What do you think bayes? I extremely value your thoughts too.
Priyanka,
Your question poses a bit of a dilemma for me, because on the one hand, I'm a "math guy". That means I respect the maths and "believe" it. On the other hand, I'm also a system junkie, and without boasting I claim to have done rather well out of roulette playing my systems.
I absolute get what the General is saying. The random game of roulette cannot be beaten because IF spins are equally likely and independent, no winning system is possible - that's one definition of what random MEANS - equally likely and independent. Simple logic.
However, how do I explain the fact that the house edge hasn't caught up with me? The general will say it's because I've essentially been lucky (riding a temporary positive variance), but I know enough about probability and statistics to know that it can't be so, because "luck" runs out eventually. I also know a few others who have been similarly "lucky".
So I propose the following hypothesis which may account for my success. The random game of roulette really only exists in some Platonic realm where mathematical equations are real (not just models of the world) and *dictate* outcomes, which is absurd. There is the random game of roulette and there's the real game which the general exploits because real wheels are not Platonic wheels.
So in the real world we can strike out one of the twin pillars of randomness - that outcomes are equally likely - at least sometimes and for some wheels it is not the case. Is it so absurd, then, to suggest that the remaining pillar of randomness - independence - also exists only in a Platonic realm?
After all, you can't *prove* independence. You can test for it, and of course outcomes really are independent in the sense that each pocket remains on the wheel between spins, but independence can be violated in other ways, and the tests for independence such as Chi-Square etc are just that - tests. And there are any number of ways of testing. Do you know how many statistical tests are out there? literally hundreds, and more being invented all the time.
Testing a simple scenario like "after 10 reds in a row black is more likely" will always return the apparently obvious and common sense result that these events are independent when using the simple tests which everyone knows about (well, all statisticians anyway). No argument from me there, but is that sufficient to put an end to the matter? I don't believe so.
You may argue that non-bias and independence are fundamentally different beasts and that no-one has ever found a wheel which generates dependent outcomes, but plenty of wheels have been found to be biased. But that just begs the question - it *assumes* the very thing to be proved.
Also, without wishing to deflect from the topic, there's a massive inconsistency going on here between Turbo and the general. I have great respect for both you guys but Turbo ain't no AP. If "math beats a math game" (and I agree, taking a broad view of "math"), how come the general always backs up Turbo when he obviously believes no such thing? The general believes that "Physics beats a physics game", and that *anything* else is fallacious. Yet he apparently indulges *Turbo's* fallacy while trashing everyone else's.