Seriously! three times...the individual vs. combined probability.

[famososMuertos]

If it happens 2 times, and it is less strange that it happens consecutively (1/1369), but 3 times or more, at least I had not seen it. And I asked myself, how difficult is it for this to happen?

The roulette in this case consists of 37 numbers so the probability that a number will come up is 1/37 point. It's that easy. And in each turn it is an independent event from the other, so the probability remains the same.

But if we combine these individual events in the probability that they repeat 1,2,3, etc. "x" times in a row we use the combined, which in this case is 1 / 37x1 / 37x1 / 37 = 1/50653

And here the point that can mislead our minds, the simple probability that it comes out for the fourth time is 1/37 because to reach that fourth time obviously the combined probability has already been exceeded.

I was able to document that moment and it can be verified at:
https://bcgame-project.github.io/bcgame-roulette/?hash=4fc8bf1f62b929c249c756bdc7a36d5dca3e519effadfdb23fff76d84a7bdd42

Capture:

^{Source: bc.game/roulette}

Hash:
https://i.imgur.com/LzWCzGC.jpg
https://i.imgur.com/DGH33AI.jpg
https://i.imgur.com/s4CDuKU.jpg

This may be a well-documented and well-known topic, but I experienced it today and wanted to share it, although I understand beforehand that the cool thing would have been to bet on green in those three rounds.  

_______
^{https://en.wikipedia.org/wiki/Roulette
Google Search:What are the odds of hitting the same number 3 times in roulette?}

^{As you can see from the above calculation hitting the same single number three consecutive times amounts to 1 chance in 50,653. This corresponds to a 0.0019% chance of winning with the same number three times in a row. Note that repeating roulette outcomes by themselves are not that rare phenomena}

<sup>Source:https://www.casinoreports.ca/roulette/odds-probabilities/

Considerations: Yes, roulette is one of those games where the house has a lot of advantage, among other side shortcuts that the topic can discuss, so it is about this point in particular.
POT.Ty</sup>

[xypos]

Thanks for sharing.

This is the infamous gambler's fallacy. People's predisposition to patterns can often mislead and misinform.

A classic example is precisely this. "If there was 2 greens in a row, then there is no chance that the third one is green!" or "if it's been high for the last 15 rolls, surely the 16th will be low!" are things that I hear so often in gambling communities. Of course, none of these are backed by logic and will break down the more rolls you do.

[khaled0111]

...

Indeed and the example above confirms that those are just fallacies.
Although the probability of hitting the same number three times in a row in Roulette is 1/50653, it can still happen! The number being "zero" makes it more odd. Well done on documenting it OP.
That being said, it's always recommended to check the fairness of the game and verify each round's result.

[Hamphser]

snip

Not surprising and this is a common behavior for most gamblers on whenever they do saw some patterns then later on they do make out presumptions that neither do hit or not and when it happens then for sure

they would really be sticking out into their minds that it does work and surely be used on future games to come but once reality do slap you in the face then you would surely tell this thing to yourself that

no guaranteed strategy works in gambling unless if you are dealing with strategic based type of games like poker but speaking with luck based then its impossible, everything is random.

[cafucafucafu]

If you do enough rolls you'll eventually come across a pattern like that.

Gambler's fallacy is very powerful and affects virtually every person that I've come across in one form or another.

People seem to think that they are all knowing and understand the patterns in the universe having no knowledge of basic probabilities or maths. It's ironic how they call certain casinos scam after such events not knowing that if these black swan events don't happen over millions of rolls, the casino is likely to be rigged.

[Kemarit]

...

Indeed and the example above confirms that those are just fallacies.
Although the probability of hitting the same number three times in a row in Roulette is 1/50653, it can still happen! The number being "zero" makes it more odd. Well done on documenting it OP.
That being said, it's always recommended to check the fairness of the game and verify each round's result.

Yup, gamblers fallacy, previous outcome doesn't influence the next result. However, there are instances, like in this one that probabilities is really very odd.

I've also been playing roulette for many years now, but I avoided double 00 because the house edge are high as compare to single 0 but still you can't discount the fact that this can happen.

[Poker Player]

...although I understand beforehand that the cool thing would have been to bet on green in those three rounds.  

That's the point. In the gambler's fallacy, which has been mentioned, the bettor confuses the probability of individual events with that of a series of events.

On the other hand, I don't usually play roulette, but playing poker I also sometimes see very improbable events, such as having a poker on the flop and being beaten with a superior poker by an opponent who only had a pair on the flop. What happens is that the less probable they are, the less frequently I see them.

[mv1986]

Thanks for sharing.

This is the infamous gambler's fallacy. People's predisposition to patterns can often mislead and misinform.

A classic example is precisely this. "If there was 2 greens in a row, then there is no chance that the third one is green!" or "if it's been high for the last 15 rolls, surely the 16th will be low!" are things that I hear so often in gambling communities. Of course, none of these are backed by logic and will break down the more rolls you do.

It depends if you look at it from a conditional probability perspective. The problem is the ROI and the double the bet size strategy. The probability for green coming 16 times in a row is extremely low, namely (roughly) 0.5 to the power of 16. Now the thing is that by the sixteenth round you have already doubled your bet size 15 times, making the ROI so small that there is no justifiable relation between the expected ROI and your then chance to win.

Apart from that, it is right that there is no reason to believe that green shows up again even after showing up 15 times in a row. It is funny to see in casinos how players cross off numbers on their paper when they play roulette because when the 30 showed up last round, it can't show up again, right?

[ralle14]

That reminds me of the jackpot you could possibly win on Primedice where you need to roll 77.77 twice in a row. I think there's one user that was manage to hit it but unfortunately he didn't have enough bet amount to reach the minimum requirement. There's that one promo where I played roulette every day for two months and placed a few hundred bets but I haven't experienced three zeroes in a row.

[paxmao]

just as you said, independent events are ... independent. It is just that people have a number of bias and those have been well determined by psychology: the authority bias, the narrative bias, ... and many many others. Among these, the narrative is usually a strong one in bets, and it is fine in sports betting in which events are not independent at a physical level, but in pure random games it is a dangerous one to have. The fact that the probability is above zero means that it will eventually happen.

Speaking of which... you could potentially devise a system that works 99.99 % of the times, but when it fails, you loose everything. If you follow it, be certain you will be at zero sooner or later.

[mv1986]

just as you said, independent events are ... independent. It is just that people have a number of bias and those have been well determined by psychology: the authority bias, the narrative bias, ... and many many others. Among these, the narrative is usually a strong one in bets, and it is fine in sports betting in which events are not independent at a physical level, but in pure random games it is a dangerous one to have. The fact that the probability is above zero means that it will eventually happen.

Speaking of which... you could potentially devise a system that works 99.99 % of the times, but when it fails, you loose everything. If you follow it, be certain you will be at zero sooner or later.

There is also the mental accounting bias. That is one reason why casinos give you chips. It feels less painful if you lose that plastic money. Same for depositing from credit cards, that feels very different than if you were to have your hard earned cash in your hands one more time before you hand it over to a casino. The industry knows about all those biases very well.

[Lanatsa]

If you do enough rolls you'll eventually come across a pattern like that.

Gambler's fallacy is very powerful and affects virtually every person that I've come across in one form or another.

People seem to think that they are all knowing and understand the patterns in the universe having no knowledge of basic probabilities or maths. It's ironic how they call certain casinos scam after such events not knowing that if these black swan events don't happen over millions of rolls, the casino is likely to be rigged.

Agree with this all knowing kind of behavior for most gamblers on where they do form up those kind mentality and would push on what they do believe in more future bets that they would make.

Once a pattern that they do really believe on hadn't work then they would find another one which they had believed or that something they had presumed on.

Common reason on where people do say its a scam when they lost and tell that its unfair or rigged when they don't have money on their pocket for them to spend on.

[STT]

Probability is not certainty, you have far better odds of some event happening but its always possible for anything to occur.   The casino itself will operate on this basis in order to leverage an average profit but at times also the casino will be paying out money all day and will not make a profit because that day the gamblers won on average.  Its part of the game that what should happen wont always occur, trips up alot of people .  
  I try to play the long game for this reason because I dont expect to get lucky off one bet even if an event is probable I need to be winning multiple times to do well usually.

[AicecreaME]

snip

Not surprising and this is a common behavior for most gamblers on whenever they do saw some patterns then later on they do make out presumptions that neither do hit or not and when it happens then for sure

they would really be sticking out into their minds that it does work and surely be used on future games to come but once reality do slap you in the face then you would surely tell this thing to yourself that

no guaranteed strategy works in gambling unless if you are dealing with strategic based type of games like poker but speaking with luck based then its impossible, everything is random.

I agree.

This kind of patterns most often are just traps, to ruin your plays, because you'll have second thoughts on what to do next, and when you bet on that number, the house will counter that by their own algorithm that assure their wins most of the time. So when you go into their trap, you're pretty messed up and your whole day would be all just about frustration saying "I should've stick to my plan".

[Hamphser]

snip

Not surprising and this is a common behavior for most gamblers on whenever they do saw some patterns then later on they do make out presumptions that neither do hit or not and when it happens then for sure

they would really be sticking out into their minds that it does work and surely be used on future games to come but once reality do slap you in the face then you would surely tell this thing to yourself that

no guaranteed strategy works in gambling unless if you are dealing with strategic based type of games like poker but speaking with luck based then its impossible, everything is random.

I agree.

This kind of patterns most often are just traps, to ruin your plays, because you'll have second thoughts on what to do next, and when you bet on that number, the house will counter that by their own algorithm that assure their wins most of the time. So when you go into their trap, you're pretty messed up and your whole day would be all just about frustration saying "I should've stick to my plan".

You should have stick to your plan? but when that plan had been busted out again then whats next? You would really be ending up on the same frustration in the end of the day.

This is how gambling works and its the reality that you should be aware on the first place and wont really be expecting that much because if you do really try to fight
on what you do believe its working then you would really be just messing your own life.

Dont come into this kind of point on where you dont have any coins left on your pocket and able to sell out all of your assets.

[cafucafucafu]

If you do enough rolls you'll eventually come across a pattern like that.

Gambler's fallacy is very powerful and affects virtually every person that I've come across in one form or another.

People seem to think that they are all knowing and understand the patterns in the universe having no knowledge of basic probabilities or maths. It's ironic how they call certain casinos scam after such events not knowing that if these black swan events don't happen over millions of rolls, the casino is likely to be rigged.

Agree with this all knowing kind of behavior for most gamblers on where they do form up those kind mentality and would push on what they do believe in more future bets that they would make.

Once a pattern that they do really believe on hadn't work then they would find another one which they had believed or that something they had presumed on.

Common reason on where people do say its a scam when they lost and tell that its unfair or rigged when they don't have money on their pocket for them to spend on.

Yeah. Psychology is a funny thing, aye.

I guess our brains are just flawed. These same people when they win think that they are the king of the world and found the best strategy ever. And when they lose they cry like a baby and think that the house is out to get them.

Absolutely ridiculous, but somehow I see it every day in chats. You're not going to beat the mathematical certainty of losing in the long run, unfortunately.

[Baofeng]

Yes, this is a classic example of Probability of Events, we gamblers are so bias that we didn't see this occurring, but when it happens, this kind of favourable outcome is hard for us to grasp and understand. I'e seen this happening when I also played roulette, and I just scratch my head because the way chances and probability works against us in gambling.

[Wexnident]

But that's wrong, isn't it? Considering the previous result as a basis for the result of the next possible result should be wrong since each result is independent of each other. If it were calculated like what you said, then it would technically be possible to identify the chances of a certain number appearing after x amount of rolls (the highest chance ones anyway) based on the previous rolls. Or I'm just stupid really, but I've never really considered each result as dependent on each other in the first place. Still it isn't really a new thing, heck I even use said logic in exams and whatnot back when I was in high school. Nothing embarrassing about it, we all do it imo.

[Woodie]

I have seen this happen once but I thought it was all manipulation because getting the same number in 3 consecutive rounds is a Longshot in roulette and especially that it's a zero makes it even a stretch because this number hardly gets rolled. I usually play some lightning roulette and for this kind where you get 3 consecutive numbers is a low probability play afaik.

Yes, this is a classic example of Probability of Events, we gamblers are so bias that we didn't see this occurring, but when it happens, this kind of favourable outcome is hard for us to grasp and understand. I'e seen this happening when I also played roulette, and I just scratch my head because the way chances and probability works against us in gambling.

If it happens once then the next time numbers would be rolled 3 consecutive times should take a long time because numbers don't lie, so does probability.

[mv1986]

I have seen this happen once but I thought it was all manipulation because getting the same number in 3 consecutive rounds is a Longshot in roulette and especially that it's a zero makes it even a stretch because this number hardly gets rolled. I usually play some lightning roulette and for this kind where you get 3 consecutive numbers is a low probability play afaik.

Yes, this is a classic example of Probability of Events, we gamblers are so bias that we didn't see this occurring, but when it happens, this kind of favourable outcome is hard for us to grasp and understand. I'e seen this happening when I also played roulette, and I just scratch my head because the way chances and probability works against us in gambling.

If it happens once then the next time numbers would be rolled 3 consecutive times should take a long time because numbers don't lie, so does probability.

Why are you saying that the zero "hardly" gets rolled? On average it gets rolled as often as any other number depending on the type of roulette. It is usually 1 : 37, with zero having the same odds as the numbers from 1 to 36. The probability for any number to get rolled three times in a row is exactly the same for every single number in the game.