Turner, Ok.
I should have known better. 

[edit: I originally tried to post this in albalaha's thread, but it was locked]

I briefly scanned XXVV's post and was going to reply but it seems to have disappeared.

Perhaps albalaha took a dislike to it, for some reason. Anyway, I noticed that XXVV said "probability is a theory, not a law". This is something I've come across quite often, but it's a misconception. The "theory" in "Probability Theory" does not mean some kind of hypothesis or tentative explanation; the meaning of "theory" in the scientific sense is something other than what is meant by it in everyday life, namely:

QuoteA scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method, and repeatedly confirmed through observation and experimentation.[1][2] As with most (if not all) forms of scientific knowledge, scientific theories are inductive in nature and aim for predictive power and explanatory force.

(Source: Wikipedia).

There are different interpretations of what probability is, but the laws (or rules) of probability are the same in all these interpretations. Furthermore, it can be shown that if you violate any of the laws of probability you are violating the laws of logic (being inconsistent), so the purpose of the laws is to keep our thinking straight.That's not to say there isn't such a thing as "empirical" probability, but that just means that your probability distribution is derived from the data, not from mathematical analysis.

The well-known Binomial distribution which I used above to get the percentages of wins in 5 outcomes can be proved mathematically, and there is a formula for it, but you could come up with the same percentages by simply counting the numbers of sequences with 0,1,2... reds and dividing by the 32 possible sequences. In the case of a theoretical distribution, however, there are always assumptions associated with them.

For example, the binomial distribution assumes that all outcomes are independent and that the probability of individual outcomes don't change between trials. Note that if we take an empirical approach and just count the outcomes (with a computer) rather than use the mathematical formula, and the results match the data predicted by the theoretical distribution, then that is a confirmation of the model's applicability to the empirical data, and hence the assumptions which underlie the model.

If there is any discrepancy between results found by theory and empirical data, it means one or more of the assumptions don't hold, and that is in fact the basis of many statistical tests used to confirm or refute a hypothesis (e.g., "This roulette wheel is biased").

Also, it's not true that "variance makes a mockery of maths", because variance can be quantified in the same way that the average or mean can. Variance is just another aspect of probability, and is one of the parameters in every probability distribution.

So, in summary, we can speculate about all kinds of possible connections in nature, and of course "everything is connected", but only in the rather trivial sense that the universe is a unity, and it's hard to see how something like our state of mind can affect the simple mechanical system which is roulette. I'm not convinced by any appeal to "personal permanence" notions, either, and besides, a similar thought experiment could be applied.

Quote from: Albalaha on August 21, 2014, 03:07:01 AM

All combinations that are of same length are equally likely and they almost happen equally too.

That's not correct. All permutations are equally likely in a string of outcomes of fixed length.  So RRRRR is as likely as RBBRB, taking order into account. But RRRRR is not as likely as RBBRB ignoring the order and just looking at the number of R versus B. That's why a long run of one color is less likely than a run which contains a mixture of R/B.

A combination is not a permutation. Combinations don't take order into account, permutations do. So "all outcomes are equally rare" only applies to permutations, not combinations.

Probability of 0 reds in 5 spins = 3.1%
Probability of 1 red in 5 spins = 15.6%
Probability of 2 reds in 5 spins = 31.3 %
Probability of 3 reds in 5 spins = 31.3%
Probability of 4 reds in 5 spins = 15.6%
Probability of 5 reds in 5 spins = 3.1%

So where is the equality?

Take one sequence "at random", say RBRBB. Sequential probability says the chance of this arising is (1/2)⁵ = 3.1% but this is the same as the probability of 0 reds or 5 reds in 5 spins. What's going on? is there a contradiction?

Nope. It's just that in one case you're looking at outcomes in terms of order and the other case you're not. So the "mystery" is solved. The reason why you think a 100 reds in a row is possible is because you're looking at each possible sequence as a permutation.

And as for memory, try the following little thought experiment. Suppose you work in a roulette wheel factory and it's your job to test each wheel as it comes off the production line. You spin the wheel only once for each wheel and record the outcome, then do the same for the next wheel. Now, clearly these wheels, being brand-spanking new, have no "memory" of any past spins: your spin is the first. Do you still think it's possible to get 100 wheels each generating red in that one spin? if you do, you have to admit it can't have anything to do with past results, because none exist.

The reason why a long run of reds is unlikely is because there are a large number of possible "paths" from spin 1 to say, spin 10 (there are 1024), but only one of them will result in 10 reds. Most of the paths have a mix of red and black, and fewer have mostly red or mostly black.

There is no memory because on each spin the conditions are the same: no bias and the same number of pockets available as there were on the last spin. This means that any of the possible paths from spin 1 to spin X is both theoretically and practically just as likely as any other. The only way the ball could fall into red 100 times in a row is if there IS some "memory" (such as the black pockets being removed).

Another way to think of it is by using the word AND. AND means more conditions need to be satisfied (OR is easier to achieve). In order to get a run of 10 reds, the first spin has to be red AND the second spin has to be red AND the third spin has to be red AND...

That's a lot of ANDs, and therefore a lot of constraints. But the ball is in no way constrained to do anything, because all paths are equally likely.

Quote from: XXVV on June 12, 2014, 11:22:06 PM
Well perhaps it is coincidental

Yes, it's a coincidence. Perhaps you don't understand what it means to run your own server; it means the server isn't hosted by any third-party company, therefore the service cannot be interrupted by any third party. In order to shut down the forum, you would have to shut down the ISP. Now I don't know whether the company you complained to is, in fact, Stef's ISP, but even if it was, are you seriously suggesting that your petty complaint has resulted in Stef's access to the internet (not just the server hosting the forum) being denied? You've got to be kidding.


And yes, I do think your complaint was petty. Xander and anyone else is entitled to their opinion, and if they doubt someone's credentials, especially when they are using those credentials to bolster sales of a book which makes some extraordinary claims, don't they have a right to question? that is not "slander". If Xander had taken out a two-page spread in The Times, saying that MB was a fraud, that would be quite another matter. There's a big difference between private communication on an internet forum and the kind of slander you'd have us believe Xander has committed, but I think you know that.

Quote

That is why I think serious research and publishing needs to be in a private domain with invitation only participation.

Then why not start your own forum? you can set one up for free in 5 minutes.

betforum.cc is NOT down for the reason that XXVV stated - it has nothing to do with him. The forum server is on Stef's home computer, and Stef has recently moved house, so naturally the forum was down for that reason. He's only just got back online, and I expect the forum to be back up shortly.


XXVV, please check the facts before making such assertions!