The Gambler's Fallacy - Casino Players Worst Enemy
One of the most famous truisms of probability is the Gambler's Fallacy.
The Gambler's Fallacy is a rule that every statistician knows, and every gambler should know as well, since in the end, gambling is all about odds and probabilities.
The Gambler's Fallacy
The Gambler's Fallacy simply states that the outcome of each individual trial of an event is independent of previous outcomes. For example the odds of flipping a coin so that it comes up heads 20 times in a row, assuming the coin is fair, are extremely long, longer than one in a million. Therefore, if you have flipped a coin and it has come up 19 times in a row, you may be eager to lay very high odds against the next flip coming up heads.
However, to do so would be a mistake. Once the 19 heads have already been flipped, the odds of the next flip coming up heads is one in two, just like every flip before it. The coin has no memory of what has gone before. Believing a certain outcome is "due" because it has not appeared in a statistically unlikely amount of time is the Gambler's Fallacy.
The Gambler's Fallacy and Casino Players
The Gambler's Fallacy can lead to problems in many casino games. Casino roulette wheels have grids showing which numbers have been played before, so that players can decide which numbers are "due." In reality, no number is "due" any more than any other. A player can just as easily decide that the numbers that have appeared frequently are "hot" and will appear again.
A player who has seen black come up ten times may confidently put a large sum on red assuming that it somehow has a better than even money chance of coming up on the next spin. Again, it does not. The wheel has no memory any more than the coin does, or any more than dice or cards do. Believing that they do and betting accordingly is the Gambler's Fallacy and can lead to bigger losses than anticipated.