Monte Carlo Roulette 26 Times
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*Monte Carlo Roulette 26 Times 26
*Monte Carlo Roulette 26 Times 16
*Monte Carlo Roulette
*Monte Carlo Roulette 26 Times 3.14
The Times; The Wall Street Journal. Run of black numbers that came up on a Monte Carlo roulette wheel in 1913? Greater piles of chips—losing everything at blacks turned up 26 times in a. Monte Carlo simulation assumes a random outcome for each individual event. If this hypothesis is run many times, we can see a distribution of the resulting returns that results from the combination of these events This informs us about the likelihood of hitting a defined hurdle rate, the most likely return level and the nature of the possible.
Record Breakers….
What is the record for the number of reds that have been recorded in a row on a roulette table? Actually, we are interested in any of the even money bets, so red/black, even/odd, high/low and so on.
This question is particularly interesting for players of the Martingale Roulette system and goes right to the heart of the Gambler’s Fallacy- that mistaken belief that if you see 5 reds in a row, the next result is more likely to be a black. This is a myth, of course- each and every roulette spin is what’s known in statistics as a mutually exclusive event. There is always an equal chance of red and black coming up on an individual spin- the result is in no way affected by previous results.
Known as the “Monte Carlo Method”, the method refers to the Monte Carlo Casino in Monaco where Ulam’s uncle gambled. Ulam developed the theory using the random results in casino games. Unfortunately for gamblers, The Monte Carlo Method proves that even when a roulette wheel lands on black 26 times, the next turn could just as likely land. Perhaps the most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in a row is ( 18 / 37 ) 26-1 or around 1 in 66.6.
UK Casino Club
Marty System
Martingale players are also interested in this question, because this system involves you doubling your bet after a loss. It’s generally played on the even money bets, and the idea is that at some point you will win and claw back all of your previous losses.
Players often look out for long strings of the same result, such as R,R,R,R,R. They’ll then bet on black in the hope that the results will flip back to black to restore the long term equilibrium, something that the D’Alembert system also tries to do.
If you are going to play the Martingale…….
Start your bets low and choose a table with a high limit. That way you will at least give yourself the biggest room for manoeuvre if you suffer a string of losses. Luxury Casino accepts Martingale bets
But if you experience 10 reds in a row, that will blow most Martingale players out of the water, as they’ll either throw in the towel or hit the table limits, after which they won’t be able to double their bets and cover their losses. It’s difficult to figure out the best roulette strategy under these circumstances.
Repeat after me……
These long strings of the same even money results are rare, but they do happen, so you need to factor this risk in if you are playing the Martingale. There are two main risks to this system- one is that you experience a very long string of the same result. The other is that the ball drops in to the zero pocket- that pesky little area that gives the casino its house edge.
You can devise strategies to counter this of course. You could bet with the flow of results rather than against it after you see, say, 5 in a row (but you might have picked the exact time that this wheel of all roulette wheels decides to behave more “normally”). You could also choose a game that offers La Partage which will at least soften the blow of the ball landing in the zero pocket. La Partage is a rule followed by some casinos where they refund half your even money bet when the zero drops in. Many French roulette games offer this.The Record For the Number Of Reds in a Row
So, this will scare you Martingale players! What is the record for the number of reds in a row? Check out this picture from the Rio All Suite Hotel and Casino in Las Vegas. This had all the punters thinking that the wheel was rigged- 7 reds came up in a row (you will see 7 in a row at some point for sure) but these were all the number 19!
Wow
The record for the number of reds in a row was set in the US in 1943 when the colour came up 32 times in a row. The probability of this happening on a European Roulette table is (18/37) to the power of 32 which comes to 1 in 10,321,314,387.
it has also been reported that red came up 39 times in a row in the Casino Monte Carlo, Monaco.
You can see how it doesn’t come up much, but it can happen! Luckily, I should think if anyone was playing the Martingale on that table, they hit the table limits WELL before the 32nd spin.
That’s a Slim Chance, But it Happened
This was probably seen on an American roulette table which makes it even more incredible, because in this case the probability of it happening was (18/38) to the power of 32 which comes to 1 in 24,230,084,485, almost 2.5 times less likely because the American wheel has 2 zeros.
Here’s the thing though- on the 32nd spin, the probability of the next spin coming up red or black was the same- 47.3%. Talking about individual spins and 32 spins is a whole different ball game, and in roulette you can only bet on one spin of the wheel.
If you do a search on Yahoo, you’ll see that many people claim to have seen over 10 in a row on the roulette table. One guy claims to have seen over 15 at least 5 times (I guess we don’t know how much roulette he plays to gauge the percentage of his visits that this represents). Even so, it does happen. 5 in a row, 6 in a row, 7 in a row, 8 in a row and so on is going to happen more frequently. 14 in a row seems to be the big one that people are talking about in their personal experiences.What About Black?
The weird thing I find about these stories, is that everyone always talks about red. I mean, what about the record number of blacks in a row? Or the record number of evens in a row? Or odds? Or high numbers? Or low numbers?
There is a famous session where a roulette ball on a specific wheel landed on black 26 times in a row in a Monte Carlo Casino in the summer of 1913- August 18 to be precise. This even spawned the name “Monte Carlo Fallacy”. Players at the table lost millions of francs betting against the black.
But generally, all the noise is on red, right?
Why People See Red and Not Black
I think here we are into human psychology. Red is an emotive colour, and it’s the one that people talk about the most. Black also gets noticed to a lesser extent, but the others? There has probably been a case of 20 high numbers or odd numbers occurring in a row in a casino, but no-one probably noticed.
So, this brings up an interesting point for us, one that we touch on in our Even Money Switcher system.
If you are tracking the even money results, you don’t just need to bet on red/black. You can look for patterns on the other bets as well. 23 reds in a row has been documented, but I have never heard of 23 high odd red numbers in a row.
Maybe it happened and no-one noticed!
The gambler’s fallacy is the mistaken belief that if an event occurred more frequently than expected in the past then it’s less likely to occur in the future (and vice versa), in a situation where these occurrences are independent of one another. For example, the gambler’s fallacy can cause someone to mistakenly assume that if a coin that they tossed landed on heads twice in a row, then it’s likely to land on tails next.
It’s important to understand the gambler’s fallacy, since it plays a crucial role in people’s thinking, both when it comes to gambling as well as when it comes to other areas of life. As such, in the following article you will learn more about the gambler’s fallacy, understand the psychology behind it, and see what you can do to avoid it.Explanation of the gambler’s fallacy
The gambler’s fallacy involves manifests in two connected ways:
*Through the belief that if a certain independent event occurred more frequently than expected in the past, then it’s less likely to occur again in the future.
*Through the belief that if a certain independent event occurred less frequently than expected in the past, then it’s more likely to occur again in the future.
These beliefs both represent an underlying expectation of systematic reversal in random sequences of independent events, which is mistaken, since when events are independent of one another, their future occurrences are unaffected by their past occurrences by definition, even if people’s intuition leads them to expect otherwise.
For example, consider a situation where you roll a pair of dice, which both land on 6. The odds of this happening in a fair roll are 1/36, since the odds of each die landing on a 6 are 1/6.
Here, the gambler’s fallacy could cause someone to assume that the odds of both dice landing on 6 again on the next roll are lower than 1/36. However, in reality, on each individual roll, the odds of the dice landing on double 6’s are still 1/36. This continues to be true regardless of how many times we roll the dice, since the dice can’t remember what they landed on last time. Essentially, there is no way for the last dice roll to affect the next one, which is why it’s incorrect to assume that these independent events affect each other.
When considering this, it helps to understand the difference between the odds of getting a certain string of outcomes, and the odds of getting a certain outcome given an independent prior string of outcomes. For example, the odds of having a fair coin land on heads 5 times in a row are 0.5^5; this represents the odds of getting a certain string of outcomes. However, the odds of having a fair coin land on heads any single time are always 0.5, regardless of what number toss it is, since each toss is independent of the prior string of outcomes, meaning that it is unaffected by the previous tosses.
As one book on the topic explains:
“If there are 10 balls in the pool bottle, and we want to draw the 1 ball, it is 9 to 1 that we don’t get it; but after five men have drawn balls ahead of us, and none of them have got the 1 ball, it is only 4 to 1 that we don’t get it, because there are only 5 balls left in the bottle.
But if you have drawn five times, not five balls, without getting the 1 ball any time, it is still 9 to 1 against your getting it on the sixth draw, if there are 10 balls in the bottle. Even if you had drawn twenty times, it would still be 9 to 1 against you, as long as 10 balls remained in that bottle…
Some persons imagine that because the odds are so great against any event happening a certain number of times in succession, that when it has happened so many times it is very unlikely to happen again…
If you will toss a coin and put down all the times that it comes one way five times running, you will find that in just half those cases it will go the same way again. Note all the times that it goes six times one way, and you will find that in half of them it will go seven.”
—From “Hoyle’s Games” (by Edmond Hoyle, 1914)Examples of the gambler’s fallacy
One example of the gambler’s fallacy is the mistaken belief that if a coin lands on heads multiple times in consecutive coin tosses, then it’s due to land on “tails” next. A similar example of the gambler’s fallacy is the mistaken belief that if a die landed on the same number (e.g. 6) multiple times in a row, then it’s less likely to land on that same number the next time.
In general, as its name suggests, the gambler’s fallacy is most commonly associated with how people think when they gamble. Beyond the previous examples of this, with coins and dice, another example of this is the incorrect belief that if a certain number was recently drawn in a lottery, then it’s less likely to be drawn again in an upcoming draw.
In addition, another notable example of the gambler’s fallacy in the context of gambling occurred in a 1913 incident, at a roulette game at the Monte Carlo Casino, where the ball fell on the color black 26 times in a row since this was such a rare occurrence, gamblers lost millions of dollars betting that the ball will fall on red throughout this streak, in the mistaken belief that the ball was due to land on it soon.
As one book notes on this phenomenon:
“If you will toss a coin and put down all the times that it comes one way five times running, you will find that in just half those cases it will go the same way again. Note all the times that it goes six times one way, and you will find that in half of them it will go seven. As they roll about 4,000 times a week at Monte Carlo, or 200,000 a year, it ought to come red fifteen times in succession at least once during that time…
Any person who offers to give odds on account of the maturity of the chances, is betting against himself. If a coin has been tossed five times heads, and a man offers to bet 2 to 1 that it will not come heads again, he is just as foolish as if he offered to bet 2 to 1 against the first toss of all.
It is by knowing the folly of such bets, and taking them up at once, that some men get rich, whether the odds are in business or in gaming. It is the acceptance of unfair odds that makes the keeping of a gambling house so profitable. If a person offers you odds that are not fair, it is your own fault if you accept them. The science of betting is to offer odds that look well but that give the bettor a little the best of it in the long run.”
—From “Hoyle’s Games” (by Edmond Hoyle, 1914)
Furthermore, the gambler’s fallacy can also influence people’s thinking and decision making in other areas of life beyond gambling. For example, in the case of childbirth, the gambler’s fallacy means that people often believe that someone is “due” to give birth to a baby of a certain gender, if they have previously given birth to several babies of the opposite gender. A similar phenomenon was described by French scholar Pierre-Simon Laplace, in the first published account of the gambler’s fallacy:
“I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls.
Thus the extraction of a white ball from an urn which contains a limited number of white balls and of black balls increases the probability of extracting a black ball at the following drawing. But this ceases to take place when the number of balls in the urn is unlimited, as one must suppose in order to compare this case with that of births.”
— From “A Philosophical Essay on Probabilities”, by Pierre-Simon Laplace (as translated by Truscott & Emory from the sixth edition of “Essai philosophique sur les probabilités”, which was originally published in 1814)
Finally, the gambler’s fallacy has been shown to affect the judgment, decision-making, and behavior of various professionals, such as loan officers, sports referees, judges, and even psychologists, despite the fact that many of them are well aware of its influence.
Note: the gambler’s fallacy is sometimes referred to as the Monte Carlo Fallacy, as a result of the aforementioned incident at the Monte Carlo casino, or as thedoctrine of the maturity of chances.The psychology behind the gambler’s fallacy
The gambler’s fallacy is a cognitive bias, meaning that it’s a systematic pattern of deviation from rationality, which occurs due to the way people’s cognitive system works. It is primarily attributed to the expectation that even short sequences of outcomes will be highly representative of the process that generated them, and to the view of chance as a fair and self-correcting process.
Essentially, people often assume that streaks of outcomes will even out in the short-term in order to be representative of what an ideal and fair random streak should look like. In the case of a fair coin toss, for example, the gambler’s fallacy can cause people to assume if a coin just landed on heads twice in a row, then it will now land on tails in order to even out the streak and maintain an equal ratio of heads to tails.Monte Carlo Roulette 26 Times 26
As one key study notes:
“People expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short.
In considering tosses of a coin for heads or tails, for example, people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T-T-T, which does not appear random, and also more likely than the sequence H-H-H-H-T-H, which does not represent the fairness of the coin… Thus, people expect that the essential characteristics of the process will be represented, not only globally in the entire sequence, but also locally in each of its parts. A locally representative sequence, however, deviates systematically from chance expectation: it contains too many alternations and too few runs.
Another consequence of the belief in local representativeness is the well-known gambler’s fallacy. After observing a long run of red on the roulette wheel, for example, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red.
Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not ‘corrected’ as a chance process unfolds, they are merely diluted.”
— From “Judgment under uncertainty: Heuristics and biases” (Tversky & Kahneman, 1974). Note that, in addition to viewing chance as a self-correcting process, people sometimes also implicitly treat certain devices, such as coins and dice, as intentional systems, with volition, memory, and ability to affect outcomes.
Furthermore, additional explanations have been proposed for the gambler’s fallacy. This includes, for example, a gestalt approach to assessing strings of events, which involves the belief that upcoming independent random events will be connected to prior ones, as a result of the tendency to perceive patterns and connections where there are none.
These explanations, together with the representativeness explanation, generally revolve around the concept of heuristics, which are mental shortcuts that can be beneficial in some cases, but that can also lead to erroneous judgments in others.
Note: the gambler’s fallacy is closely associated with the la
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*Monte Carlo Roulette 26 Times 26
*Monte Carlo Roulette 26 Times 16
*Monte Carlo Roulette
*Monte Carlo Roulette 26 Times 3.14
The Times; The Wall Street Journal. Run of black numbers that came up on a Monte Carlo roulette wheel in 1913? Greater piles of chips—losing everything at blacks turned up 26 times in a. Monte Carlo simulation assumes a random outcome for each individual event. If this hypothesis is run many times, we can see a distribution of the resulting returns that results from the combination of these events This informs us about the likelihood of hitting a defined hurdle rate, the most likely return level and the nature of the possible.
Record Breakers….
What is the record for the number of reds that have been recorded in a row on a roulette table? Actually, we are interested in any of the even money bets, so red/black, even/odd, high/low and so on.
This question is particularly interesting for players of the Martingale Roulette system and goes right to the heart of the Gambler’s Fallacy- that mistaken belief that if you see 5 reds in a row, the next result is more likely to be a black. This is a myth, of course- each and every roulette spin is what’s known in statistics as a mutually exclusive event. There is always an equal chance of red and black coming up on an individual spin- the result is in no way affected by previous results.
Known as the “Monte Carlo Method”, the method refers to the Monte Carlo Casino in Monaco where Ulam’s uncle gambled. Ulam developed the theory using the random results in casino games. Unfortunately for gamblers, The Monte Carlo Method proves that even when a roulette wheel lands on black 26 times, the next turn could just as likely land. Perhaps the most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in a row is ( 18 / 37 ) 26-1 or around 1 in 66.6.
UK Casino Club
Marty System
Martingale players are also interested in this question, because this system involves you doubling your bet after a loss. It’s generally played on the even money bets, and the idea is that at some point you will win and claw back all of your previous losses.
Players often look out for long strings of the same result, such as R,R,R,R,R. They’ll then bet on black in the hope that the results will flip back to black to restore the long term equilibrium, something that the D’Alembert system also tries to do.
If you are going to play the Martingale…….
Start your bets low and choose a table with a high limit. That way you will at least give yourself the biggest room for manoeuvre if you suffer a string of losses. Luxury Casino accepts Martingale bets
But if you experience 10 reds in a row, that will blow most Martingale players out of the water, as they’ll either throw in the towel or hit the table limits, after which they won’t be able to double their bets and cover their losses. It’s difficult to figure out the best roulette strategy under these circumstances.
Repeat after me……
These long strings of the same even money results are rare, but they do happen, so you need to factor this risk in if you are playing the Martingale. There are two main risks to this system- one is that you experience a very long string of the same result. The other is that the ball drops in to the zero pocket- that pesky little area that gives the casino its house edge.
You can devise strategies to counter this of course. You could bet with the flow of results rather than against it after you see, say, 5 in a row (but you might have picked the exact time that this wheel of all roulette wheels decides to behave more “normally”). You could also choose a game that offers La Partage which will at least soften the blow of the ball landing in the zero pocket. La Partage is a rule followed by some casinos where they refund half your even money bet when the zero drops in. Many French roulette games offer this.The Record For the Number Of Reds in a Row
So, this will scare you Martingale players! What is the record for the number of reds in a row? Check out this picture from the Rio All Suite Hotel and Casino in Las Vegas. This had all the punters thinking that the wheel was rigged- 7 reds came up in a row (you will see 7 in a row at some point for sure) but these were all the number 19!
Wow
The record for the number of reds in a row was set in the US in 1943 when the colour came up 32 times in a row. The probability of this happening on a European Roulette table is (18/37) to the power of 32 which comes to 1 in 10,321,314,387.
it has also been reported that red came up 39 times in a row in the Casino Monte Carlo, Monaco.
You can see how it doesn’t come up much, but it can happen! Luckily, I should think if anyone was playing the Martingale on that table, they hit the table limits WELL before the 32nd spin.
That’s a Slim Chance, But it Happened
This was probably seen on an American roulette table which makes it even more incredible, because in this case the probability of it happening was (18/38) to the power of 32 which comes to 1 in 24,230,084,485, almost 2.5 times less likely because the American wheel has 2 zeros.
Here’s the thing though- on the 32nd spin, the probability of the next spin coming up red or black was the same- 47.3%. Talking about individual spins and 32 spins is a whole different ball game, and in roulette you can only bet on one spin of the wheel.
If you do a search on Yahoo, you’ll see that many people claim to have seen over 10 in a row on the roulette table. One guy claims to have seen over 15 at least 5 times (I guess we don’t know how much roulette he plays to gauge the percentage of his visits that this represents). Even so, it does happen. 5 in a row, 6 in a row, 7 in a row, 8 in a row and so on is going to happen more frequently. 14 in a row seems to be the big one that people are talking about in their personal experiences.What About Black?
The weird thing I find about these stories, is that everyone always talks about red. I mean, what about the record number of blacks in a row? Or the record number of evens in a row? Or odds? Or high numbers? Or low numbers?
There is a famous session where a roulette ball on a specific wheel landed on black 26 times in a row in a Monte Carlo Casino in the summer of 1913- August 18 to be precise. This even spawned the name “Monte Carlo Fallacy”. Players at the table lost millions of francs betting against the black.
But generally, all the noise is on red, right?
Why People See Red and Not Black
I think here we are into human psychology. Red is an emotive colour, and it’s the one that people talk about the most. Black also gets noticed to a lesser extent, but the others? There has probably been a case of 20 high numbers or odd numbers occurring in a row in a casino, but no-one probably noticed.
So, this brings up an interesting point for us, one that we touch on in our Even Money Switcher system.
If you are tracking the even money results, you don’t just need to bet on red/black. You can look for patterns on the other bets as well. 23 reds in a row has been documented, but I have never heard of 23 high odd red numbers in a row.
Maybe it happened and no-one noticed!
The gambler’s fallacy is the mistaken belief that if an event occurred more frequently than expected in the past then it’s less likely to occur in the future (and vice versa), in a situation where these occurrences are independent of one another. For example, the gambler’s fallacy can cause someone to mistakenly assume that if a coin that they tossed landed on heads twice in a row, then it’s likely to land on tails next.
It’s important to understand the gambler’s fallacy, since it plays a crucial role in people’s thinking, both when it comes to gambling as well as when it comes to other areas of life. As such, in the following article you will learn more about the gambler’s fallacy, understand the psychology behind it, and see what you can do to avoid it.Explanation of the gambler’s fallacy
The gambler’s fallacy involves manifests in two connected ways:
*Through the belief that if a certain independent event occurred more frequently than expected in the past, then it’s less likely to occur again in the future.
*Through the belief that if a certain independent event occurred less frequently than expected in the past, then it’s more likely to occur again in the future.
These beliefs both represent an underlying expectation of systematic reversal in random sequences of independent events, which is mistaken, since when events are independent of one another, their future occurrences are unaffected by their past occurrences by definition, even if people’s intuition leads them to expect otherwise.
For example, consider a situation where you roll a pair of dice, which both land on 6. The odds of this happening in a fair roll are 1/36, since the odds of each die landing on a 6 are 1/6.
Here, the gambler’s fallacy could cause someone to assume that the odds of both dice landing on 6 again on the next roll are lower than 1/36. However, in reality, on each individual roll, the odds of the dice landing on double 6’s are still 1/36. This continues to be true regardless of how many times we roll the dice, since the dice can’t remember what they landed on last time. Essentially, there is no way for the last dice roll to affect the next one, which is why it’s incorrect to assume that these independent events affect each other.
When considering this, it helps to understand the difference between the odds of getting a certain string of outcomes, and the odds of getting a certain outcome given an independent prior string of outcomes. For example, the odds of having a fair coin land on heads 5 times in a row are 0.5^5; this represents the odds of getting a certain string of outcomes. However, the odds of having a fair coin land on heads any single time are always 0.5, regardless of what number toss it is, since each toss is independent of the prior string of outcomes, meaning that it is unaffected by the previous tosses.
As one book on the topic explains:
“If there are 10 balls in the pool bottle, and we want to draw the 1 ball, it is 9 to 1 that we don’t get it; but after five men have drawn balls ahead of us, and none of them have got the 1 ball, it is only 4 to 1 that we don’t get it, because there are only 5 balls left in the bottle.
But if you have drawn five times, not five balls, without getting the 1 ball any time, it is still 9 to 1 against your getting it on the sixth draw, if there are 10 balls in the bottle. Even if you had drawn twenty times, it would still be 9 to 1 against you, as long as 10 balls remained in that bottle…
Some persons imagine that because the odds are so great against any event happening a certain number of times in succession, that when it has happened so many times it is very unlikely to happen again…
If you will toss a coin and put down all the times that it comes one way five times running, you will find that in just half those cases it will go the same way again. Note all the times that it goes six times one way, and you will find that in half of them it will go seven.”
—From “Hoyle’s Games” (by Edmond Hoyle, 1914)Examples of the gambler’s fallacy
One example of the gambler’s fallacy is the mistaken belief that if a coin lands on heads multiple times in consecutive coin tosses, then it’s due to land on “tails” next. A similar example of the gambler’s fallacy is the mistaken belief that if a die landed on the same number (e.g. 6) multiple times in a row, then it’s less likely to land on that same number the next time.
In general, as its name suggests, the gambler’s fallacy is most commonly associated with how people think when they gamble. Beyond the previous examples of this, with coins and dice, another example of this is the incorrect belief that if a certain number was recently drawn in a lottery, then it’s less likely to be drawn again in an upcoming draw.
In addition, another notable example of the gambler’s fallacy in the context of gambling occurred in a 1913 incident, at a roulette game at the Monte Carlo Casino, where the ball fell on the color black 26 times in a row since this was such a rare occurrence, gamblers lost millions of dollars betting that the ball will fall on red throughout this streak, in the mistaken belief that the ball was due to land on it soon.
As one book notes on this phenomenon:
“If you will toss a coin and put down all the times that it comes one way five times running, you will find that in just half those cases it will go the same way again. Note all the times that it goes six times one way, and you will find that in half of them it will go seven. As they roll about 4,000 times a week at Monte Carlo, or 200,000 a year, it ought to come red fifteen times in succession at least once during that time…
Any person who offers to give odds on account of the maturity of the chances, is betting against himself. If a coin has been tossed five times heads, and a man offers to bet 2 to 1 that it will not come heads again, he is just as foolish as if he offered to bet 2 to 1 against the first toss of all.
It is by knowing the folly of such bets, and taking them up at once, that some men get rich, whether the odds are in business or in gaming. It is the acceptance of unfair odds that makes the keeping of a gambling house so profitable. If a person offers you odds that are not fair, it is your own fault if you accept them. The science of betting is to offer odds that look well but that give the bettor a little the best of it in the long run.”
—From “Hoyle’s Games” (by Edmond Hoyle, 1914)
Furthermore, the gambler’s fallacy can also influence people’s thinking and decision making in other areas of life beyond gambling. For example, in the case of childbirth, the gambler’s fallacy means that people often believe that someone is “due” to give birth to a baby of a certain gender, if they have previously given birth to several babies of the opposite gender. A similar phenomenon was described by French scholar Pierre-Simon Laplace, in the first published account of the gambler’s fallacy:
“I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls.
Thus the extraction of a white ball from an urn which contains a limited number of white balls and of black balls increases the probability of extracting a black ball at the following drawing. But this ceases to take place when the number of balls in the urn is unlimited, as one must suppose in order to compare this case with that of births.”
— From “A Philosophical Essay on Probabilities”, by Pierre-Simon Laplace (as translated by Truscott & Emory from the sixth edition of “Essai philosophique sur les probabilités”, which was originally published in 1814)
Finally, the gambler’s fallacy has been shown to affect the judgment, decision-making, and behavior of various professionals, such as loan officers, sports referees, judges, and even psychologists, despite the fact that many of them are well aware of its influence.
Note: the gambler’s fallacy is sometimes referred to as the Monte Carlo Fallacy, as a result of the aforementioned incident at the Monte Carlo casino, or as thedoctrine of the maturity of chances.The psychology behind the gambler’s fallacy
The gambler’s fallacy is a cognitive bias, meaning that it’s a systematic pattern of deviation from rationality, which occurs due to the way people’s cognitive system works. It is primarily attributed to the expectation that even short sequences of outcomes will be highly representative of the process that generated them, and to the view of chance as a fair and self-correcting process.
Essentially, people often assume that streaks of outcomes will even out in the short-term in order to be representative of what an ideal and fair random streak should look like. In the case of a fair coin toss, for example, the gambler’s fallacy can cause people to assume if a coin just landed on heads twice in a row, then it will now land on tails in order to even out the streak and maintain an equal ratio of heads to tails.Monte Carlo Roulette 26 Times 26
As one key study notes:
“People expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short.
In considering tosses of a coin for heads or tails, for example, people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T-T-T, which does not appear random, and also more likely than the sequence H-H-H-H-T-H, which does not represent the fairness of the coin… Thus, people expect that the essential characteristics of the process will be represented, not only globally in the entire sequence, but also locally in each of its parts. A locally representative sequence, however, deviates systematically from chance expectation: it contains too many alternations and too few runs.
Another consequence of the belief in local representativeness is the well-known gambler’s fallacy. After observing a long run of red on the roulette wheel, for example, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red.
Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not ‘corrected’ as a chance process unfolds, they are merely diluted.”
— From “Judgment under uncertainty: Heuristics and biases” (Tversky & Kahneman, 1974). Note that, in addition to viewing chance as a self-correcting process, people sometimes also implicitly treat certain devices, such as coins and dice, as intentional systems, with volition, memory, and ability to affect outcomes.
Furthermore, additional explanations have been proposed for the gambler’s fallacy. This includes, for example, a gestalt approach to assessing strings of events, which involves the belief that upcoming independent random events will be connected to prior ones, as a result of the tendency to perceive patterns and connections where there are none.
These explanations, together with the representativeness explanation, generally revolve around the concept of heuristics, which are mental shortcuts that can be beneficial in some cases, but that can also lead to erroneous judgments in others.
Note: the gambler’s fallacy is closely associated with the la
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