Scepticus,

My definition is completely consistent with the one on Wiki. It seems you haven't understood or read it carefully (the wiki definition) because after the first part it says

In situations where the outcome being observed is truly random and consists of independent trials of a random process, this belief is false.

So what makes the argument a fallacy is the ASSUMPTION that outcomes are independent, because if that's true, then it is NOT true that outcomes will "catch up". The premise that outcomes are independent must be in the argument, either implicitly or explicitly, in order for the argument to be invalid. If it's there, then the conclusion that outcomes will catch up doesn't follow, so it's a fallacious argument. It's irrelevant whether outcomes really are independent or not; that's a matter for empirical investigation.

Look at cht's example:

Past 50000 spins shows 60% hit rate for red. You believe this hit rate will remain based on statistical count. That's gamblers fallacy

No, it's not. Where is the premise that outcomes are independent? And in fact, it's sensible to assume in this case that outcomes are biased in favour of red because the probability that this would occur by chance is astronomically low. But this isn't the same as the REVERSE GF, which in order to be classed as such, must also imply independence between outcomes. So the hot number system advocates aren't really committing reverse GF if they believe that that's just the way the wheel behaves, ie that repeats are more numerous than not, and they are trying to capitalize on it. It's a subtle point.

AP's are often accused by system players that they use past spins, so, (they continue) why can't us system players do it too? What makes collecting past spins for the purpose of discovering possible bias different from the way most system players use past spins?

Well I've just explained what the difference is.There's a lot more to GF than meets the eye.