"We think future possibilities are affected by past events."
Some possibilities are affected by past events. Others aren't.
Like the Sunk Cost Fallacy this cognitive bias leads us astray when we misconstrue discrete events as parts of an ongoing process.
While the Sunk Cost Fallacy addresses physical events the Gambler's Fallacy addresses information events.
As with the Sunk Cost Fallacy if past events change the task being worked upon this fallacy is not a fallacy at all. If a gambler knows what cards have been drawn from a deck he knows the probability of drawing the remaining cards changes. Something finite is being acted upon which changes the remainder.
However when events occur without regard to previous events this cognitive bias will lead the gambler astray. Dice may be rolled an unlimited number of times, and each roll of the dice is unconnected with the previous roll. We do not 'use up' numbers such that yet-unrolled numbers become increasingly likely. The probability of each roll is the same whether it was rolled each of the previous ten rolls or not at all.
The storytelling portion of our brains often has difficulty discerning which is which.
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