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I just want to point out here that the GF is not an objective proveable fact but a theory; statisticians know that it can't actually be proven.

oh I can feel all the intense appeals to authority coming oh boy I just can't wait!

Reyth,

This is an example of a

category mistake. The GF isn't a "theory", which is a proposition or set of propositions which are either true or false, but an ARGUMENT (and an invalid one, which is why GF is a fallacy). Statisticians, or anyone else, can't prove that roulette outcomes are independent for any given wheel without empirical evidence (they could use the diehard tests, for example). If GF WAS a theory, then you would be correct, because outcomes may NOT be independent in any given case (I''ve already given an example of how dependence could arise in the other thread).

An argument is valid or invalid, not true-or-false. The argument implicity made by those who commit GF is something like this:

- This wheel (or sequence of outcomes generated by it) is random (meaning that spins are neither biased nor dependent).
- A lot of events of type X have just occurred.
- THEREFORE, events of type NON-X will occur soon, so I'll start betting on the non-X's.

1 + 2 are the premises, 3 is the conclusion. The fallacy arises because the player doesn't understand independence very well, or forgets that "random" means that outcomes are unbiased AND independent. If outcomes are independent then the conclusion doesn't follow from the premises. The conclusion is inconsistent with premise 1, because if outcomes are truly random then the occurrence of a lot of events of type X would NOT affect the probability of future X's.

It's not the business of the argument to determine the TRUTH of premise 1. Indeed, the outcomes may NOT be random (in the sense of being both unbiased and independent), but that doesn't affect the logic, which can only tell you that IF the premises are true, then the conclusion must also be true. The above argument is invalid because the conclusion could be false even if the premises are true.