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[Albalaha]

Once the variance has drifted off track, what prompts it to return?? Bear in mind that each event is Completely independent and has no connection with what has gone before.

                 Well. This statement is only partially true. If we have two equal and unbiased probability of an event, both have equal opportunity to hit every trial. This creates a virtual limit to temporary variance  against any bet. Head may come 10/10 but how about 20/20, 30/30, 50/50 or 100/100? The answer is not possible. Reasons, read "regression towards mean" and "law of large numbers". You may refer to : http://albalaha.lefora.com/topic/17231561#.UvZeBWKSxA4

[Bayes]

Dragoner is right of course; there are more paths which lead to equilibrium than not. See this article. But also you have to remember that the 'equilibrium' is with respect to proportion, not absolute numbers. In terms of the actual numbers of reds vs blacks, outcomes actually get further away from equilibrium as you do more trials. I've lost count of the number of times I've said this over the years.

And anyway, strictly speaking, equilibrium only applies to even chances.

Also, I think what some people find confusing is that from one aspect, every sequence of a given length has the same probability, so RRRRRRRRRR has exactly the same probability as RRBRBRBBBR. This is true when looking at the sequence as a permutation (where order of R/B counts), but when viewed as a combination (all you are concerned with is the numbers of reds vs blacks), there are obviously more ways of getting 5 reds and 5 blacks than the particular sequence above, so in that sense, the sequence does not have the same probability as 10 reds in a row.

[Xander]

Dragoner is right of course; there are more paths which lead to equilibrium than not. See this article. But also you have to remember that the 'equilibrium' is with respect to proportion, not absolute numbers. In terms of the actual numbers of reds vs blacks, outcomes actually get further away from equilibrium as you do more trials. I've lost count of the number of times I've said this over the years. -Bayes

So true.

I've always believed that there's really two types of "long run". 

(Bayes, I know you already know the next part)

Long run type one: The first one is the point at which a 3,4 or 5 standard deviation fluctuation is no longer enough to break even.  This happens more quickly than most people realize, and if you're an avid gambler, then you'll reach this type of "long run" within a year or two.  I used a range of standard deviation on purpose.  Think of them as your own personal confidence levels.  If you're losing at 3 standard deviations of variance, then chances are, you're done, and unlikely to break even again with your system.  If you're winning after such a fluctuation, then keep testing.  See if you can reach 4 standard deviations.  The key is that the standard deviation continues to climb, as the sample climbs.  When talking about standard deviation, it's always important to specify the number of trials. 

Many avid gambler's have reached the type one long run, and live in denial.  Others will admit that over the years they have lost far more than they have won.


Long run type two: The other type of "long run" has to do with the point at which equilibrium begins to occur with respect to proportion and the law of large numbers.  Think of this type as being the "longer run"    I really belief that most gambler's need to focus more intention on the type 1 "long run" rather than the type 2 "longer run"

In terms of the actual numbers of reds vs blacks, outcomes actually get further away from equilibrium as you do more trials. I've lost count of the number of times I've said this over the years. -Bayes

I wish more system junkies would read the quote above.



-Xander

[Albalaha]

If you're losing at 3 standard deviations of variance, then chances are, you're done, and unlikely to break even again with your system.  If you're winning after such a fluctuation, then keep testing.  See if you can reach 4 standard deviations.

This is the real stuff and challenge in gambling which none wants to talk about.