Regarding The Law Of Large Numbers/Strong Law Of Convergence And The Random Walk

[The General]

Regarding the law of large numbers/ strong law of convergence in roulette.  Regression to the mean nonsense in the system player's world (this isn't really what regression to the mean means, but it's what players often think it means). (Random walk)
 
 
Let's say the wheel has only two possible outcomes, red or black.
 
Our expectation moving forward is that black will hit about half of the time, and that red will hit about half of the time.
 
After ten spins our results with a little variance thrown in is as follows:
RBRRRRRBRB
 
30% Black (3 hits)
70% Red hit.  (7 hits)
 
Now that there's an imbalance, what do you suppose our expectation is moving forward for the next set of 20 spins?   Is black due to hit more frequently than red?  Does black have to hit more than red for "system player's regression to the mean" or "system player's law of averages" to occur?   
 

 
Moving forward, we have 20 more spins below. Our expectation once again is that each color will hit equally.  But with a little variance thrown in the results are as follows.
RBRBBRBRBBRRRBBRRRBR
 
45% Black (9 hits)
55% Red (11hits)
 
Now take a close look at the grand totals for all 30 spins below.
 
40% Black (12 hits)
60% Red (18 hits)
 
Because black went from hitting only 30% of the times to hitting 40% of the time in the larger sample,  here's where some of you will say that "regression to the mean" is taking place.   (Some of you are probably also saying that it's the "law of averages".)

It's true that black hit more frequently, but it's still a net loser! In order for it to appear to regress to the mean, it didn't have to hit more than red in order to appear to catch up, all that needed to really take place was the spin sample had to grow larger!

In small spin samples, the difference between how often the red and black hit can be quite large...percentage wise. moving forward, our expectation should always be just expectation, not that one color will hit more than the other to even out the imbalance!   Again, as the spin samples grow exponentially larger, The strong law of convergence/law of large numbers/regression to the mean appears to happen, even if the losing color never catches back up!

The strong law of convergence/law of large numbers/regression to the mean doesn't, can't, won't, will not make anyone's roulette system work!  Not in small samples, big samples, wide samples, short samples, short term, near term, long term.  Ever!

-Real

[Priyanka]

The strong law of convergence/law of large numbers/regression to the mean doesn't, can't, won't, will not make anyone's roulette system work!  Not in small samples, big samples, wide samples, short samples, short term, near term, long term.  Ever!

-Real

I think you believe in emphasizing. I think this is probably the umpteenth time you are posting it. I dont think any one is disagreeing this. Any one?
Its funny that "Real" is surfacing again

[The General]

I think you believe in emphasizing. I think this is probably the umpteenth time you are posting it. I dont think any one is disagreeing this. Any one?

This is only an assumption and not a fact. No one has been able to prove yet the strong law of convergence. Only the week law has been proven. This is in direct contradiction to equidistribution theorem which can be proven through Weyl's criterion.

oOPS! Then perhaps you shouldn't have used it in your post. 

[Priyanka]

oOPS! Then perhaps you shouldn't have used it in your post. 

Did I say I am using strong law of convergence. Read again. I said strong law of convergence is never proven and hence your proof which uses strong law of convergence as a "mathematical fact" is not valid. Why would i use a law that is never proven and use it to beat roulette. Quite funny. 

[The General]

Priyanka,

Whatever you say, but you know you were attempting to use it as an example on how/why you felt the random game of roulette could be exploited.   

[Priyanka]

but you know you were attempting to use it as an example on how the random game of roulette could be exploited. 

No. Never.

[The General]

ok