is it just me, or is roulette easy to make money on?

Actually, I dimly remember from when I studied Statistics (a long time ago, I`m afraid) that mathematically that 101st spin would be (fractionally) more likely to be heads again.

There is an observed phenomenon called "Uneven Distribution in Large Samples" which suggests that random results do not alternate in the way that humans intuitively expect (heads, tails, heads, tails etc.) but rather appear in chaotic and unpredictable groups.

Please note that this is a miniscule effect, of interest only to maths geeks, and is definitely not a sound basis for a roulette system. As has already been stated, there is no such thing as a truly sound roulette system.

For all you doubters:

Claim: In 1873 a British mill engineer "broke the bank" at a Monte Carlo casino.
Status: True.
Origins: The year was 1873 when Englishman Joseph Jaggers (1830-1892) made his fantastic run on the Beaux-Arts Monte Carlo Casino. An engineer and mechanic in the cotton industry in Yorkshire, his nuts-and-bolts background led him to ponder the mechanics of roulette wheels. Were they perfectly balanced? Were the numbers the shiny little ball landed on truly random, or were some numbers more likely to come up than others?
Those questions in mind, Jaggers hired six clerks to record every number that came up on the roulette wheels in the 12 hours a day the casino was open. He then spent the next six days poring over the numbers, searching for patterns that randomness alone wouldn't account for.
He found what he was looking for. Though five of the casino's six wheels produced predictably random results, nine numbers in particular kept showing up on the sixth at a rate far exceeding what natural probability would have indicated. Clearly, the wheel was biased.
The first day's foray against the casino netted him roughly $70,000. By the fourth day his winnings pushed $300,000.
The casino fought back. In the dead of night each of the wheels was re-housed into a different table. The next morning though Jaggers went to his usual table, he was up against an unbiased wheel.
He lost (some say heavily). It was then it dawned on him that a certain miniscule scratch he'd previously noted on his Jaggers-friendly wheel was no longer in evidence. Finally, suspecting a switch, he made a quick survey of the other roulette tables, and the discovery of a certain scratch led him to be reunited with his faithful lady. From there he went on to push his total winnings to $450,000, an astronomical sum for 1873.
In the end the casino prevailed. They had their wheel manufacturer in Paris design a set of movable frets, the metal barriers that separate numbers on the wheel. Each night after closing, the frets would be moved to new locations around the wheel. Playing into the teeth of this, Jaggers went on a two-day losing streak. He finally bowed to the inevitable, escaping with his $325,000 remaining profit. He left Monte Carlo, never to return.

Egon, I don't get it. Are you saying that the chances of flipping heads is not exactly 50:50 on the 101st spin? I'm pretty sure that's wrong, unless the coin is biased.

Not exactly. It`s a difficult and counter-intuitive concept, and I am rusty on it (so if there are any more recently trained statisticians here, by all means help me out).

Obv, a coinflip is a 50/50 chance. The coin has no memory and no single result can be predicted.

At the same time, the nature of randomness is chaotic. Results clump together unevenly.

A human might expect (because the brain expects pattern) that there will be a heads/tails/heads/tails pattern and that, therefore, a tail will be followed by a head.

But, because of the clumping effect, in a large sample of results, a tail will be (fractionally) more likely to be followed by another tail, rather than by a head.

Although it seems contradictory, both ideas are mathematically correct.

Still can't get my head around the bit in red. If the next result is (fractionally) more likely to be a tail if this result is a tail, then it's not true that no single result can be predicted.

Isn't the point that the random results don't "look" random, but actually are?

I`m not sure I ever really understood it myself. Some of the more far-out mathemetical concepts do seem illogical if one applies normal common-sense principles. We were taught that this effect can`t predict the result of the next coinflip, but can be observed when analysing large series of past coinflips.

If you think about it, if it is true that the results tend to occur in groups, rather than heads/tails/heads/tails, then it must also be true that, at any point in the series, an event is more likely to be part of a group than not.

Key thing to realise, though, is that this has no application to a roulette table, because the 1 in 37 chance of hitting a zero (even on a single-zero table) is a much larger factor.

Actually, I heard the weight differences in the sides of the coin actually make one of them a ridiculously miniscule favorite. Could be wrong though, can't find any backup on the intertubes.

I think the reason you fail to wrap your head around it is because you're not really supposed to. What Egon is talking about is apparently true, but I think the importance here is the difference between causation and correlation. This is why it's an "observed phenomenon" and not, as most other mathematics, a proven theorem.

That doesn't make it untrue, it just means that the process behind this phenomenon has yet to be found. One such process, in the case of flipping a coin, would be any slight anomaly in the true randomness of the flips. Maybe there's an extra atom or two on the head-side. Maybe there's quite a few extra. Maybe it's dented. Etc.

We use complete randomness as a model for reality, but it's important to remember that the model isn't reality. So when we observe reality and realize that it doesn't match our model, it may be dangerous to try to explain the difference in results within that model. It could simply be that some of the things we presume to be true in the model aren't true in the real world. Reality may not be as random as our model is. It may in fact not be random at all. But it may well seem completely random for all intents and purposes... except, perhaps, for analyzing distributions of large samples.

Anyway, I don't know very much about the theory behind what Egon is talking about, so take what I'm saying with a grain of salt. I could be completely wrong. In which case I'd like to be set straight.

I'm speculating as well as I don't know exactly which theory Egon is referring to...

Random events bunch and in fact this is a product of their randomness. If you set all the balls moving on a pool table they will never (well almost never) finish evening spaced, or even anything close to evenly spaced. You will find large areas of the table empty and balls almost touching or in little clusters (this is true even of modelled rather than actual pool tables, to take FPs point which is also true though a different one).

So I'm assuming that Egon is in a similar area re the clustering of random events. If you look back at any really large sample of coinflips you will see clustering (at a smaller level toss a coin 100 times and you have a 50/50 chance of getting seven heads or tails in a row). This means that in looking back there may be a greater chance of a head being the result following a head....

I don't know, but I do know it's of no use in predicting the future

This is the thing to look at. They are do statistical analysis after the fact on a very large sample size. They then try to find patterns scattered over millions of turns or flips of a coin. These two things can show patterns that looking at hundred or even thousands of flips won't show. You could never play enough roulette in your lifetime to even come close to getting that edge it is so small.

Keep in mind the people who come up with this stuff don't get out much to play roulette , have girlfriend or look at cardschat.

I thought maybe what we're talking about is the fact that if you analyse a series of coinflips, say 1000, you'll always find that there is some correlation between one flip and the next, albeit not a statistically significant one: you might find that 510 times the next flip is the same as the previous one, and 490 times it isn't. You would expect it not to be exactly 500, and can estimate how much it will differ from the mean of 500.

But I realised this can't be it because it's just as likely you'll find that there is a (non statistically-significant) negative correlation, i.e. the following flip is more often different to the previous one.

This would also be more relevant to a "small" rather than "large" sample, although it applies to any non-infinite sample.

So ya, still confused.