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Topic: Conditional Probability + Substitution into the live stream of the moving window  (Read 13578 times)

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Offline XXVV

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This is a new thread that has been suggested to me through a most interesting post by Gizmotron on the 'worth a read' thread in the Baccarat Forum.

I am inviting some expert opinions and experience here in the context of breaking free of some of the linear blocks of conventional mathematical theory, and some of the conventional (false) assumptions regarding roulette outcomes.

We are working toward finding new and improved ways to beat the game of roulette, not the odds.


Offline XXVV

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This is the text of the recent post by Gizmotron. Editorial notes and emphasis has been added by xxvv.

"With Conditional Probability Roulette can have large stretches that are truly 50/50 both in chances of hitting odds and pay off odds. The zeroes (0 and 00) sleep just like the D/C and E/C (groups) do. I see it all the time. If you track the sleepers you can trade out 2 sleepers from the inside layout and substitute them with the two zeroes, while they are wide awake, while still covering only 18 numbers. This little bit of logic confounds the 'frequentest' camp of probability fans, but to those of us that 'play by current conditions' ( ie responsive to live trending) it makes perfect sense.

Sometimes the greens pop up when they should, once every 19 or 37 spins respectively. So you can substitute when you come close to these steady intervals. It's just a casual form of playing what you are getting.

To take that one step further, you can use substitution to give yourself a psuedo house advantage with this technique. Sleeping numbers being substituted for hottest numbers in all your otherwise grouping type bets slightly improves in the big picture of hundreds of bets.

I've never written a sim to see if playing the Red/Black 50/50 game could be improved by substituting hot for cold numbers in the sets- in a large numbers of this theory kind of a test I mean. It's easy to see if the greens are sleeping or wide awake. It's not so easy to see the other numbers that way - perhaps the sim should be looking at every number the way I do for greens? There must be a way to watch for hot and cold numbers in my hand written charts. "

Offline XXVV

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Here are some first notes in response.
Define Conditional Probability.
Adapt to single zero table as option #1 ( the number Zero is the first on the table). Option #2 is the 0=00 space applied to current wheels in NZ and Australia where 00 is placed between 5 and 10 on the usual French Wheel number distribution.
Comments on Probability Theory and current conventional mathematical views of the 'independence' of every spin outcome.
Example of 'substitution' in a live game record where the hottest number/ coldest sleeper is substituted and work through the implications.

This principle interests me because my Loss Bet technique relies on 0 being played as an independent 'outside' of the game strategy. If however 0 can be substituted by a number least likely to appear in sessions of 74 spin duration ( multiples of 37 spin duration) then the risk is mitigated and permits the DC performance to be less subject to house edge.

Degree of hot to warm to cold number substitutions can be evaluated.

In regard to an effective playing cycle for maximum efficiency I nominate for a first test 111 spins ( 2 hours play) and 37 numbers.

Therefore the live window is 74 spins and on a casino roulette playing card the 37 ( or 38 numbers) can be marked up so that prior to the live window of play the first 37 spins can indicate the likely candidates. I simply write the 37 numbers down the page from 0 to 36 and mark the spin number appearances beside each number. At the same time I write a schedule of the hottest numbers down the page, focusing very much on the current top 4-6 targets ( this is based on my WF game experience). Such spin number charts I have seen spread over a day or even a week's play for one wheel, recorded and observed live.

Empirical testing can tune this to be greater or less for efficiency based on a sample of say 30 sessions tested and evaluated.

The live game can be halted once a reasonable target goal for wins has been achieved. My suggestion is a target of +9 units. If this can be achieved in 20 spins or less - take the profit and close.


Offline Gizmotron

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Quote
Define Conditional Probability.
Adapt to single zero table as option #1 ( the number Zero is the first on the table). Option #2 is the 0=00 space applied to current wheels in NZ and Australia where 00 is placed between 5 and 10 on the usual French Wheel number distribution.

These questions are the very most intelligent questions I've ever been asked regarding randomness. I'm going to answer as many as I have experience with, one idea at a time.

I discovered that the randomness of 37 or 38 slots makes no difference on the trend characteristics, whether you are charting zones of the wheel itself as partial sections of the groupings you create with them or not. I have dozens made up from spokes (zones) of the American Wheel, the European Wheel, and the European Wheel configured as the American Wheel. In all those groupings the characteristics of sleeping numbers, sleeping dozens, singles, and series all end up taking on the same characteristics of trends, just at different times. The more groupings you can track, the more opportunities you can find that work.

If you ignore the groupings, made up from location of zones on the wheel, and just look at it as a stream of random numbers, then it doesn't matter what wheel you use. The point is to find trends that work for you.
"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline Gizmotron

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This principle interests me because my Loss Bet technique relies on 0 being played as an independent 'outside' of the game strategy. If however 0 can be substituted by a number least likely to appear in sessions of 74 spin duration ( multiples of 37 spin duration) then the risk is mitigated and permits the DC performance to be less subject to house edge.

This comment, combined with the notion of substation, made me realize that the House's Edge is in fact a moving target, and not necessarily the one or two greens respectively. There are 37 or 38 slots where one or two of those slots are temporarily hot while another one or two slots are cold. If that occurs inside your groupings, to your favor, then that's an advantage to you, if not, then that is the house's edge correcting itself, as the absolutist might put it. I've just stopped being married to the greens. Now I'm free to search for any slot that I like, taking advantage of conditional probability.  :o
"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline Gizmotron

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With regards to Hot and Cold numbers, I cut my teeth on trying to exploit the three hottest numbers in 300 spin tests, and real sessions. That is how I learned about randomness. At the time I had not learned yet that it was my superstitions and unrealistic goals that got in the way of my success. Going after the hot numbers is a game that takes more patience than any other bet selection technique there is in Roulette.

The effectiveness of bet selection flows in waves. It is unreasonable to expect to recover from a downturn in a session that starts or leads you into a negative position. The single rising wave only goes as high as it goes. It might not reach all the way back to what you want. Just accept the upward waves and take what they give. If you can tread water very good then the upward waves all work out good enough. My problem was focusing on where I was at in a session and wanting more. I didn't know about accepting wins as they happened. The win streaks set their own amount. They last as long as they do, regardless of what I want. Many people have talked about reasonable expectation over the years. It's a tough nut to crack. At Least it was for me for years.
"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline XXVV

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This thread will be continued over the coming weeks. Thanks for all the very helpful ideas.

Offline Gizmotron

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OK, so I ran some large numbers in a sim.

One set = 380 spins after 76 non selected spins. ( 76 = (2 X 38))

38 spins = 1 cycle.

My tests run 10 times a cycle, or 380 spins.

I set the sim to run 3800 spins, that's 100 times 38 spins (cycles).

I did it ten times to get a large number statistic, 38000 spins.

The substituted two numbers lost 2006 times for an average percentage of 0.052789, virtually the House's Advantage mathematically.

The two numbers, the zeros, lost 2010 times for an average percentage of 0.052895, virtually the House's Advantage mathematically also.

Years ago, on another forum, several of us ran a very large numbered test to see if it would make a difference trying to avoid the zeros using one single rule for all the tests. We did it in several different languages using each programmer's unique way of solving the algorithm. We got the same kind of results that I did just now. There was a minute capability to avoid some of the zeros mathematically. But no significant advantage in even trying. Once again, the House's Advantage is not mathematically written in stone.

Our tests included 10's of millions of spins, so don't think that the difference you see here is caused by standard deviation. There really is a very small difference.

Next, I'll test to see how many spins occur while the zeros sleep during 380 spin tests. If they were to hit at the average rate they would hit every 19 or 37 spins respectively. But they don't do that do they.
"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline XXVV

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Thanks. No surprises at that stage.

You have established the fundamental equilibrium of the sample with the substitution of (any) two numbers for the zeroes. So yes this supports the theory that an internal substitution can be equivalent to exposure to zeroes. This may have strategic benefits to the bet construction later.

What about an ongoing interactive sampling where (say) every 78 spins** the two coldest sleepers are selected and used to replace the zeroes, then after every additional 78 spins the sleepers are reviewed and if necessary replaced, and so on, with the theory that the selection of the two substitutes will provide a diminished number of hits, and in fact thus magnify  the return on the other selections which will be free of the frozen ones.

** or even truly iteratively, the review cycle could be reduced, or the moving 'window' could slide forward spin by spin.

This iterative process can  steamroller along and enable a theoretical negation of the 'house edge'.

There can be empirical testing to see if 1,2,3,4 or 5 sleepers is the most effective model.

The testing I take it is being done on RNG data.

My experience teaches me that played in smaller quantum packets such as 39 or 78 spins then a further 2 or 4 x 78 to complete ( say a day/night at Wiesbaden #3) then the clumping and clustering of warm/ hots may be greater and thus maybe the cold ones may also be greater - but that can be tested in further experiments. I prefer live data on which to test and W3 can provide 300-400+ sample sizes in one session. The sessions must be played in interlinked but independent clusters, so the process of the selection of the 2 sleepers again needs to be conducted afresh at the start of a new day.

The logic can be reversed and the warm/ hotter numbers can be extracted in an iterative process for theoretically hot results. What is the optimum hot window spins - 2 or 3 x the numbers on the wheel I suspect, but as the 2 cycles are necessary to selected for the next spin cycle only, the window is an ongoing moving feature once the session is underway.

Now all this is most interesting and in due course I would be quite prepared to test such ideas live. This appeals to a part of my personality.  Moon in Virgo for the scientists out there - 5000 years of Mesopotamian and Indian wisdom is not faulty - a long way from the daily generalised snippet nonsense.

Having seen Dr Oz today go through the 7 Chakras with a neurologist professional very successfully linking ancient assignations with food/ colour/sound and yoga, then we can see Medicine is becoming more attuned to East meets West meets Body + Mind. Holistic Medicine.

Questions arising out of this.

Numeracy characteristics for RNG compared to live for more 'co-operative' patterning behaviour for hot/ warm especially, and also cold.

Even today, I experienced the mental awareness of a slot machine being in 'co-operative' behavioral mode.  In fact, as I related to a friend of mine by email today, I have had three such winning sessions exclusively playing slot machines and achieving a 60 unit to 300 unit end result over a week (on holiday) with an average gain of +80 units per session ( three sessions). I play attuned to a machine and judge the correct level of positive leverage to be applied to a winning stake, and time the ideal exit point - achieving +100 to +200% returns per session based on small amount of risk capital utilised.

Had any one of the 5 machines used in the week signaled a sign of correction  (non-co-operation) then I would have quit at break even or stop loss. It was quite uncanny, cool and very rewarding to do this.

Notice how the human mind is able to 'form' the responsive best adaptive model to suit such wide differences as a clunky slot machine, smooth RNG data flows on sim, and live play sections within a session that runs till 3am in opulent surroundings.


Offline Gizmotron

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"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline Gizmotron

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Numeracy characteristics for RNG compared to live for more 'co-operative' patterning behavior[sp] for hot/ warm especially, and also cold.

Yes, I used RNG. You should know that a modern, unmolested RNG running in a modern, up to date, operating system uses an algorithm that produces truly random numbers up to about 1/2 million results. At that point somewhere it begins to repeat itself. When the random function is called to get a random number it continues toward that 1/2 million without starting over. Every time I restart my computer it sets a new random seed so that it never repeats the same 1/2 million spins. The old systems didn't change the random seed. So when they were used in modern slot machines the sequence became predictable. It was the gambling world that forced the change in all operating systems, this random seed changing method. I'm not worried about RNG testing in my sims because they give accurate large number theory results.

People have funny beliefs about recognition of an unmolested set of RNG spins compared to a same sized set of real spins from an active wheel being tracked. There is no difference. Nobody can tell the difference. I've seen them try on other Roulette forums. Even though they think they know a certain characteristic would never happen on a real wheel, it does. The same goes for true RNG too. It does things that are believed to be only true of a real wheel.

Now the RNG in some airball machines and RNG Roulette slot machines that are admittedly set to pay off somehow at 7% advantage to the casino, well they are not really random.
"...IT'S AGAINST THE LAW TO BREAK THE LAW OF AVERAGES." 

Offline XXVV

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Most interesting, and not surprising because dealing with sleepers and cold numbers at one end of the polarity is not necessarily symmetrical with warm/ hot number behaviour and response. In the cold, energy is low and movement is slow.

With the sim terms and conditions set out as done it is probably worth a little more effort to run some tests over a range of differently spread criteria to ascertain that it is indeed a cul de sac while looking for aberrations. For that is what I do, I search, and they do occur - just consider the humble flat stake WF bet bell curve which shows a peak frequency of hits in the 3 to 4 target range, and which slides on the horizontal axis depending on a hot or cold context session - like a spring being wound. When peaking at closer to the 3 ***, the earnings are great. When tracking beyond 4 it is close to break even flat staking and in small samples can go to 5 or more which is a loss. Nevertheless this demonstrates some fertile application of a short burst of progression at suitable phases which can be read in the game simply, and is a subset of WF theory about which I have shared a lot on this Forum and several members play this to advantage.

*** as per my other notes on the WF bet the number quoted is the number of targets within a bet cycle that successfully closed the cycle and thus achieves the goal that one of the 3 targets actually hits for a third time and wins. Games of 1 WF have maximum return flat staking. Games of 2, and 3 have good positive net gains flat staking. Games of 4 or more ( 17 was the max I saw over several thousands game cycles tested). The range of average targets in a sample of 100 games or more - average 22 spins per game- is about 3.5, but varies between 3 and 5 depending on the 'co-operation mode of the ecart flow ( 'tight' or 'loose' are the terms I use for the polarities with tight as hot and loose as cold).

So, with regard to the conversation with Gizmotron I suggest a switch of attention in empirical testing to warm and hot number appearances and behavior, and this exhibits a lot more short cycle energy/ behaviour. The analogy is thermo- dynamic behaviour. When cool the atoms are spaced widely and are not excited. When heated they cluster more and move around in increasingly excited states. This is what we are looking for. Aberrations in uniform probablistic behaviour expectations. When hot it gets skewed and perhaps under the best chosen terms / criteria/ window frame for analysis and application, this can enable us to set up a bet which may suit our purpose- ie that which can negate the house edge and can actually in short cycle behaviour can give us a strong positive edge to our advantage.

I emphasise short cycle and perhaps the sim testing can enable a renewal/ refresh every 37/38/39 spins or can refresh on an ongoing spin by spin analysis review.

Playing hot numbers I am not convinced that RNG is as suitable and 'co-operative' as live data cycles. It may be fine on the cool side, but not the hot. I have experience through trusted colleagues who generate vast arrays of spin data, and they use this for testing. I use only constantly fresh live data from the casino - much more fun ( but time consuming). Because my work and interests are so skewed to short cycle analysis that in a suitable short time I can access the 100 spin tranches needed, and within that sample is a whole world of opportunity - this depends on the nature of the bet of course and its characteristics.

On the big picture I am really interested in this ongoing conversation and simply am advocating a call to explore warm and hot number behaviour of short cycles within the larger cycles being studied. Thank you for your effort, interest and time involvement to date Gizmotron.

In this and the prior reply there is a lot of valuable information for those who wish to research further.

Offline XXVV

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Conditional Probability

References available through Google, and I like this one : www.cut-the-knot.org/Probability/ConditionalProbability.shtml

Offline XXVV

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Dramatic Cab Action in Sydney

Bayes Ratio is illustrated here.

A cab was involved in a nasty hit and run accident at night in Kings Cross, Sydney.

There are two cab companies, Green and Blue operating in the city centre. The Green lot are eco-friendly.

Here are the data facts that will enable your analysis to be completed. Read on....

#1  85% of the cabs in the city are Green, and 15% are Blue.

#2  An eye witness ( an off duty cop) identified the delinquent cab as Blue.

#3  The Court tested the reliability of the witness (under the same circumstances that existed on the night of the accident) and concluded that the
      witness correctly identified each of the two colours 80% of the time, and falsely 20% of the time, ie 4x more accurate.

What is the probability that the cab involved in the accident was Blue ( as identified) rather than Green?

In spite of the witness testimony, the hit and run cab is more likely to be Green rather than Blue in the ratio 59:41 ( nearly 3:2).


The cab was Green.

So much for eye-witnesses.


Offline Mike

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Conditional probability can only apply to roulette in the sense of some one particular outcome having a characteristic conditional on another being assumed. In other words, you can speak of the conditional probability of an outcome being for example red, given that it's in a particular street. In that case the chance of it being red does depend on whether it's a particular street or not.

But since outcomes between successive spins are independent, conditional probability cannot apply to that scenario. For example the "conditional" probability of 5 reds in a row given that 5 reds in a row has just occurred is the same as that in the case where any other pattern has just occurred.

In other words, P(A|B) = P(A). Where B is some prior event. That is in fact the definition of independence. In roulette, future outcomes are not conditional on past outcomes.