Roulette Fallacy
The Gambler's Fallacy is the misconception that something that has not happened for a long time has become 'overdue', such a coin coming up heads after a series of tails. This is part of a wider doctrine of 'the maturity of chances' that falsely assumes that each play in a game of chance is connected with other events.
- Roulette Fallacy
- Russian Roulette Fallacy
- Roulette Fallacy
- Roulette Strategy Gambler's Fallacy
- Russian Roulette Fallacy
The Gambler’s Fallacy has multiple names. It’s also described as the “Fallacy of the Maturity of Chances.” I’ve also seen it called “The Monte Carlo Fallacy.”
- The Gambler's Fallacy is the idea that past behavior influences future behavior. In everyday life, it's a good strategy — there are all kinds of ways that events in the past affect events in the.
- Roulette is a game that is full of fallacies and myths, especially when it comes to playing roulette on the Internet. Here are a full list of myths and misconceptions that need to be cleared up. Online Roulette Is Rigged – Lots of disgruntled players like to go onto message boards and blogs to tell the world that online roulette is rigged.
- A fallacy in which an inference is drawn on the assumption that a series of chance events will determine the outcome of a subsequent event. Also called the Monte Carlo fallacy, the negative recency effect, or the fallacy of the maturity of chances.
- The gambler's fallacy is defined as an (incorrect) belief in negative autocorrelation of a non-autocorrelated random sequence. 2 For example, individuals who believe in the gambler's fallacy believe that after three red numbers appearing on the roulette wheel, a black number is 'due,' that is, is more likely to appear than a red number.
No matter what you call it, gamblers love it.
The Gambler’s Fallacy is the belief that a random event affects subsequent random events in a game of independent events.
It shouldn’t be confused with the understanding that some games do have a memory. As the composition of a deck of cards changes in blackjack, so do the odds.
But in a game like roulette, where each spin of the wheel is an independent event, past events have no bearing on the probability of future events.
In this post, I’m going to show you how to disprove the Gambler’s Fallacy.
Random Events Don’t Become Overdue
I took a trip to the Winstar Casino once with a lovely woman. On the way there, she explained to me that she didn’t just play slot machines. She played slot machines with a strategy.
And, her strategy was simplicity itself:
She just made sure to play the same slot machine every time she visited. The longer she played that one machine, the likelier she was to eventually hit a win on it when it came “due.”
I tried to explain to her that she could switch from machine to machine and probably have the same increased probability of eventually winning, but she just wouldn’t hear it.
She believed in the Gambler’s Fallacy.
How a Slot Machine Works
Suppose you have a simple slot machine with three reels and 10 symbols on each reel. And you should also suppose that each of those symbols has a 1/10 probability of coming up.
To get the probability of a specific symbol coming up on all three reels at the same time on the payline, you just multiply the probabilities together. When dealing with multiple events and wanting them all to happen at the same time, you multiply the probabilities together.
Your results are 1/10 X 1/10 X 1/10, or 1/1000.
When you spin the reels and hope to win, you have a 1/1000 probability of hitting that combination.
If you miss it and spin the reels again, you have the same number of symbols on each reel with the same probability of coming up.
The formula doesn’t change. The slot machine game doesn’t remember what happened before. The results are entirely random and, most of all, the results are independent of each other.
People think that real money slots pay out less after a winning spin to catch up with their theoretically predicted payback percentage, but that’s not even necessary. The difference between the payout odds and the odds of winning take care of that over the long run.
This phenomenon is called The Law of Large Numbers.
What About the Law of Large Numbers?
The Law of Large Numbers suggests that the more trials you have, the close your results will get to the mathematically predicted results. This would seem to contradict the Gambler’s Fallacy, but the truth is more complicated than that.
Yes, the Law of Large Numbers suggests that your results will PROBABLY get closer to the predicted results, but the large numbers in question are SO large that the result of the next spin has a minimal effect on the averages.
But once you’ve made 100,000 spins, the results are probably starting to get closer to the average.
If you win 1000 to 1 on the 100,001st spin, though, it doesn’t affect the average that much. The number has gotten too big for an individual outcome to affect it much.
So, even though the odds don’t change as you play, the Gambler’s Fallacy still isn’t true.
What About the Gambler’s Fallacy and the Game of Roulette?
Roulette is perfect for understanding how to disprove the Gambler’s Fallacy. In fact, most roulette betting systems are products of the Gambler’s Fallacy.
When you bet on a single number in roulette, you can easily calculate the probability of winning that bet. You just compare the number of ways to win with the total number of possible outcomes.
A roulette wheel has 38 numbers on it, and every number has an equal probability of coming up. This makes the probability of winning a single-number bet just 1/38.
If you bet on the number 17 and hit the 17, what is the probability that the 17 will hit on your next spin?
The formula doesn’t change based on your previous result. You still have 38 numbers on the wheel, and only one of them is numbered 17.
The probability remains 1/38.
Frank Scoblete would like you to think that the numbers get “hot” at the roulette table. He would have you look at the historical results on the board and find a number that has hit more than once in the last hour to bet on.
His assumption that one of these numbers has gotten “hot” is just as erroneous as thinking it’s gotten cold.
The probability is the same – 1/38.
If the 17 got removed from the wheel after hitting, that WOULD change the probability of every outcome on the table.
But that 17 is still there, and it’s still just one number out of 38 numbers.
How Do Betting Systems Try to Use the Gambler’s Fallacy?
I bring up the Martingale System pretty often here. It’s the classic betting system where you double the size of your bet after every loss. The idea is that eventually the worm has to turn, and when it does, you’ll win back the money you lose on the previous bets.
The trouble is, you’re not betting on the ball landing on black eight times in a row.
You’re betting that it will land on black on the next spin.
Since you have 38 numbers, and 18 of them are black, the probability remains 18/38, or 47.37%.
The conclusion is that eventually you’ll have a losing streak that lasts long enough that you won’t be able to afford the next bet. Or, even if you can afford it, the casino won’t let you place the bet because of their maximum betting limits.
But the Martingale isn’t the same betting system that relies on believing in the Gambler’s Fallacy.
The Paroli System
The almost direct opposite of the Martingale System is the Paroli System. It doesn’t work, either, but it’s illustrative of the diametrically opposite approach working at least some of the time.
In the Paroli System, instead of doubling the size of your bet after a loss, you double the size of your bet after a win. Most of the time, you have a win goal in mind where you reset to your initial bet size.
The idea behind the Paroli System is that sometimes outcomes get hot, and when they do, you can take advantage of it by letting your bet ride.
For example, you set a goal of winning $40.
You start by betting $5 on black. You win, so now you bet $10 on black. You win again, and so you now bet $20 on black. This time when you win, you have your $40 win goal. So you start over again by betting $5 on black.
After a loss, you just start with your initial betting unit again.
Like the Martingale System, the Paroli System doesn’t work, because the fantasy that numbers get hot or cold in any kind of predictable way is just not how reality works.
If it were this easy to guarantee yourself a win at a casino, the casinos would go out of business.
And I’ve never seen a player at a roulette table get backed off for using any kind of betting system.
Conclusion
Believing in the Gambler’s Fallacy is one of the major mistakes that gamblers make, so how can you disprove it?
It’s easy.
Just spend a little time using one of the many betting systems that assume that past events have some kind of influence over future results.
It won’t take long before your system fails – disproving the Gambler’s Fallacy.
The Gambler’s Fallacy is the misleading belief that the probability of a specific occurrence in a random sequence is dependent on preceding events—that its probability will increase with each successive occasion on which it fails to occur.
Suppose that you roll a fair die 14 times and don’t get a six even once. According to the Gambler’s Fallacy, a six is “long overdue.” Thus, it must be a good wager for the 15th roll of the dice. This conjecture is irrational; the probability of a six is the same as for every other roll of the dice: that is, 1/6.
Chance Events Don’t Have Memories
In practical terms, the Gambler’s Fallacy is the hunch that if you play long enough, you will eventually win. For example, if you toss a fair coin and flip heads five times in a row, the Gambler’s Fallacy suggests that the next toss may well flip a tail because it is “due.” In actuality, the results of previous coin flips have no bearing on future coin flips. Therefore, it is poor reasoning to assume that the probability of flipping tails on the next coin-toss is better than one-half.
Roulette Fallacy
A classic example of the Gambler’s Fallacy is when parents who’ve had children of the same sex anticipate that their next child ought to be of the opposite sex. The French mathematician Pierre-Simon Laplace (1749–1827) was the first to document the Gambler’s Fallacy. In Philosophical Essay on Probabilities (1796,) Laplace identified an instance of expectant fathers trying to predict the probability of having sons. These men assumed that the ratio of boys to girls born must be fifty-fifty. If adjacent villages had high male birth rates in the recent past, they could predict more birth of girls in their own village.
Russian Roulette Fallacy
There Isn’t a Lady Luck or an “Invisible Hand” in Charge of Your Game
Roulette Fallacy
The Gambler’s Fallacy is what makes gambling so addictive. Gamblers normally think that gambling is an intrinsically fair-minded system in which any losses they’ll incur will eventually be corrected by a winning streak.
In buying lottery tickets, as in gambling, perseverance will not pay. However, human nature is such that gamblers have an irrational hunch that if they keep playing, they will eventually win, even if the odds of winning a lottery are remote. However, the odds of winning the jackpot remain unchanged … every time people buy lottery tickets. Playing week after week doesn’t change their chances. What’s more, the odds remain the same even for people who have previously won the lottery.
Gambler’s Fallacy Coaxed People to Lose Millions in Monte Carlo in 1913
The Gambler’s Fallacy is also called the Monte Carlo Fallacy because of an extraordinary event that happened in the renowned Monte Carlo Casino in the Principality of Monaco.
Roulette Strategy Gambler's Fallacy
On 18-August-1913, black fell 26 times in a row at a roulette table. Seeing that that the roulette ball had fallen on black for quite some time, gamblers kept pushing more money onto the table assuming that, after the sequence of blacks, a red was “due” at each subsequent spin of the roulette wheel. The sequence of blacks that occurred that night is an unusual statistical occurrence, but it is still among the possibilities, as is any other sequence of red or black. As you may guess, gamblers at that roulette table lost millions of francs that night.
Gambler’s Fallacy is The False Assumption That Probability is Affected by Past Events
The Gambler’s Fallacy is frequently in force in casual judgments, casinos, sporting events, and, alas, in everyday business and personal decision-making. This common fallacy is manifest by the belief that a random event is more likely to occur because it has not happened for a time (or a random event is less likely to occur because it recently happened.)
- While growing up in India, I often heard farmers discuss rainwater observing that, if the season’s rainfall was below average, they worry about protecting their crops during imminent protracted rains because the rainfall needs to “catch-up to a seasonal average.”
- In soccer / football, kickers and goalkeepers are frequently prone to the Gambler’s Fallacy during penalty shootouts. For instance, after a series of three kicks in the same direction, goalkeepers are more likely to dive in the opposite direction at the fourth kick.
- In the episode “Stress Relief” of the fifth season of the American TV series The Office, when the character Jim Halpert learns that his fiancee Pam Beesley’s parents are divorcing, he quotes the common statistic that 50% of marriages wind up in divorce. Halpert then comments that, because his parents are not divorced, it is only reasonable that Pam’s parents are getting divorced.
The Gambler’s Fallacy is a Powerful and Seductive Illusion of Control Over Events That are Not Controllable
Don’t be misled by the Gambler’s Fallacy. Be aware of the certainty of statistical independence. The occurrence of one random event has no statistical bearing upon the occurrence of the other random event. In other words, the probability of the occurrence of a random event is never influenced by a previous, or series of previous, arbitrary events.
Idea for Impact: Be skeptical of most judgments about probabilities. Never rely exclusively on your intuitive sense in evaluating probable events. In general, relying exclusively on your gut feeling or your hunches in assessing probabilities is usually not a reason to trust the assessment, but to distrust it.