The Gambler's Fallacy - Casino Players Worst Enemy
One of the most famous truisms of probability is the Gambler's Fallacy – the false belief that it’s possible to predict the future by examining the past.
This is something every statistician knows and every gambler should know. In the end, gambling is all about odds and probabilities, and if a gambler is unfamiliar with how probabilities work, chances are that he will start seeing patterns that don't exist. It's a road to ruin.
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.
-I call Heads... Again...
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.
Inverse Gambler's Fallacy
Say that you walk in to a casino and hear the bells and whistles go off on a slot machine. You locate the sound and see a man screaming and running around euphorically. He just hit the million-dollar jackpot. For how long do you think he has been playing? Is it more likely that he has been sitting there spinning the reels for hours compared to this being his first game?
Instinctively most would say that he probably has played for a long time, that he is a slots junkie who finally got his payoff. That is, however, just a case of Inverse Gambler's Fallacy.
The Gamblers Fallacy explains that we can't predict the outcome of a random event based on prior outcomes. Likewise we can't say anything about the prior events - it's even impossible to guess if there have been any - based on the present.
There is no way we can know anything about the past by looking at a single random event. That's the Inverse Gambler's Fallacy.
Inverse Gambler's Fallacy - Creation of the World
What are the odds of you sitting here reading this article? That the big bang created a sun where all elements were made, including the coal you're made up of, and that this coal became small marine animals that finally crawled up from the ocean and was transformed into humans by evolution. Pretty slim I suppose.
One might suspect that millions and millions of universes have been created and that something has fine tuned everything to reach where we are today. When you think about it, the fact that you are sitting there is a proof of multiple universes.
-What are the odds?
But remember the example when you walk in to the casino and saw the lucky man hit that jackpot. This is the same false belief. If you could step out of our universe and watch all the (unlikely) life that is going on - workers stuck in traffic jams on the highway, people falling in love and you reading this - you couldn't determine if you saw the first or one millionth attempt of the universe creating life.
It's tempting to think that we're not universe's first try but our existence is no proof of that. Again, that belief would be the Inverse Gambler's Fallacy.
Since we are used to finding patterns in life - if I do A then B will happen - we are drawn to think that there are patterns everywhere. Even though we can intellectually understand randomness, we often look for explanations when faced with a series of random events not affecting one another.
The little voice in the head goes: "I understand the gamblers fallacy, but now the roulette ball has ended up on red nine times in a row. Next one must be black. I would be a fool not to bet."
If that happens, try to the listen to the logic side of your brain. Your instincts are very often a fallacy.
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