The Mathematics Of Gambling

The Mathematics Of Gambling

Anyone who has worked with people who gamble come to realize that they often have a number of erroneous beliefs and attitudes about control, luck, prediction and chance. The main purpose of this chapter is to draw a connection between the folk beliefs of the individual who gambles and the reality of the physical world, to illustrate where people make errors and to explore the origin of these errors.

The basic problem is that people who gamble often believe they can beat the odds and win. Even those who know the odds still believe they can win. Turner (2000) has argued that much of this is the result of experience with random events: random events fool people into believing they can predict their random outcomes.

Another problem is that the human mind is predisposed to find patterns and does so very efficiently. For example, natural formations like the “face” in the Cydonia Mensae region of Mars or the Sleeping Giant peninsula on the shore of Lake Superior in Northern Ontario, which have human-like features, are interpreted as images of people. In addition, deviations from expected results, such as winning or losing streaks, are often perceived as too unlikely to be a coincidence. As an example of our willingness of find patterns, a few years ago Eric Von Daniken (1969) wrote a book in which he claimed to have found evidence for the influence of extraterrestrial beings on human history. Much of his “evidence” was based on such things as the coincidental similarity between a rock drawing in the Sahara desert and the appearance of a modern astronaut’s space suit. The book has sold 7 million copies, testifying to the ease with which people can be swayed by the argument that patterns cannot be random coincidence. Some people believe that “random” events have no cause and are thus mysterious. As a result, they may believe there is a greater opportunity to influence the random outcome through prayer or similar means. In the past, some religions have used dice games to divine the will of the gods (Gabriel, 2003). Related to this is the notion that everything happens for a reason and thus random outcomes must contain a message.

Some people who gamble believe that there is no such thing as a random event and that they can therefore figure out how to win. In a sense, they are correct in that all random events are the result of physical forces or mathematical algorithms. In practice, however, they are completely wrong. A random event occurs when a difficult problem (e.g., controlling the exact speed, movement and height of a dice throw) is combined with a complex process (e.g., the dice rolling across a table and bouncing against a bumper on its far side). This combination leads to complete uncertainty as to what will actually occur.

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