Gambler’s fallacy

The Gambler’s fallacy is the logical fallacy of assuming that a short-term deviation from statistical probability will be eventually corrected In a totally random event, past performance has no effect on the next attempt.  

Arguing that a totally random event may have a result that will self-correct to the “average” is fallacious. It is based on the false belief that a random process becomes less random, and more predictable, as it is repeated.  

This is most commonly observed in gambling, hence the name of the fallacy. For example, a person playing craps may feel that the dice are “due” for a certain number, based on their failure to win after multiple rolls. This is a false belief since the odds of rolling a certain number are the same for each roll, independent of previous or future rolls of the dice.  

Example of Gambler’s fallacy

  1. This coin has landed heads-up nine times in a row. Therefore,
  2. It will probably land tails-up next time it is tossed.

When a fair coin (one that has no bias for heads or tails) is tossed, the probability of it landing heads-up is 50%, and the probability of it landing tails-up is 50%. These probabilities are unaffected by the results of previous tosses.  

The gambler’s fallacy appears to be a reasonable way of thinking because we know that a coin tossed ten times is very unlikely to land heads-up every time. If we observe a tossed coin landing heads-up nine times in a row we, therefore, infer that the unlikely sequence will not be continued, that next time the coin will land tails up. In fact, though, the probability of the coin landing heads-up on the tenth toss is exactly the same as it was on the first toss. Past results don’t control what will happen next.