Gambler’s fallacy – logical fallacies

Description
The Gambler’s Fallacy is the fallacy of assuming that a short-term deviation from statistical probability will be corrected in the short-term. 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 as the odds of rolling a certain number are the same for each roll, independent of previous or future rolls.
Example

  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.