Statistical Consultants Ltd


Gambler's Fallacy

Statistical Theory, Probability, Psychology, Gambling, Addiction

roulette wheel

The gambler’s fallacy is one of several types of faulty thinking common to people with gambling problems. 
Gambler’s fallacy can involve either of the following:
  • Thinking the system is biased in favour of certain outcomes, when it isn’t.  This is also known as reverse gambler’s fallacy.
  • Assuming the combined outcome will conform closely to the marginal outcome probabilities, even though each observation is drawn independently.
For example, let’s say an unbiased roulette wheel is spun several times.  If the ball lands on red, five times in a row, someone prone to gambler's fallacy might believe one of the following:
  • Since red has shown up so many times in a row, it must be a safe bet, therefore I should bet red.
  • Since red has shown up so many times in a row, it must be black’s turn soon, therefore I should bet black.
In reality, black and red would be equally likely to show up next.  Those who see the roulette wheel for what it is would realise that neither bet would be safer than the other.

Sometimes people are so conscious of avoiding the gambler’s fallacy they end up applying it to scenarios where they shouldn’t, with the false assumption that the probabilities of each outcome are equal.  The Monty Hall problem is an example of this.


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