# Gamblers fallacy Vs reality

#### Odds4slots

##### Newbie member
I assume that we all know that house always wins and they have PHD guys to mathematically prove it,but....random ,means random according to our observations,that means random outcome in short therm must have a pattern in long run. That's what PRNG try to mimick. So the question is if in long run Pseudo RNG must reach the pattern,is there any way to exploit it?

#### Odds4slots

##### Newbie member
If roulette wheel fail to produce a number over a 10000 spins ,then it will be discarded as biased for sure. So we can safely assume that particular number MUST show up within 10000 spins. Infeasible at that point,but that's just a start, what do you guys think?

#### Odds4slots

##### Newbie member
Therefore after 50 blacks in roulette there's still 50/50 percent chances for black or red , although in long run reds will have to "catch up" somehowe because that's what we observe.

#### Mr_Slot5

##### Senior Member
Therefore after 50 blacks in roulette there's still 50/50 percent chances for black or red , although in long run reds will have to "catch up" somehowe because that's what we observe.
This is something I've never grasped and is where maths does simply not add up.

After 50 black results, the next spin (if we ignore the green) is a 50/50 chance, right? Except it's not because the more times a black result is shown consecutively, the rule of large numbers suggests red becomes more likely. There is an outright discrepancy between the odds of red or black for that spin and the odds of red or black in context of longer term odds/part of a larger sequence.

Okay

#### Odds4slots

##### Newbie member
This is something I've never grasped and is where maths does simply not add up.

After 50 black results, the next spin (if we ignore the green) is a 50/50 chance, right? Except it's not because the more times a black result is shown consecutively, the rule of large numbers suggests red becomes more likely. There is an outright discrepancy between the odds of red or black for that spin and the odds of red or black in context of longer term odds/part of a larger sequence.
That's exactly my point. So is it really gambler fallacy to bet on red at that point? Or its just kind of card counting advantage at that point

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#### Odds4slots

##### Newbie member
This is something I've never grasped and is where maths does simply not add up.

After 50 black results, the next spin (if we ignore the green) is a 50/50 chance, right? Except it's not because the more times a black result is shown consecutively, the rule of large numbers suggests red becomes more likely. There is an outright discrepancy between the odds of red or black for that spin and the odds of red or black in context of longer term odds/part of a larger sequence.
Just because at that point math simply doesn't ad up. Mr Slots5 is absolutely right.

#### Odds4slots

##### Newbie member
For me there's no reason why the red couldn't land 8000 in the row,but because of observation we assume that random means...pattern in long run and we created PNRG to mimick that

##### Ueber Meister
MM
Try doing a simulation of few miilion runs of heads or tails and
check the difference between the two results, you will always
find they are very close, a run of one result seems to be cancelled out
by runs of the other so is some form of compensation active, I know
it sounds daft but consider another situation...
Some sequences are so rare that they have never happenned or likely to
happen ever in the future, they say that any deal of the entire pack of cards randomly shuffled will be unique and will have never
occurred before.
If you can accept that some situations are unique, is there any advantage to only bet for the opposite to land when a sequence of heads/tails , blacks/ reds or whatever have landed a number of times which is just about feasable, as a few more of the same
results will end up in a chance that has never ever happened.Hope I explained it ok.
Randomness is not as simple as it may seem

#### Buffalo Bill

##### Experienced Member
MM
While stats like these are theoretically possible, the probability of landing red or black even 1000 time in a row is so low that it is effectively zero.
You could spin a roulette wheel from now until the heat death of the universe and not get this result.
There is no possible way of predicting the outcome of the next spin regardless of any previous result or sample size.

#### ChopleyIOM

webby
This is something I've never grasped and is where maths does simply not add up.

After 50 black results, the next spin (if we ignore the green) is a 50/50 chance, right? Except it's not because the more times a black result is shown consecutively, the rule of large numbers suggests red becomes more likely. There is an outright discrepancy between the odds of red or black for that spin and the odds of red or black in context of longer term odds/part of a larger sequence.

Without the green and assuming a fair wheel, the chance of red or black on any given spin is 50/50, irrespective of whatever sequence of results preceded the current spin.

Each spin is an entirely random and independent event, the previous spins of the wheel 'don't exist' in terms of exerting any influence whatsoever over the current spin, or changing the probability of any given result.

Try this as a thought experiment, you have just seen a roulette wheel spin ten blacks in a row when someone walks in off the street into the casino, so he has no idea what the last ten spins were.

He bets on black, you bet on red, do you have a better chance of winning with your bet on red than he does with his bet on black?

#### Mr_Slot5

##### Senior Member
Without the green and assuming a fair wheel, the chance of red or black on any given spin is 50/50, irrespective of whatever sequence of results preceded the current spin.

Each spin is an entirely random and independent event, the previous spins of the wheel 'don't exist' in terms of exerting any influence whatsoever over the current spin, or changing the probability of any given result.

Try this as a thought experiment, you have just seen a roulette wheel spin ten blacks in a row when someone walks in off the street into the casino, so he has no idea what the last ten spins were.

He bets on black, you bet on red, do you have a better chance of winning with your bet on red than he does with his bet on black?
Well quite, but that doesn’t change the fact that the odds of spinning black 10 times consecutively are really quite small. Imagine 99 black results have just occurred- the odds of another black result are infinitesimally small. However as an independent spin the odds are 50/50.

The point I’m making is there is a disconnect between the odds of the sequence and the odds of the independent result.

#### Odds4slots

##### Newbie member
Try doing a simulation of few miilion runs of heads or tails and
check the difference between the two results, you will always
find they are very close, a run of one result seems to be cancelled out
by runs of the other so is some form of compensation active, I know
it sounds daft but consider another situation...
Some sequences are so rare that they have never happenned or likely to
happen ever in the future, they say that any deal of the entire pack of cards randomly shuffled will be unique and will have never
occurred before.
If you can accept that some situations are unique, is there any advantage to only bet for the opposite to land when a sequence of heads/tails , blacks/ reds or whatever have landed a number of times which is just about feasable, as a few more of the same
results will end up in a chance that has never ever happened.Hope I explained it ok.
Randomness is not as simple as it may seem
We defined "randomness" . I am just pointing out on that fact. We didn't invented,it's just our observations. That's the way the things seems to work in this universe and there's no point to argue about that ( or is it? Have anyone any explanation why coin flips have a tendency to "cancel out" in n the long run,what's the mechanism behind that?!) ,but the fact is that we're trying mimick that behaviour in Pseudo RNG, therefore it is predictable to some degree.

#### ChopleyIOM

webby
Well quite, but that doesn’t change the fact that the odds of spinning black 10 times consecutively are really quite small. Imagine 99 black results have just occurred- the odds of another black result are infinitesimally small. However as an independent spin the odds are 50/50.

The point I’m making is there is a disconnect between the odds of the sequence and the odds of the independent result.

There's a disconnect for us as humans because we're programmed at an evolutionary level to look for patterns, unusual behaviours, aberrations and so on, but maths doesn't care.

Mathematically there is no difference between the chances of these precise two sequences of events occurring.

B-B-B-B-B-B-B-B-B-B-R
B-R-B-R-B-R-B-R-B-R-B

Chain one might stand out to you because of all blacks, chain two might stand out to you because of the perfect distribution of red and black.

B-B-R-B-R-R-B-B-R-R-B

Exactly the same odds as that specific combo coming out as either of the first two.

What is mathematically unlikely is getting a preponderance of a specific colour over an increasingly large number of spins, certainly by the time you get to a sample of size of 1000, you're going to be pretty close to 500/500 - but along the way to that equilibrium, no one sequence is more or less likely than the other, and each independent result is always exactly 50/50.

You mention the law of large numbers above but that doesn't apply to the sample sizes we're talking about here.

On a related sort of note, some people would never pick the numbers 1-2-3-4-5-6 on the lottery because they don't think it's 'likely' that sequential numbers will be picked, but mathematically it's exactly the same odds as any other six balls being picked.

#### Mr_Slot5

##### Senior Member
On a related sort of note, some people would never pick the numbers 1-2-3-4-5-6 on the lottery because they don't think it's 'likely' that sequential numbers will be picked, but mathematically it's exactly the same odds as any other six balls being picked.
I’ve made this point to people before.

#### Odds4slots

##### Newbie member
I was talking about general distribution. There's no difference between probability of occurrence of particular sequence...but in general strings containing close to 50/50 B's and R's in any order are much more likely than mentioned single B-B-B-B-B-B-B-B-B-R one. Sequence with one R or one B out of 11 will be far less likely than your second example whit 6B's to 5R's if we ignore the order.

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#### JohnSnow

##### Experienced Member
PABnononaccred2
Just because at that point math simply doesn't ad up. Mr Slots5 is absolutely right.
The math has to add up (somewhere sometime). It doesn't matter if you get 4 times black or 40 times black. A player can also bet 40 times black and win 40 times in a row or lose 40 times in a row. Casino's do not ALWAYS win. There are days where they lose a lot of money. In the long run they always win.. that's why we have RTP's that suck more with time and the casino house edge getting larger. Slots is where most of their income comes from (I believe). With the exception of sports betting.

#### dunover

##### Unofficial T&C's Editor
Staff member
webmeister
PABnonaccred
PABnononaccred
CAG
mm3
Without the green and assuming a fair wheel, the chance of red or black on any given spin is 50/50, irrespective of whatever sequence of results preceded the current spin.

Each spin is an entirely random and independent event, the previous spins of the wheel 'don't exist' in terms of exerting any influence whatsoever over the current spin, or changing the probability of any given result.

Try this as a thought experiment, you have just seen a roulette wheel spin ten blacks in a row when someone walks in off the street into the casino, so he has no idea what the last ten spins were.

He bets on black, you bet on red, do you have a better chance of winning with your bet on red than he does with his bet on black?
This is an age old mathematical problem that has never really been explained. In games of chance, people often forget the time aspect as well as the 'in the moment' odds which you correctly state are 50%. The odds of spinning black 10 consecutive times are 1024/1. The odds against 11 times are 2048-1. So the perspective of the guy walking in from the street is a simple 50-50 as you say. The guy in the casino's perspective is that for black to come, it's going to stretch an already unlikely sequence to a very unlikely and far rarer event so he is essentially correct to back red.

This was researched once, a game show where the winner had 2 picks from 3 boxes to get the main prize. As you know, chronologically (irrespective of whether you name the boxes A-B-C or 1-2-3) there is a 67% chance the contestant will have the car keys in the first two boxes he picks in time. The research demonstrated that if the these were laid out in a line, and the main contestant had picked the left box first (going in logical reading sequence L-R) and it was empty, then a new person was sent in with the two boxes remaining (with the perception of a 50-50 chance obviously) and was told to pick the middle box or the left one of the remaining two in other words, he would 'win' 67% of the time, thus defying the apparent 50-50 odds.

A good example is the fiendish DOND game show. You can check this out yourself. There is a 22/1 chance at the start of the contestant picking the premium £250,000 box. Every show. In the instances where the £250,000 box was still present when players were down to the final two boxes, purely mathematically the perspective of the onlooker is that there is a 50-50 chance of the contestant having it on the table. Then consider this was unlikely at the start. The banker offers a swap to the player. Over time, the correct thing to do would be swap, but of course from the player's perspective having had it and then given it away would be unbearable afterwards so they tended (when brave enough) to open their own box. Let's just say this went badly over the series for the reasons above.

It's very tempting for people like you did in your post to see odds and individual events/choices in purely binary black-and-white mathematics. Alas, although not always quantifiable and explainable, sequences and time DO affect these seemingly simple calculations. There was a Canadian mathematician who observed this sequence factor in new national lotteries. After the first 20-30 draws he would identify numbers which hadn't come out at all, or only once or twice and suggested these would be more likely in the coming weeks (despite, again, the seemingly unconnected and random nature of each individual draw) and was right, every time. I even saw this on the UK lotto when it started in 1994, I got a few tenners after the start when I noticed a few of the '8' numbers like 18, 38 etc. were hitherto very scarce. So I backed those until they balanced out and did better than I would expect randomly.

The reason apparently is that due to the huge permutations and combinations with drawing 6+ numbers from 49, the odds against certain numbers having a huge differential in frequency after a certain amount draws gets progressively higher and hugely unlikely! Yet these draws are seemingly independent, unconnected to us. He did explain that his observations were less and less relevant as the lottery 'matured' and had run for so many years.

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#### Odds4slots

##### Newbie member
Are we inventing general relativity of gambling here now?! From casino perspective it is 1000000 spins what matters,therefore they look at that size of the sequence to calculate probabilities of each of one. Players perspective is focus on the very next spin usually and probability with different expectations follows.

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