Gambler’s fallacy:

Definition Example
When it is suggested that the likelihood of a random event can be affected by or predicted from other, independent events. The coin flip has resulted in 5 “heads” in a row. I’m overdue for a “tails”.
Also known as: monte carlo fallacy / hot hand fallacy
True randomness will contain patches of what often looks like a non-random pattern to human minds which are highly prone to extract patterns. The converse of the gambler’s fallacy is the “hot hand fallacy” in which a winning steak is irrationally expected to continue.

For most gambling games, the chances of winning or losing the same amount remains constant with each game played. However, if coins are accumulating in a machine that must eventually pay out, there is an increased chance of winning with each play. This fallacy also does not apply when there is additional information available such as which cards have been played as determined by “card counting” by skilled blackjack and poker players.

External links

Case Study One

People often irrationally suppose that their 50th airplane flight is much more likely to end in tragedy than their 1st airplane flight. All things being equal, the risk is the same for each flight.

Case Study Two

After throwing a “six” with a fair 6-sided die, the probability of throwing a second “six” remains the same as as it was when throwing the first “six”; 16.33%.

Keep in mind that a fallacious argument does not entail an erroneous position.

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