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 So,
Ross is wrong. Why? Slot payouts are random events. Slot machines use
a computer that creates an erratic sequence of numbers generated continuously.
When the player presses the spin button, these numbers determine the positions
of the reels. A microsecond difference in pressing the button would result
in a different outcome. Whether a machine has or hasn’t paid out
is irrelevant.
Considerable
research suggests that gambling behaviour is associated with a wide variety
of erroneous beliefs or cognitive distortions about gambling. These include
mistaken myths about ways to beat the odds, superstitions and the personification
of gambling machines. Since many of these errors are related to misunderstandings
about the nature of randomness, or probability, it is important to consider
the extent to which understanding probability contributes to the development
of a gambling problem – and to treatment, recovery and prevention.
It
is often said that gambling isn’t about the money, it’s about
excitement or escape. This argument suggests that problem gamblers’
erroneous beliefs are irrelevant because they aren’t trying to win.
However, if you took away the possibility of winning, or asked a gambler
to play games without betting, there wouldn’t be any escape or excitement.
Gambling is only exciting because of the possibility of winning real money.
And that possibility seems plausible because of erroneous beliefs. Thus,
beliefs, excitement and winning aren’t really separate issues and
there is no clear line separating the cognitive thoughts and emotional
experiences of gambling.
Does
this mean that gamblers rationally weigh the pros and cons of a bet? No.
In fact, when I talk about the logic of gambling, in most cases I’m
talking about unconscious beliefs about the way things work – schemas
or mental models. Most of our "rational" thinking, such as understanding
the words in a sentence, takes place automatically. Most often our unconscious
mental processes produce schemas that are accurate, but when it comes
to randomness, our minds often come up with the wrong schema.
Randomness explained
Why
do our minds mess up so badly when it comes to randomness? My thesis is
that the nature of randomness itself messes up our minds. I’ll begin
by considering where randomness comes from. Every movement is caused by
some force. For example, when you throw a ball it doesn’t always
go where you want it to go. There are always tiny little changes in how
you throw it: error variance or uncertainty. Even the greatest pitcher
doesn’t always throw the ball accurately. In addition, randomness
is the result of complexity – too many things happening to keep track
of. The squareness of a dice causes it to bounce erratically. If it lands
on its side it bounces one way; if it lands on an edge it bounces in a
different way. In contrast, the weight and smoothness of a bowling ball
make its movement fairly uncomplicated. The complexity of the dice amplifies
the tiny variations in how the dice is thrown so that rolling a dice produces
a much more erratic movement than rolling a ball. Statisticians would
say that a ball is more reliable than a dice.
Many
people, including scientists, underestimate the impact of a little error.
But mathematicians have found that under some conditions, a tiny change
can have a huge and unpredictable effect on the final result. In the movie
Jurassic Park, Jeff Goldblum's character, a self-declared chaos
theorist, gives the following description of this effect, "…A
butterfly flaps its wings in Central Park and then it rains in China."
Chaos
is in fact a very disturbing idea to many traditional physicists (Gleick,
1987) because it suggests that prediction is not possible in some situations.
However, complete randomness probably does not exist. Everything is the
result of some force and if you knew exactly what those forces were and
you could precisely measure all aspects of the complexity of the system,
you could predict outcomes. In the early 1980s a group of California engineers
spent several years building a computer to predict the outcome of roulette
(Bass, 1985). In theory it is possible, however, in practice, exact measurement
or control is not possible and therefore many gambling devices are very
good at producing randomness.
Regression to the mean
Random
numbers are erratic and unpredictable. You cannot predict which number
will occur based on previous numbers because each number is independent
of each other. On average a coin comes up heads 50% of the time. But coins
have no memory! Even if heads come up 1000 times in a row, the next flip
could be a head or a tail. If a coin flip is truly random, then it must
be possible (although very unlikely) for it to come up heads 1 million
times in a row. Furthermore, the number of heads and tails does not have
to even out. A head is just as likely to occur after five heads as after
five tails. The more flips you make the closer the average gets to 50%,
but nothing can force it to even out.
Yet
sometimes it seems to even out. What fools many people into believing
that it is self-correcting is that the more times you flip a coin, the
closer the average of heads or tails gets to 50%. After 18 flips, 10 more
heads than tails is a very noticeable difference (See Figure 1).
Figure 1: After flipping a coin 18 times, a difference of 10 heads is
noticeable.
Even
after 400 flips there could still be 10 more heads than tails, but the
difference becomes less noticeable (See Figure 2). The per cent gets closer
to 50 but the actual number of heads and tails doesn’t have to even
out. After 1 million flips a difference of 8000 would still round off
to 50%. This process of gradually converging on 50% is called regression
to the mean.
Figure 2: After flipping a coin 400 times, a difference of 10 heads is
barely noticeable.
I
believe that the belief that randomness is self-correcting stems from
our experiences of witnessing regression to the mean. A number is never
due to come up but the odds are it will sooner or later. There is a subtle
but important distinction between "due" to come up and "likely"
to come up in that observing the past flips of a coin will not tell you
when tails will come up. So, information about past numbers, flips or
spins tells you nothing, and yet it often seems to.You cannot beat the
odds by lurking, looking for the machine that is "due" to come
up.
Experience leads to errors
Some
of my recent research indicates that problem gamblers have a poorer understanding
of randomness compared to non-problem gamblers (Turner & Liu, 1999).
For example, problem gamblers were more likely to believe that betting
on a number that looks random gives you a better chance of winning. Random
numbers don’t necessarily look random. A ticket with the numbers
1 - 2 - 3 - 4 - 5 - 6 has exactly the same chance of winning as
a ticket with the numbers 3 - 17 - 21 - 28 - 32 - 47 but many people
have trouble believing this. Most of the time random numbers look random.
In a lotto 6-49 there are only 43 possible consecutive sequenced number
tickets out of approximately 14 million possible tickets. Consequently,
sequenced numbers rarely seem to come up in a lottery although all ticket
numbers have the same chance of winning. As a contrast, consider lotto
2/2; a lottery where the only possible ticket numbers are 1-2, 2-1,
1-1 and 2-2. In this case, all tickets appear to have a pattern
or sequence so that whatever number is drawn, the winning ticket does
not appear to be a random number.
Chasing
Another
important aspect of understanding randomness is "chasing." Chasing
often involves betting larger and larger sums to win back what you’ve
lost. The problem with chasing is not that it doesn’t work but that
it often does. If you double your bet every time you lose, your chance
of winning back what you have lost is as high as 99% depending on your
bankroll and the betting limit (Turner, 1998). In contrast, betting the
same amount each time gives a person at best a 45% chance of winning back
what he has lost. The downside is that when chasing doesn’t work
the result is catastrophic.
Last
year, at Casino Rama in Orillia, Ontario, I calculated that I could work
out a Martingale system (doubling after each loss) starting at $5 a hand
and doubling with each bet until I won, to a maximum bet of $2000. This
would require changing tables occasionally since each table had a maximum
bet about 10 times its minimum (e.g., min = $5, max = $50; min = $50,
max = $500). I could work it so that I would have a 99% chance of winning
$5 and less than a 1% chance of losing $2555. Since it works so often
people may come to believe that it always works. When that one 1% event
occurs, the result is as much a shock as it is a nightmare.
The role of mind
The
human mind is not very good at dealing with randomness. Our minds are
designed to find order, not to appreciate chaos. Ever notice how easy
it is to find faces in clouds? We are wired to look for patterns and find
connections, and when we find patterns we interpret them as real. Consequently,
many people will see patterns in random numbers. When people see patterns
in randomness (e.g., repeated numbers, apparent sequences or winning streaks)
they may believe that the numbers aren’t truly random, and therefore,
can be predicted.
Many
gamblers have experienced a wave-like roller coaster effect of wins and
losses and may believe that you just have to ride out the down slope of
the wave to follow the wave back up. Much of this learning process takes
place unconsciously. The problem is that betting based on these patterns
sometimes appears to work in the short term, reinforcing the belief. But
it will not work in the long term; these patterns are flukes. Suppose
you start playing roulette and you have a lucky winning streak by alternating
your bets between red and black, it will actually take quite a while before
you realise that the betting strategy is not working. Your initial wins
may keep you on the plus side for quite a while because randomness doesn’t
correct for winning streaks either.
The
same is true for superstitious beliefs. Because we don’t understand
randomness we interpret coincidences as meaningful, and consciously or
unconsciously we learn associations that are merely due to chance. Implicit
learning is the driving force behind both betting systems and superstitious
playing strategies. Furthermore, our memory of an event is not just about
what happened but about the emotional experience of what happened. An
important area for future research is the interplay between emotion, experience
and belief.
Randomness, prevention and treatment
My
point is that these beliefs and expectations are not irrational; they
are often logically induced from a person’s experience with random
events. In a sense we are programmed by experience, the implicit learning
of expectations. Theoretically, if a person experiences enough random
events, he should have a pretty good sense of its nature. However, our
minds tend to focus on early experiences, and we often pay more attention
to experiences that support our beliefs than to those that don’t,
so what we expect tends to be distorted. An early win, for example, will
result in distorted expectations. Our data suggest that as many as 50%
of problem gamblers have experienced a large early win (Turner & Liu,
1999). Another key factor is need. If the win fills an emotional, spiritual
or practical need, the distorting effect of the win will be greater.
Our
research has shown that problem gamblers tend to have a poorer understanding
of random events compared to non-problem social gamblers, and that untreated
recovery from gambling problems is associated with higher levels of understanding
about randomness (Turner & Liu, 1999). These findings suggest that
teaching people about randomness may be an important part of both treatment
and prevention.
In
conclusion, often problem gamblers don’t have distorted thoughts,
but unrepresentative experiences which have resulted in distorted beliefs.
I believe that altering or preventing these erroneous beliefs is at least
one important ingredient in effective prevention and treatment programs.
References
Bass, T.A. (1985). The Eudaemonic Pie. Boston: Houghton Mifflin.
Gleick, J. (1987). Chaos: Making a New Science. New York: Penguin
Books.
Turner, N.E. (1998). Doubling vs. constant bets as strategies for gambling.
Journal of Gambling Studies, 14(4), 413–429.
Turner, N.E. & Liu, E. (1999, August). The naive human concept of
random events. Paper presented at the 1999 conference of the American
Psychological Association, Boston.
Submitted: March 22, 2000
Accepted: June 28, 2000
Nigel Turner received his doctorate in cognitive psychology from the
University of Western Ontario in 1995. He has worked at the Addiction
Research Division of the Centre for Addiction and Mental Health for the
past five years where he has developed psychometric tools to measure addiction
processes. He is currently focused on understanding the mental processes
related to gambling addiction. He has extensive experience in various
research methods including psychometrics, surveys, experimental studies,
computer simulations, interviews and focus groups. He has published 10
papers in peer-reviewed journals, including three on problem gambling,
and he has made numerous conference presentations.
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