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Topic: Seriously! three times...the individual vs. combined probability. (Read 367 times)

sr. member
Activity: 1414
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Odds are low, but not impossible. Would like to suppose you're being subjected to Gambler's Fallacy due to the fact that it sounded as if you assumed there is no chance that such a pattern will come out on your roll. Gambler's Fallacy happens when your heuristics and biases make you assume that there are patterns you can exploit in a game that would guarantee you wins.
Well the real question is: are you really going to argue with the mathematics of probability just because you saw/might have seen a pattern? Sounds dangerously close to the edge of hopeful thinking and superstition to me. Indeed math says that the probability of getting the same 1/37 for 4 times is less than a 50000th or if you prefer percentages: then about 0.002%. I think you should go with the math with this one.
Sad to say the human brain loves patterns, so it wouldn't be able to avoid pining on these things even if its life depended on it. It has helped us survive the deserts of Africa back when we are still hunter-gatherers, nowadays it serves to cost us a lot in situations where randomness is king. But with enough practice and self-discipline anyone could at least turn a blind eye on these flimsy patterns and help the gambler see the situation for what it really is.
legendary
Activity: 1610
Merit: 2563
LE ☮︎ Halving es la purga
Well the real question is: are you really going to argue with the mathematics of probability just because you saw/might have seen a pattern? Sounds dangerously close to the edge of hopeful thinking and superstition to me. Indeed math says that the probability of getting the same 1/37 for 4 times is less than a 50000th or if you prefer percentages: then about 0.002%. I think you should go with the math with this one.
Hi,
I think the dangerous thing here is to say that if the green come out 4 times the probability is 0.002%.
So "you can't go against math"; the probability that 0 or any number will come out 4 times is 0.00005%.
Smiley
__________
____
__

...//...:
+1
Part of the point of bringing the OP to discussion lies in what is commented on in its source:
 
Quote
... He claims to have personally been at the table in the summer of 2000 on roulette wheel number 211 in Caesar’s Palace. At approximately half past one in the afternoon, the ball landed in the number 7 six times in a row.
Fuente:https://www.roulette17.com/resources/record-same-number-results/

I was a witness...  ; )

legendary
Activity: 2002
Merit: 1586
BTC 100k 2024
Well the real question is: are you really going to argue with the mathematics of probability just because you saw/might have seen a pattern? Sounds dangerously close to the edge of hopeful thinking and superstition to me. Indeed math says that the probability of getting the same 1/37 for 4 times is less than a 50000th or if you prefer percentages: then about 0.002%. I think you should go with the math with this one.
hero member
Activity: 2226
Merit: 953
Temporary forum vacation
If you play at crypto casinos with challenges,,, you will see that this possibility happens many times daily. Imagine every day at a casino like bitvest, you will see players hit over 1000x many times in the high roller or high wins leaderboard.

I have even seen challenges for roulette to hit a number 4 or 5 times in a row and many players will get it.

I play auto of 100k rolls easily in a few hours so by math, you can easily hit a streak like that in 1 session Smiley
full member
Activity: 1708
Merit: 126
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 types of games like poker but speaking with luck-based then it's impossible, everything is random.

That's also the reason why gamblers are advised not to believe presumptions because it could only lead to confusion and later on make it a strategy that could also give us losses. We should keep in mind that gambling could mostly give us a good profit by luck.
legendary
Activity: 2506
Merit: 1823
🙏🏼Padayon...🙏
That's cool. Although, yeah, it is not that rare, but it's something to have encountered it yourself. Of course, it was kind of cool to have placed a bet on a green when the previous winning number was the same, and cooler even on the third time, but I doubt somebody would easily do that given the fact that there are 37 numbers all in all and hitting the same number three times in a row is highly unlikely. But there you have it, that's random gambling right there.
hero member
Activity: 1974
Merit: 775
Leading Crypto Sports Betting & Casino Platform
Even though you don't win anything with this sequence, someone must be really lucky to face it during a live roulette session.

Just got curious to see what was the maximum repeated number sequence rolled and found out it was six times registered twice in history: one in 2000 at Caesar’s Palace, when the number 7 appeared six times in a following sequence and another in 1959 at San Juan Hotel (Puerto Rico), when number 10 also appeared six times. It means 1 chance in 3.01 billion of happening. Do you know a higher record?

If 3 times in a roll is already shocking for many, imagine how 6 times would look like if you suddenly faced it during your peaceful daily game.

https://www.roulette17.com/resources/record-same-number-results/
legendary
Activity: 2534
Merit: 2270
That's probably a coincidence but at the same time a thing that can happen. It's not like the odds said that the wins shouldn't be consecutive.
Exactly, the odds says the chances of you winning the gamble. I don't see why it's a big issue other than the fact that that person is just probably in the right place at the right time with his gamble, it's the way of the game, sometimes it favors others more than us.
"that person is just probably in the right place at the right time with his gamble"? I'm sorry but I don't understand who the hell you're talking about zanezane? Three green zeros consecutively came out according to the picture and from what famososMuertos has told, then it means that nobody has won anything around the table, it's the first rule of the roulette game and certainly the most important of all of them.
full member
Activity: 868
Merit: 150
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That's probably a coincidence but at the same time a thing that can happen. It's not like the odds said that the wins shouldn't be consecutive.
Exactly, the odds says the chances of you winning the gamble. I don't see why it's a big issue other than the fact that that person is just probably in the right place at the right time with his gamble, it's the way of the game, sometimes it favors others more than us.
legendary
Activity: 2254
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1396 odds isn't that big
-snip-
The odds are 1: 50653. That means it happens about once in 51,000 games. I don't know how busy OP's casino is, but I can well imagine that 51k games are played here in a relatively short period of time - possibly even within one day. So if that's the case that's about once a day. So the whole thing no longer sounds quite so unlikely.
member
Activity: 882
Merit: 63
1396 odds isn't that big and sometimes the wins can really happen consecutively so it's nothing to worry about and it's not like it's a rare occasion, pretty sure that with so many people gambling, it's more unlikely for this to not happen than for it to happen.
legendary
Activity: 1610
Merit: 2563
LE ☮︎ Halving es la purga
Hi, RealMalatesta  

In the development of the thread it is has been commented in fact if you look at post above #27 it is commented.

As for the other that you comment, there are also those that allow 0 and double 00, in a certain way the house advantage grows, in the so-called American roulette.

House edge
Quote
The house average or house edge or house advantage (also called the expected value) is the amount the player loses relative for any bet made, on average. If a player bets on a single number in the American game there is a probability of 1⁄38 that the player wins 35 times the bet, and a 37⁄38 chance that the player loses their bet. The expected value is:
−1 × 37⁄38 + 35 × 1⁄38 = −0.0526 (5.26% house edge)

For European roulette, a single number wins 1⁄37 and loses 36⁄37:
−1 × 36⁄37 + 35 × 1⁄37 = −0.0270 (2.70% house edge)

For triple-zero wheels, a single number wins 1⁄39 and loses 38⁄39:
−1 × 38⁄39 + 35 × 1⁄39 = −0.0769 (7.69% house edge)
Source:https://en.wikipedia.org/wiki/Roulette#House_edge
full member
Activity: 1064
Merit: 158
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In the end, probability is just a guide to help us think of our action that will give us the best chance to win, and the thing is that the probability will always be true, but the expected outcome is not.

one great example of the gambler's fallacy that was specifically mentioned many times already is that moment when your number in a roulette does not show for 15 times in a row so you bet that it will show in the next 15.
full member
Activity: 1498
Merit: 146
It can happen, the odds says 1:1369 not 1 after 1369, there's always the chances that stuff can happen consecutive times in a row. Probably it was just the right time and betting that made those things happen.
Simply a coincidence I guess because we can't really test this and prove the strategies especially in roulette like games on the online platform.

Gambling is just an entertainment factor but when you got enough luck you can make money with it.
legendary
Activity: 2338
Merit: 1124
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?
To be honest, as strange and near impossible it is to land the same 3 numbers one after the other, it's the same odds of any number landing. I will explain with an example

Imagine if numbers 12, 18 and 30 arrived in 3 random spins of the roulette wheel. Now, what was the probability of each of them occurring? It's again the same 1/37 x 1/37  x 1/37

Getting three 0s can be devastating for a roulette game where casino doesn't give the choice of betting on 0, believe me, there are such roulette games. I don't remember where I saw it but they consider 0 as their house edge and give you the rate-rate odds for the other numbers. So, basically you get 2x on red and black instead of 1.98 or so but then you lose if green 0 is the result.
legendary
Activity: 1610
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LE ☮︎ Halving es la purga
hi,
Smiley I understand your point, but if it is difficult very difficult, you just don't understand it or I think you are a bit confused in the utility of probabilities for your benefit.

Let's start with the fact that roulette has independent events, so that any combination that you think of with 3 or 4 numbers comes out, for example 23,12,9 is difficult. Not because such a combination does not happen in the randomness of roulette, but because of the fact that for someone betting to hit the number 3 times in a row; whether this number is the same or different, it requires a probability of 0.002%.

What you mention, although it is understood, because it was said is the same as "independent events".

Now, in this case you only bet on "0" the probability that it comes out three times is the same as 23,12,9 or any other, it seems that not but all combinations of three numbers have the same probability, it is that way simple.

There is something called the principle of improbability, some call it rarities, e.g. in the case that the same number is repeated it is a rarity, so that, we believe it, but not because the probability is different it is because someone achieves that feat.


...//...:
The correct notation is 1:36 (odds for hit)
hero member
Activity: 2828
Merit: 793
I am terrible at Fantasy Football!!!
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.
This happens a lot, however it may seem to be very unlikely that something like this happens, however lets take a look at the next sequence: 23, 12 and 9, nothing special seems to be going on however the odds of this sequence appearing are the same 1 in 50653, however since the numbers are all different and with no apparent relationship then we think nothing of it, but if we see three zeros coming in a row then that sequence seems special when in fact it is not.
legendary
Activity: 3010
Merit: 1127
It can happen, the odds says 1:1369 not 1 after 1369, there's always the chances that stuff can happen consecutive times in a row. Probably it was just the right time and betting that made those things happen.
Probabilities is indeed there but knowing those odds or chances then its really hard to consider on having that consecutive hits that it do follow up some pattern but hey its plausible.

When someone do able to hit up something and have attached some activity or something like charm or anything a gambler could attached of then this is where new belief comes in.

This would be used more in future gambling activities to come and thats how dumb human brain is.
legendary
Activity: 2534
Merit: 2270
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.
It seems you didn't get it, it was a roulette wheel game then getting a 3 green zeros streak is not a bad day for the casino, it's the jackpot day, because when one green zero comes out at the roulette game not any player wins at the table, only the house does. And usually after a green zero outcome players bet bigger stakes because they think there are less chances to get a second green zero in a row. Then after two green zeros I think no one at the table thought a third green zero in a row could come out.
member
Activity: 1120
Merit: 68
It can happen, the odds says 1:1369 not 1 after 1369, there's always the chances that stuff can happen consecutive times in a row. Probably it was just the right time and betting that made those things happen.
tz
sr. member
Activity: 350
Merit: 251
Yes, this stuff happens more commonly than you would expect.

Casinos handle millions of bets and this pattern occurs around one in 50000 times, which means that for every million bets you're expecting 3 greens to come together around 20 times.

Gambler's fallacy is a hell of a drug sometimes...
legendary
Activity: 2030
Merit: 1157
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.
hero member
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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.
hero member
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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.
legendary
Activity: 2534
Merit: 1655
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.
hero member
Activity: 812
Merit: 509
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.
sr. member
Activity: 2436
Merit: 324
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.
sr. member
Activity: 2310
Merit: 454
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".
STT
legendary
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Leading Crypto Sports Betting & Casino Platform
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.
hero member
Activity: 2786
Merit: 646
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.
legendary
Activity: 2030
Merit: 1157
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. Wink
legendary
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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.
legendary
Activity: 3136
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dice9.win
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.
legendary
Activity: 2030
Merit: 1157
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? Wink
legendary
Activity: 1232
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...although I understand beforehand that the cool thing would have been to bet on green in those three rounds.  Smiley

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.
legendary
Activity: 3038
Merit: 1350
...
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.
hero member
Activity: 812
Merit: 509
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.
sr. member
Activity: 2436
Merit: 324
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.
legendary
Activity: 2478
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...
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.
sr. member
Activity: 532
Merit: 250
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.
legendary
Activity: 1610
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LE ☮︎ Halving es la purga
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.  Smiley

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

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