My understanding of the gambler fallacy is that the gambler acts as if the roulette wheel can learn and remember how it has behaved previously and then adjust its own behavior accordingly. The wheel can think and is real! (Just to go along with Briggs’ way of explaining things.). Certainly one of the more interesting topics in roulette is that of the 'Gambler's Fallacy'. 'Something is Due based on past spins' Let's run off an example, because it so easy to prove that this 'Fallacy' is no fallacy at all but is instead a predictable event. Using a 00 wheel - After 114 spins we have 5 numbers that haven't appeared. But the core principles of gambler’s fallacy are the same. But other roulette systems use a much more complicated bet selection. However, the result is the same. 4.3 The Gambler’s Fallacy Gambling often involves fair processes: fair dice, fair roulette wheels, fair decks of cards, etc. But people sometimes forget that fair processes are independent. If a roulette wheel comes up black nine times in a row, they figure it’s “due” for red.
The gambler’s fallacy, which is also known as “the fallacy of the maturity of chances” or the Monte Carlo fallacy, is a false assumption that whenever some random event occurs frequently over some time period, it is less likely to occur in the near future. The reasons why this line of thinking is so popular among the less experienced gamblers are fairly simple: most people are prone to assume that every small streak must eventually even out in order to keep the action in balance and fair.
This kind of assumption gives the player a false sense of control over the flow of the game, allowing him to believe that he can predict the course of events. Unfortunately, this belief is invariably false, as subsequent random events don’t stop being random because of previous outcomes.
In order to illustrate this point, let’s consider a simplified game of Roulette with no 0 or 00 fields on the wheel. In such a case, the probability of the ball landing on a Red field is exactly 1/2, which means that the probability of winning two subsequent Red bets is 1/4, while the probability of winning three subsequent Red bets is 1/8.
After winning two subsequent Red bets, a person falling back on the gambler’s fallacy will generally assume that the outcome of the third game is more likely to be Black than Red, because the probability of winning three subsequent Red bets is only 1/8. However, at this point the probability of winning that bet is 1/2, because the previous outcomes are no longer unknown, which means that their probabilities are 1. While a streak of three Red wins indeed has a chance of 1/8, this is true only before the first of three balls is tossed onto the Roulette wheel.
The reason why gambler’s fallacy is so dangerous is that it may lead players to relying on betting systems that increase their chance of ruin, such as the Martingale. In this betting system, the player is required to double his bet after every loss, particularly when placing even money wagers such as Red or Black in Roulette and Pass or Don’t Pass in Craps. The gambler utilizing the Martingale assumes that this allows him to cover all of his past losses and gain one unit.
For example, if the opening bet is $1 and the player loses three bets in a row, the total losses will equal $1+$2+$4 = $7. Consequently, winning on the fourth game allows the player to win $8 and profit $1. Unfortunately, the possibility of suffering a string of defeats that will deprive you of your money in total is very real and in fact quite likely once you reach wagers that you can hardly afford.
The truth is that regardless of the system you use, the ratio of money lost to money wagered will always be close to the normal house advantage. The only difference between playing the Martingale and betting flat is in fact the speed at which you accelerate your game, which means that you’re quite likely to run out of money significantly faster and that you won’t be able to enjoy yourself at the tables as much as you normally would.
There are many dishonest people that take advantage of the gambler’s fallacy to sell their betting systems – if you ever stumble onto a site advertising for an offer of this kind, you should definitely give it a pass and take everything written there with a grain of salt.
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.”
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 every spin of the reels on a slot machine is a discrete, independent event, but she wasn’t hearing it. She was absolutely convinced that if she just stuck with that machine, the longer she played, the likelier she would be to win.
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.
Roulette Gambler Fallacy Example
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.
For example, if you make 100 spins on a slot machine, you’re still playing in the short term. The long run hasn’t even come close to getting there. The outcome of the next spin can heavily skew the average results per spin.
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 idea is that when a bet hits several times in a row, it’s less likely to hit again. In the Martingale System, you assume that if black has hit seven times in a row, it’s less likely to hit on the next spin because of how unlikely it is that you’ll have the ball land on black eight times in a row.
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.
Roulette Gambler Fallacy Meaning
It won’t take long before your system fails – disproving the Gambler’s Fallacy.