“The Gambler’s Fallacy, also known as the Monte Carlo Fallacy, is the false belief that the probability of an event in a random sequence is dependent on preceding events, its probability increasing with each successive occasion on which it fails to occur.”
Seated at a roulette table, a gambler must decide on what color to place his next bet, red or black. He knows there is a 50 percent chance of getting either red or black and that the first four spins of the wheel yielded all reds. The gambler reasons that because half of all spins should result in black and the first four were red, it is more likely the fifth spin of the roulette wheel will be black and places his bet. While his logic appears reasonable, the roulette player has just fallen victim to the Gambler’s Fallacy.
Circumstances like this one are not limited to gamblers; they plague executives and managers in the business world every day. Decision-makers are victimized by the Gambler’s Fallacy because, like all logic errors, it appears reasonable and typically justifies the desired course of action. Recognizing the Gambler’s Fallacy is therefore difficult but necessary.
The Gambler’s Fallacy logic error occurs when a decision-maker incorrectly believes the probability of an independent event is in some way influenced by preceding occurrences. In the roulette example, the player wrongly assumed the first four results would influence the outcome of the fifth spin. Prior to the five spins, the likelihood of spinning five consecutive reds is calculated as:
- Possible Outcomes: Red or Black
- Outcome Distribution: Equal number of Red and Black opportunities
- Probability of Spinning Red: 50 percent
- Probability of Spinning Black: 50 percent
- First Spin is Red: 50 percent
- First and Second Spins are Red: (50 percent) x (50 percent) = 25 percent
- First, Second, and Third Spins are Red: (50 percent) x (50 percent) x (50 percent) = 12.5 percent
- First, Second, Third, and Fourth Spins are Red: (50 percent) x (50 percent) x (50 percent) x (50 percent) = 6.25 percent
- First, Second, Third, Fourth, and Fifth Spins are Red: (50 percent) x (50 percent) x (50 percent) x (50 percent) x (50 percent) = 3.125 percent
Therefore, prior to the first spin of the roulette wheel the change of realizing a Red outcome five consecutive times is a mere 3.125 percent. However, because each spin is an independent event, not in any way influenced by the preceding outcomes, the chance of spinning Red on the fifth attempt having already spun four consecutive Reds is one in two or 50 percent. As long as the game is fair, it will always be 50 percent!
Recognizing the Gambler’s Fallacy
Logic errors are often difficult to recognize, the Gambler’s Fallacy being no exception. Questions decision-makers should consider in order to avoid the Gambler’s Fallacy include:
- Was logic applied to support the desired decision option rather than independently identify the best option?
- Has the decision’s logic been aggressively challenged, preferably by the team’s Devil’s Advocate or a disinterested third party?
- Was an event’s outcome prediction influenced by preceding events, especially if the event occurs independently?
- Was an event’s independence thoroughly assessed or naturally assumed?
- Were the event’s independence and the probability of its outcome calculated by an individual or group having in-depth knowledge and experience of statistics?
Additional insight to the warning signs, causes, and results of logic errors can be found in the StrategyDriven website feature: Decision-Making Warning Flag 1 – Logic Fallacies Introduction.
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