Elements of the gambler's fallacy:
(1) an recurring event occurs with a known, fixed probability
(2) a belief that the frequency of the event in the recent past may influence its future frequency
If an event has a true, known probability then the chances of its next occurrence is fixed. There is no edge.
Example of the fallacy: A perfect coin will have a 50% chance of being heads or tails. With the gambler's fallacy a person believes that having a series of "tails" will increase the chances that the next try will be "heads".
Example of the fallacy: A lottery site listing the frequency of numbers hit. A gambler may believe that numbers that have not been hit in the past will have a greater chance of being hit in the future.
Example of the fallacy: A string of good luck in the past does not guarantee a greater likelihood of winning a game of chance.
Factors contributing:
(1) wanting to win (wishful thinking)
(2) wanting to have a sense of control
Observations:
(1) If the frequency of past occurrences impacts the frequency of a future event, then the probability of its occurrence is not fixed. The coin may not be "true".
(2) Natural events like the weather may vary about a mean. If the weather has been warmer for a period of time then there is a good chance that the weather will be cooler as it gravitates to the mean. However, weather does not have a fixed probability and is affected by many variables.
