The Gambler’s Fallacy is a cognitive bias that occurs when an individual erroneously believes that the likelihood of a particular outcome is influenced by previous outcomes, even when the events are independent and unrelated. It is the mistaken notion that, in a random sequence of events, a deviation from what is expected in the short term must be corrected in the immediate future.

The fallacy gets its name from its association with gambling situations, where people may believe that if a particular outcome (such as the flip of a coin or the roll of a die) has occurred repeatedly, the opposite outcome is more likely to happen soon. In reality, the outcomes of truly random events are statistically independent, and the probability of each outcome remains the same regardless of past results.

For example, consider a fair coin toss. If the coin comes up heads five times in a row, someone succumbing to the Gambler’s Fallacy might believe that tails is “due” to come up on the next toss. In reality, the probability of getting heads or tails on the next toss is always 1 in 2 (assuming a fair coin).

Key points about the Gambler’s Fallacy:

1. **Independence of Events:** The fallacy arises from a misunderstanding of probability and the assumption that past events influence future ones, even when they are independent.

2. **Random Processes:** The fallacy is most commonly associated with games of chance, like roulette, dice rolls, or coin flips, where each event is independent and has no impact on subsequent events.

3. **Regression to the Mean:** The belief in the Gambler’s Fallacy can lead people to expect a “correction” in outcomes, assuming that extreme events are followed by more typical ones, which may not be the case.

4. **Risk of Misguided Decision-Making:** Believing in the Gambler’s Fallacy can lead individuals to make poor decisions, such as changing their strategy in a game of chance based on a perceived pattern.

5. **Hot Hand Fallacy:** The opposite of the Gambler’s Fallacy is the “Hot Hand Fallacy,” where individuals believe that a winning streak is likely to continue, despite the outcomes being independent events.

Understanding probability and recognizing the independence of random events are essential in avoiding the Gambler’s Fallacy. In situations involving chance, each event is its own occurrence, and past outcomes do not influence future ones in truly random processes.