within the context of a theory of cognitive processes. At least two such contexts present themselves. One is the context of normative decision theory, which contains as one of its postulates that every decision problem can be modelled as a choice among gambles. The theory claims that it can predict a rational decision maker’s preferences for gambles. The least such a theory should be able to do is predict gamblers’ preferences for gambles unless it is claimed that 60% of the population is not rational. But in that case the theory would not have much practical value. We can smell a rat here, because in its simplest form normative decision theory predicts that gamblers will not gamble. This prediction is obviously not borne out by the facts.

The other theoretical context in which gambling behaviour can be placed is generally known as “heuristics and biases.” The basic, somewhat hidden, underlying assumption is that strategies for decision making are chosen from a large and variable repertoire. The strategies are selected on the basis of similarity between the actual situation and previous situations in which a strategy worked out well. The bulk of experimental studies in this tradition attempted to demonstrate the variety of strategies in the repertoire, but little attention has been paid to the rules governing selection from the repertoire.

Both theoretical contexts have their weaknesses, and it is even questionable whether, in the end, they will help us to understand the behaviour of gamblers. But since I intend to refer to these contexts throughout the book, I will describe both of them in some detail in the following paragraphs. A discussion of their usefulness will be postponed till the last chapter, where more actual data about gambling behaviour and its paradoxes are presented.

NORMATIVE DECISION THEORY

In normative decision theory decisions are modelled as choices among alternatives. A decision to go skiing is modelled as a choice between skiing and not skiing. Decisions are usually complicated by the fact that the alternatives have uncertain outcomes. It is not certain that there will be enough snow to ski, or that you will not break your legs. There is no way to evade uncertainty completely. You cannot wait till there is more snow, without running the risk that, in fact, there will be less snow. This means that the decision must be based on expectancies. According to the theory, the expectancy related to a choice alternative consists of two elements: the utility of that alternative and an estimated probability that this utility will indeed be effectuated. These aspects are combined in some way, in order to obtain one characteristic of the attractiveness of an alternative. The combination rule is chosen such that the expected utility equals the mean utility obtained in the long run. In practice this means multiplication of probability and utility. The outcome of a gamble is a good example. Suppose that I want to decide whether I should buy a ticket in a lottery. There is only one prize of Dfl. 1000, 500 tickets are sold, and each ticket costs Dfl. 10. The outcome of not buying a ticket is clear: I keep my 10 guilders, and I will not win 1000 guilders. But the outcome of buying a ticket is more complex. The investment may yield a prize of Dfl. 1000 which amounts to a net profit of Dfl. 990. I may also just lose 10 guilders. The proposal of normative theory is that the mean result that will be achieved when the gamble is played an infinite number of times, is taken as the quantity that characterises the attractiveness of the lottery, even when the lottery is played only once. If, for sake of simplicity, we equate the utility of money to the amount of money, the mean obtained utility will be equal to the mean outcome. In the long run, if the lottery is fair, we will lose Dfl. 10 in 499 times out of 500, and win Dfl. 990 only once in 500 times. The mean result is:

Thus the choice is between losing an average Dfl. 8, or the status quo in which nothing is lost or won. The wisdom of this reduction to long run expectancies was questioned by Lopes (1981) and Keren and Wagenaar (1987). The argument is that it is only natural for people to consider the outcomes actually possible of +990 and -10 when the gamble is a unique event. The expected outcome will in the unique case never materialise. Tversky and Bar-Hillel (1983) argued that a rational decision maker should use the long run expectancy as a decision criterion, even in the unique case. The logical reasons that support this view could appeal to some theorists, but there is of course no reason why gamblers must share this theoretical position. On the contrary, it is quite possible that gamblers, who play so often that long-term considerations will apply, do in fact consider each gamble as a separate and unique event, which is in no way related to previous or future gambles. An example may help to illustrate the point. Let us assume that a person owns Dfl. 50 after a night of gambling, but needs Dfl. 1000 to fly home. Placing the whole sum on one number of the roulette table will solve the problem in the event of a win, while the situation is not essentially worsened after a loss. Seen in the perspective of the real possible outcomes of a unique event the gamble may be acceptable. The mean outcome in the long run is a loss of Dfl. 1.35, which will not solve the problem. The long run perspective discards the solution that could be reached after one round of playing.

The model is considerably more complicated when utility and monetary value are not equated. If utility is ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Original Title Page
• Original Copyright Page
• Table of Contents
• Foreword
• 1. Theoretical Contexts
• 2. Blackjack: The Game Players Refuse to Win
• 3. Objectives of Blackjack Players
• 4. Roulette: The Game Players Should Not Hope to Win
• 5. Lotteries: Big Prizes and Small Expectations
• 6. Games of Chance and Games of Skill
• 7. Chanceand Luck
• 8. Theoretical Explanations
• References
• Author Index
• Subject Index