Probability, Random Events, and the Mathematics of Gambling

that one can beat the odds (Turner et al., 2002). Furthermore, it is argued that prevention
requires disseminating accurate information about the reality of gambling and the way these
games can fool individuals into believing they can win. A second goal of this chapter is to demystify
random events.
The following parts of this chapter:
• provide a list of some of the more common misconceptions that people who gamble have
about the nature of random chance;
• give definitions and examples of probability, odds and other key concepts related to
random chance;
• examine, from a theoretical point of view, how a mechanistic universe filled with causeand-effect
relationships can produce random events;
• describe how specific types of games produce random events, including how slot
machines work; and
• discuss the origins of some erroneous beliefs.
Erroneous Beliefs
People hold a number of misconceptions about the nature of random events. Many of these
misconceptions are due to the nature of random events and to misunderstandings about the
words used to describe the phenomenon. Table 1 summarized these misunderstandings. The
first column lists a number of the common misconceptions, or “naive concepts,” that
individuals with a gambling problem may express concerning random events. The second
column provides a series of statements that describe the true nature of these events. The
subsequent few pages provide resource information on probability, odds and randomness to
help the therapist understand the difference between the naive concept of randomness and the
actual nature of random events.
Table 1. Random events: Naive concepts vs. actual nature
Naive Concept of Random Events Actual Nature of Random Events
Events are consistently erratic. Events are just plain erratic (fundamental
uncertainty). Random events are often
described as “clumpy” because clumps of wins
or losses sometimes occur.
Things even out. Things do not have to even out, but sometimes
seem to, as more observations are added (law of
large numbers).
If a number hasn’t come up, it’s due. If heads
has occurred too often, tails is due.
Numbers that haven’t come up are never due to
come up. Coins and dice have no memories
(independence of events).
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