Oh - and one further difference that comes to mind as I think about it some more - the house can vary the odds but they can't change the probabilities.  I think in certain South American countries the odds for a single number in roulette are 34 to 1, for example. I'm sure somebody told me this recently - but in any case, the odds are a choice whereas probabilities are not.

On a single number -
odds = 35 to 1, or 36 for 1.
Probability = 1 in 37.


Totally different things.

It is the difference between the odds and the probability that makes the house money. It is REALLY important to make this difference clear when in discussion - all sorts of misunderstandings will occur if you do not.

Probability and Odds are two different things - you must know that by now surely? And the if the 3 heads have already shown up then the probability AND chance for the next toss is still 50%.

Mike - the answer lies in this statement from Sputnik (referring to the example he posted above).

QuoteI can only play when i see two events growing and one event being regression component, underrepresented.

Take for example -
1 1 S
2 1 O
2 1 O
1 2 O L
1 1 S W
2 2 S

The series is S-O-O so now we see that the O-O represents "two events growing" and the first S is the "one event being regression". So the bet would be S, which loses in this case. But we bet S again and win and this is the end for that group of 6. Then we copy the outcomes we had here (1-2-2-1-1-2) for the next 6 and watch again.

2 1 O
2 2 S
1 2 O
1 1 S W
2 1 O
2 2 S

O-S-O shows 2 O's and one S and so the bet again is S and this time wins - end for this group of 6.

And so on. Sputnik will correct me I am sure if I have this wrong.

I like this very much for several reasons - it does not try to subvert the math but rather flows with it; an attack is limited to a maximum of 3 losses; and a long unending series is always avoided.

This is what I would call both elegant and efficient.  Well done Sputnik.

That will be really interesting Bally - I'll look forward to your results. And thanks for taking the time to do it. I had not heard of this COR measure before so I have learned something new - love it when that happens!

From a personal perspective I would have to say that I am not a supporter of either of these propositions (the RB idea or the sleeper one). In my view after a strange situation such as you describe, or in other words a statistical anomaly, "normality" returns, which is a generally accepted mathematical phenomenon known as Regression toward the Mean, or RTM for short. I believe that there is no scientific basis to the law of attraction. In any case, that is a theory based on energy such as thought for example - unless you are referring to something else of course.

QuoteAfter a sleeper returns it takes up with drive to balance out

Again, in my view completely false. See RTM above.

Why wait for 15 reds or blacks?  The last 15 outcomes has exactly the same probability of appearing as 15 reds or blacks.  Just bet against the last series - it has the same z-score after all. Only if that is your game of course. Or just make up a series yourself - again, any series is just as likely as any other series - there is nothing special about 15 reds or blacks.

Probability measures are between 0 and 1 so I don't understand what a probability of 121.7 is, plolp. What are you measuring?

Anyway, just to add to this a little bit - following the last 2 outcomes rather than any random 2 or even hot numbers is a sound strategy I believe, because of the "efficiency" inherent in that choice. It is easy to show that the best time to bet any number is right after it has appeared. If you graph the number of appearances vs. the gaps between appearances you will see a standard exponential decay curve, i.e. highest point on the left. So the most efficient time to bet a number is immediately after it has appeared.  This doesn't guarantee an overall winning strategy of course, just a less volatile experience I would suggest.

QuoteThe problem with discussions about independent trials, gambler's fallacy etc is that the so-called "math boyz" never seem to give any credence to anything that can't be mathematical formulated. According to them, if something can't be predicted mathematically, it must be a fallacy

Spencer-Brown argued that a fundamental flaw exists in our view of randomness.  To quote from an interesting article (URL below) -

QuoteClassical probability focuses on the 'atomic' level. For example, if we throw a six-sided die 100 times, we treat this as 100 independent events. To work out the likelihood of two successive results of '6', we combine these 'atomic' events.  But this is begging the question, according to Spencer-Brown. It assumes independence instead of proving it empirically. There is no reason in principle why a series cannot gradually become less and less biased at the 'atomic' level, but remain biased on the various higher 'molecular' levels for arbitrarily long spans

The paper I am quoting from, which I find immensely interesting, is "Probability in Decline" by Dean M. Brooks and can be found here - http://www.statlit.org/pdf/2010BrooksASA.pdf#page=1&zoom=auto,0,792

Now, don't think that this is "the Answer" - sadly, the decline is not large enough to overcome the house edge in any game of chance.  But it is an interesting view and one that supports Bayes' view of the attitude of the math boyz.

Personally I suspect that "an Answer" lies in the combination of what Spencer-Brown refers to as "molecular events" and RTM of these events.  Probably combined with a suitably constructed progression since the effect from a practical perspective is small - but real.  It might even be worth considering a discussion topic of "molecular events" so that we could all gain a better understanding of these phenomena.

Yeah - me too. I don 't know why these missionaries have to come along and hijack our perfectly fine chat. We know the maths and we don't care! We're having fun just chatting away and having our little dreams so just leave us alone!

To all the people who have posted in this thread advising us that there is no way it can be done, and so on, yada yada yada - I'd like to say thanks very much, you may now leave and feel very satisfied with yourselves that you have saved us so much time and effort and protected us from a fruitless search. Your job is done!

Great!  Now that they are gone - how about the rest of us who quite enjoy the search and are happy to waste our time on it get down to some specifics and leave opinions out of it.

I am sure I read in one of Shikamaru's posts that the movement he was looking at was specifically in the columns.  May be wrong - but anyway that is what I have done, although I have looked at the dozens as well.  Can't see anything.  I've produced a list of spin-by-spin results on columns and dozens for a series of 100 spin samples. It all looks pretty much as expected to me.  The data also shows the movement from the last spin to the new one for each spin with a summary of the movements at the bottom.  It all fits to the expected distribution.  I don't see anything that I could consider "less than expected".

Has anybody else done anything similar? Or looked at it in a different way to what I have done?  Be specific - what exactly have you examined?

So - here's a quote from My Keynes. His Treatise on Probability has been mentioned before but how many of you have actually looked at it - even just to the referred chapter?  It's not that tough if you just ignore the math and try to grasp the meaning.

Anyway - 2 quotes follow.

the actual frequency in a series of trials of an event, of which the probability at each trial is less than 1/2 (i.e. 0.5), is likely to fall short of its most probable value more often than it exceeds it.

and

it is sometimes worth the statistician's while to bear in mind this appreciable want of symmetry in the distribution about the mode or most probable value

He is saying that "the dispersion about the most probable value, even when the conditions for the applicability of Bernoulli's Theorem in its non-approximate form are strictly fulfilled, is unsymmetrical".

So there is some good support for the assertion that something happens less frequently than expected - i.e. falls short of its most probable value MORE OFTEN THAN IT EXCEEDS IT. Note, however, that this refers only to "probabilities less than 0.5" so EC's, INDEPENDENTLY, are insufficient.  However, in the table provided in the document which shows the calculated value of the excess delta there are some entries for a probability of 1/4 (i.e. 0.25) and this is very close to the combination of 2 EC's.  How convenient!

Another important principal from the Treatise is "the difference between the two probabilities being a maximum when n = 1, constantly diminishing as n increases ...".  So if you are trying to capitalize on this principal then SHORT games are more favorable than LONG games.  Again, mathematically proven (as far as anything is "provable" in maths - remembering that the whole area of probability is still referred to as a theory).

Final quote, which is a specific example, to assist with understanding.

Thus it is easily found that in 100 sets of 4 trials each, where p = 1/4, the actual frequency is likely to exceed the most probable 26 times and to fall short of it 31 times.

Food for thought?

Bryan

Just throwing a few random thoughts into the ring (along with my hat).

Clues that I have gleaned:
1) 4 chips.
2) 4 locations (a column plus 3 others is what I think was stated - but that could have just been an example).
3) euro wheel only. (Pretty sure I read somewhere that it doesn't work on American wheel - although maybe that was just "doesn't work as well" and so doesn't defeat the increased number of losses due to 2 zeros).
4) Le partage makes little difference to final outcome (again, I think I read that in Shik's comments).
5) Zero is considered a loss wrt the formula.
6) Objective: trap runs and changes.
7) symmetry (or lack thereof) seems to be important.
8] EC's are included - in fact I suspect it is ONLY EC's, columns and/or dozens.
9) something occurs less frequently than it should.

Some random thoughts relating to the above -

If you want to trap a run of High's or Low's then you would bet 3rd or 1st dozen resp.
If you want to trap a run of Black or Red then you would bet Col 2 or 3 resp.
Odd/Even is perfectly symmetrical in both dozens and columns so these are probably not included in the bet - unless they are used for some sort of independent purpose.
The above traps are not perfect - you could still lose because the run just happened to be avoiding the area of your trap - but this is not unexpected because I think the goal was 29 out of 30 successful games so even in perfect circumstances, when the gods of gambling are toying with you, you could still lose.
Trapping changes is just the opposite of the above - but still with HL or RB only.  So, for example, to trap a change from H to L you would bet 1st dozen, and so on.

So the question then becomes - what are the rules around going for the runs or the changes?  Has there been any mention of whether or not you bet continuously or wait for a condition to be fulfilled?  Perhaps the essence of these rules relate to clue 9.

See next post for a few thoughts on the philosophy expounded that "something occurs less frequently than it should".

Bryan

I'm comfortable with the size - can't miss them. Perhaps the colour could be different but they do need to stand out I think.

I have no problem with them at all - in fact I like the idea. Although, TBH, I've only used the Home one, but I do use that all the time. And I like the way they have been implemented - I think the built-in intelligence to when they display is very smart.