Sorry if I bother you again, I wish to hear you opinion about this topic.

About a century ago, one gambling expert stated that some 50/50 quite rare events tend to come out in clusters, so not following the general probability laws.

To be more specific, at 50/50 random games some same lenght streaks will come out in clusters more often than not, that is the counterpart same superior streaks' probability will have a slight lower occurence in the long run.

For example, a 2/256 eight streak appearance will be most likely followed by another eigth streak apperance and not by the same superior streaks' class, in this istance a 8+ streak.

Actually very long term data seem to confirm this assumption, unfortunately not reaching the point to invert the house edge, at least for most part of so called 50/50 games.

What do you think?

Thanks in advance.

as.

Show me the long term data or gtfo

Edited to add: or, design me an experiment that could prove or disprove your assertion

Gtfo is your answer.

Thanks.

as.

Just in case, I quote it.

as.

There have been several similar threads started here recently, some of which were started by OP. I am not sure why the recent activity in this direction. Maybe this topic has bubbled up in some colleges and universities.

"Clusters" are indeed a phenomenon that we witness quite a bit even when the underlying process is "random". But this is as expected.

Consider a standard deck of 52 playing cards. Deal out all 52 cards and keep track of suits. You may initially believe that a 4-card sequence is very likely to come out with all four different suits appearing (spades, hearts, diamonds, clubs in some order). But the odds of getting a random sequence of the 52 cards with all 13 consecutive 4-card sequences in a "4-suited" pattern is really quite low.

"Randomness" does not necessarily mean "regularity". "Randomness" and "lumpiness" can go hand in hand.

Anyway, I am skeptical that anything meaningful will come out of this thread. As they say, extraordinary claims require extraordinary evidence. And it is on the evidence front that these claimants come up short.

Thanks whosnext for your answer.

Yes, you guessed right, many ideas I recently posted where taken from university fellows studying the subject.

I'm not the ambassador of such claims, I just asked for your opinions.

.
as.

If I did this calculation correctly, this probability would be given by:

[(13!)^4] / [C(52,4)*C(48,4)*C(44,4)*C(40,4)*C(36,4)*C(32,4)*C( 28,4)*C(24,4)*C(20,4)*C(16,4)*C(12,4)*C(8,4)*C(4,4 )]

= around 1 in 61 billion

You don't get to claim that "very long term data seem to confirm this assumption" without pointing to the data.

And it's pretty silly to claim that something happens "more often than it should" if you aren't willing to give a framework for testing that hypothesis, and/or tell me how often it "should" happen vs how often it "does" happen.

And whosnext, he's not really talking about clustering. Like his previous thread, he's saying that the occurrence of clusters is different than what you would calculate using our "so called probability theory"

This isn't a place for conspiracy theories. If you have an actual question about probability, form it in a way that it can be addressed.

So, do you have some "very long term data?"

If no, do you have a thought as to how this could be proved or disproved? We could flip a trillion virtual coins in a computer today, is that enough? If so, tell me what the experiment should be.

Thanks Rusty for the answer.
I'll try to summarize.

Hypothesis: certain "rare" 50/50 events tend to distribute in clusters, meaning that there should be a slight propensity to get one or more repetitions after a first apparition opposed to the general 50/50 probability.

We have chosen to consider streaks on both sides starting from 8 to 14.
Thus after an 8 streak the slight more likely outcome of the next streak reaching the 8 value should be another 8 streak.
The same about the 9 streaks and so on.

Of course in the long run 8=8+, 9=9+, etc but the distribution of those 50/50 events should be different slightly favoring a "cluster effect".

We know very well that according to probability laws every single 50/50 event (rare or frequent) will place by isolated vs clustered patterns, by clusters of two vs superior clusters, by clusters of three vs superior clusters and so on.
After our tests it seems that those rare events tend to privilige a clustered or "nothing" distribution, so damaging the isolated formation side.

Naturally a streak is just an 8 or 9... same side sequence so this propensity should work on every other 8 or 9 hand pattern but it's more difficult to test mixed patterns on both side (not speaking about the possible practical applications).

We made the tests mostly utilizing real outcomes, if you want to run virtual coin flips and give us your results you're very welcome.

as.

I am not sure your post accomplished what you intended.

Can I ask, is English your native language (please don't take offense, I am just finding it difficult to follow what you are saying)?

And your use of terms in non-standard ways makes me wonder what is your background.

Finally, if you are looking for discussions of so-called phenomena which exhibit behavior not consistent with traditional probability precepts, then I don't think a Probability Forum on a Poker website is the best place to look.

Hi.

Fortunately English isn't my first language. I can't think about a person writing a worse English than mine.

Mmmh do you think there are better forums to look for?
I don't think so.

Yes this is a poker forum but after all the probability section is under the "general gambling" section.

as.

Well, I can't make any sense of what you said. But here's my hypothesis, tell me where you disagree.

After a series of 8 or more heads or tails in a row, the next streak has:
* probability of 1/2 to be of length 1
* a probability of 1/4 to be of length 2
* a probability of 1/8 to be of length 3
and so forth.

From what you've written, I take it you disagree?

Nope, of course.
Definitely in the long run (itlr) the total amount of those events will follow such probability, I'm talking about the distribution of certain rare events (longer streaks) tending to get more consecutive patterns than what a 50/50 law dictates.

Thus it seems that after let's say a streak of 9 the next slight more likely outcome will be another streak of 9 and not a superior streak (9+).
Should this be true, a possible reason could be related to the high concentration-dilution effect typical of rarer events.

as.

OK, so you're saying:
If a streak of 9 occurs, you expect to see another streak of exactly 9 before you see a longer streak?

Perfect.



as.

OK. But I think that's to be expected.

Let's call P(n) the probability of a streak of length n.
P(n) = (1/2)^n

So the chance of a streak of 9 is P(n) = (1/2)^9 = .001953125

The chance of a streak longer than 9 is the same as
1 - (P(1) + P(2) + P(3) + ... + P(9))
which is to say, you can add up the probability of getting a streak 9 or less. 1 minus that is a streak longer than 9.

This value is also .001953125

As an aside, this is a long winded way of saying something that is obviously true. P(n) = P(more than n) for all n.

I can write a simple program that tests this, unless you think for some reason that it only happens for physical events like coin flips? It's a very simple hypothesis.

Note that my calculation for the above shows the probability for each case of it happening in the *next* streak - which is not what you're talking about. However, because the probability is the same for each of them I expect that at the end of any streak, the chance of the next 9-or-longer streak being "exactly 9" or "more than 9" would be the same. I can't see an obvious reason why it wouldn't be true.

Well, if you want me to throw a bunch of dice, I'm not going to.

You keep referring to existing research without a cite. Don't do that. If the research exists, point to it. If you can't, don't refer to it as if it's true.

Yes it would be good if you would run such program, but as you have pointed out we have tested this hypothesis on real live outcomes where in some way there's the human intervention (roulette and hand made shuffling).

Ok I won't cite any research I'm referring to anymore.

as.

All I'm saying is, if you're going to cite it, then cite it. But just saying "some data exists that shows..." means absolutely nothing to anyone who can't see the data and the protocol that produced it.

It would take an unbelievably long time to get enough samples to make any kind of reasonable statement about this problem through physical means. Only 1/512 streaks is of length 9 and then after you get that first streak of length 9 now you have to wait again for 9 or 10+. Each "sample" is therefore going to be hundreds to thousands of throws.

100,000 throws at 10 seconds/throw (I don't know how long one throw takes but it probably is on the order of 10 seconds because you have to both throw and record the result) is 278 hours, and it would produce only a few hundred samples of data.

For 50/50 events a streak of nine being next is way more likely than a streak of ten being next (double) a streak of eleven being next (quadruple) or any longer streak.

I agree, and perhaps that's why the world of rare events distribution is so interesting and probably not deeply analyzed just for the reasons you mentioned.

I've found intriguing that each class of rare events tend to produce the same slight deviated features even at different gambling games..

It could be a coincidence, after all our samples are relatively small, actually I mispelled at all the world "very long term data".

Later I'll try to provide some data.

as.

I think you misinterpreted my words.
We are talking about a precise starting point of intervention.

According to classic probability any streak of a precise lenght will have the same identical probability to repeat it or to form a longer streak, each class of streaks separately considered.


as.

Just like your other thread, what you're really arguing here boils down to saying that independent events, are not independent. That dice and roulette wheels and coins have a memory.

There's no getting around the need for this requirement with your theory.

So how does this help me choose the correct bet in baccarat?

When you see 4 Banker wins in a row, the next time you see 3 in a row, bet hard on Banker, then laugh your way to the cage!