There might be hidden variables. Maybe the previous results are a sign that a particular croupier is working that day, which is why you can count on some specific bias for the next numbers.
I.e. some hidden process is causing both of the events, the first event is not causing the second. What you will observe is a high probably of the second event conditioned on the first.
> Maybe the previous results are a sign that a particular croupier is working that day
A more reliable indicator would be, oh, I don't know, looking at the croupier's face and seeing who it is? Just an idea.
Ok, maybe the croupier is not a "hidden" variable, but it could be whether he had coffee that day, which roulette wheel is being used, the lighting conditions in the room, whether he was able to park in front of the building or had to walk from the parking lot, etc. Any event that happens some of the time and causes 1, 2, 3 as the first three numbers can very well be causing a specific distribution of the next numbers.
I.e. correlation doesn't imply causation but translates to dependent probability distributions and therefore a "if A then B is likely" just because A can be observed before B.
I can believe that too, but that's not the claim being made here. The claim is that the bias was bound to particular roulette wheels, not particular croupiers. Also, even if a croupier had a reliable contingent bias, you'd still need a ridiculous number of data points to figure that out.