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[sqzbox]

Esoito's story of his friend Hans is tantalising. The concept of combining results from different statistical measures is something I have been wrestling with for a while.  I don't think I am sufficiently strong in pure math to be able to derive stuff myself - I just don't know how to go about it.  So I thought maybe we could discuss it a bit and see if those who can handle it might like to weigh in.

I guess we should start with basics.  It seems to me that the first thing we need to ensure is that of statistical independence.  Am I right in figuring that the statistical measures ARE independent?  That is, for example, we can calculate the probability of an outcome being in the first dozen AND black by simply multiplying the respective probabilities.  12/37 x 18/37 = 0.1578.  But this is only true if the probabilities are statistically independent.  Is this a true assumption?

[Bayes]

It certainly is!

Likewise, the probability of black AND high AND even (or any other combination) is (18/37)³, which is why you don't see all 3 ECs "streaking" for long. Louis G. Holloway in his book "Full Time Gambler" said betting all 3 ECs simultaneously was his favourite bet.

Roulette probabilities are fairly easy to calculate because all bets are independent. Basically you just multiply the respective probabilities to get the final result.

[sqzbox]

Right then - that's that sorted.  Now let's see what clues we can take from Hans's email.

1. Boolean combinatorics.  This implies to me algebraic combinatorics and specifically boolean, which further implies 50/50 situations.  Note I have not said EC's because obviously 50/50 can apply to inside bets also. Roughly of course since we have a zero to contend with.

2. Complex bets. Hmmm - my take would be that this means either a) a combination of different bet types such as en plein, columns, EC's etc. or b) betting en plein based on a complex derivation.

3. Class of thousands ...  Um - that seems excessive.  I guess if you were to calculate all the possible bets from all the possible bet types it could get to a pretty large number.  But even if there are not thousands he obviously believes there to be "lots".  This implies to me a selection of numbers to be bet on the inside - I doubt that you can get to a really large number only using outside bets.

4. A set of rules.  OK - that's good for us because it means that it is mechanical in nature, albeit complicated.

5. Pure math.  Again, as per number 4 above - good for us.  We should be able to do this.

Have I missed anything?

[Gizmotron]

I guess we should start with basics.  It seems to me that the first thing we need to ensure is that of statistical independence.  Am I right in figuring that the statistical measures ARE independent?  That is, for example, we can calculate the probability of an outcome being in the first dozen AND black by simply multiplying the respective probabilities.  12/37 x 18/37 = 0.1578.  But this is only true if the probabilities are statistically independent.  Is this a true assumption?

I think what you are looking for might be best described as simultaneous. You can win the black bet but lose the first dozen bet. Furthermore, some of the black numbers are part of the first dozen. They are combined as a process of being the same slot on the wheel as well as different groupings from the table construct, at the same time. I'm suggesting that the way to combine them can only be achieved by using the inside numbers only. This way the formula becomes 12/37 x 6/37 = ##.#

[Gizmotron]

P.S. or it just becomes 6/37 = ##.#

interesting - compare:

12/37 x 18/37 = 0.1578

6/37 = 0.1621

If you round them both, then both percentages are 16%

[sqzbox]

"Simultaneous" doesn't ring my bell.  To me, this means doing tricky-dicky things with different bet types simultaneously, inside or not, that is nothing more than trying to defeat the odds - a futile endeavour.

This is, I believe, not what combinatorics is about - at least, for me anyway.  This is a concept that is hard to explain - tackling the "game", not the "odds". 

It is about - monitoring the ecart, seeing the variations, and constructing a complex bet to suit the occasion based on the distortions arising as the flow of outcomes strives to retain normality elsewhere. 

I am pretty sure that that will always result in inside bets, even though the measures may include, for example, the EC's.

Folks, I am going to be out of town for a few days.  I hope to see lots of worthwhile posts on my return.

[VLS]

[...]tackling the "game", not the "odds". 

I like the sound of that.

It reminds of what a fellow poster said. You must act as if spins weren't independent.

Independent spins mentality is clearly that of the game being 1-spin long, past outcomes being detached from anything in the future as well as regarding every bet in every moment of the numerical stream as the same... but if you pretend the game does keep a correlation, that it paints an "statistical picture" where past, present and future correlate, then you might devise bets that make sense, as long as the game behaves within the boundaries it usually does.

If I recall right, even if "anything can happen" in an independent trials game, in practice not everything happens, the game does keep itself within certain "statistical walls" or "boundaries". always with the possibility of breaking them to unlimited amounts (i.e. 100 reds and more), but in reality behaving as if past spins and future spins could communicate up to a point (less than 40 reds); leading to the expected "painting" or "picture", made out of officially non-correlated happenings, bearing no sense of boundaries by itself due to its independence, but yet presenting a set of boundaries in practice.



I like to think of it as throwing a fist of sand to the air with all your strength. Given the wind is random "anything can happen". Your grains of sand could be picked by an air stream and end up in the middle of the Sahara desert. But in reality, chances are it lands within the boundaries of your eyesight.

[Gizmotron]

"Simultaneous" doesn't ring my bell.  To me, this means doing tricky-dicky things ...

" It seems to me that the first thing we need to ensure is that of statistical independence. Am I right in figuring that the statistical measures ARE independent?"

You might like this, statistical independence does not ring my bell either.

[MarignyGrilleau]

It certainly is!

Likewise, the probability of black AND high AND even (or any other combination) is (18/37)³, which is why you don't see all 3 ECs "streaking" for long. Louis G. Holloway in his book "Full Time Gambler" said betting all 3 ECs simultaneously was his favourite bet.

Roulette probabilities are fairly easy to calculate because all bets are independent. Basically you just multiply the respective probabilities to get the final result.

Interestingly one tends to this common Fallacies:


1.
A tendency to interpret the probability of successive independent events as additive rather than multiplicative. Thus the chance of throwing a given number on a die is considered twice as large with two throws of the die as it is with a single throw.
2.
The psychological probability of the occurrence of an event exceeds its mathematical probability if the event is favorable, and conversely. For example, the probability of success of drawing the winning ticket in a lottery and the probability of being killed during the next year in an automobile accident may both be one chance in 10,000; yet the former is considered much more probable from a personal viewpoint.
3.
The value of the probability of a multiple additive choice tends to be underestimated, and the value of a multiplicative probability tends to be over- estimated.




Cheers

[sqzbox]

Very true MG, which is why I always check my assumptions or fundamental principles as best I can, and the math too of course.
Gizmo - looks like we have found our fundamental "point of difference". 

Thanks also to Vic and Bayes for their intelligent responses - I appreciate it, from all of you.

However, given only the 5 of us seem to be talking about it and it looks like we can't move the thing forwards in any meaningful way, I'll give it a couple more days and then perhaps take it off-line.

[Gizmotron]

I've spent enough time on collisions, even though I was impressed by their obvious excellent payoff value. I've decided to regulate them to Elegant Pattern status. Now that's not bad. But it's not optimal for times when extreme opportunity are few and far between. I've gone back to the proof sim.

[esoito]

"I'll give it a couple more days and then perhaps take it off-line."

@Bryan

A good idea to leave it.

Why?

'Cos  future member/s might pick up the ball and run further with it.

At least they have that option if it stays...

[VLS]

"I'll give it a couple more days and then perhaps take it off-line."

@Bryan

A good idea to leave it.

+1

It's always a good idea to leave the door open for future contributions. I've been gotten activity (forum/email) for messages from YEARS past. It happens and can be fulfilling. It costs nothing to leave it there for fellow readers in the future 

[sqzbox]

Understood - will do.

[VLS]

Understood - will do.

Thanks for that