Aside from above, you never used that term, not once. You talked about an a priori hypothesis, which is completely different. That can be based on air or on knowledge.

So instead of either accepting your mistake or backing up your claim, now you resort to lying?

I've read every post, what I told you earlier is that I saw no need to RE-read it to know you were wrong.

So we have moved from
(a) trivially true; and
(b) utterly false

at the same time, to the the difference between "a priori hypothesis" and "a priori knowledge."

We're done. Sorry.

Correct, there is nothing the same about them other than coming before. So I suppose you also don't understand that and think the common Latin phrase "a priori" has one use no matter what it modifies.

You've made your point, that you "meant" to talk about a priori knowledge, and that you "meant" to say that this allows you to confirm something with fewer trials than not having it, but you didn't say any of those things. What you did say was false. And you were corrected by me and others. Instead of continuing to argue and try to say you said things you didn't, you should just admit your mistake and move on.

QED

oooookkkkkkk, now I see where you are going with this.

Yes, this is true. the odds of a particular number coming up >rand are different than the odds of 'any' number coming up >rand.

You have been arguing the wrong point. You should be arguing that a person who forms a hypothesis after looking at data 'should' come up with a more general hypothesis to account for this symmetry, and this general hypothesis would therefore require more spins to confirm.

This is definitely apples to oranges territory since of course it will take different numbers of spins to prove different hypotheses. But this whole thread you have been talking about the same hypothesis - which I now don't think is what you meant.

You have been trying to say that you can form a specific (#1 will be >rand) hypothesis before looking at data, but should try to confirm a general hypothesis (any number >rand) after looking at data. These are 2 completely different hypotheses, which obviously require different amounts of data to confirm.

but that's not what you've been saying. You've been saying that trying to confirm the same hypothesis (eg '#1>rand') after looking at data is somehow different simply by virtue of when the idea formulated in your brain. which is nonsense.

This Mark guy seems dumb.

I'm sorry it beggars you, but I have no interest in defending your statements.

Seems like they're biased against me atm, 6 big bets on red in a row I've lost [in a row as in my last 6 bets total spread over like the last month, not all in one session straight after each other].

So, per your NASCAR parallel, the wheels wear out in an accelerated manner? As the wheel and its parts show wear and tear through results, the neglected numbers will appear less and less and the numbers subject to hitting will become hotter and hotter?? Why are you wasting your time posting then-- there are minorly exploitable wheels just waiting to crumble and roll out 33, 15x in a row for you, aren't there?!

thats not what he was saying at all

Mark, do you still play biased wheels actively?

I think the factor that puts most people off is the relative frequency of biased wheels, compared to the comparative accessibility of say, card-counting or poker.
How many wheels do you think are biased to the extent that a practical advantage could be obtained?

Have you found it profitable? What sort of ROI do you/did you obtain?

I hope Mr. Billings hasn't been run off. I would like to think the forum is here to help each other. I hope he continues to post.

I haven't read every post so this may have already been mentioned.

It is important to realize that there is no specific answer to the original question. Suppose you spin the wheel a million times and a few numbers come up significantly more frequently than one in 36. And the mathematics say that the chances a fair wheel will come up witth such a skewed result is one in 200. This certainly doesn't mean that the chances the wheel is biased is 199/200. In fact it doesn't even mean that the wheel is more than 50% to be biased. To get the right number You need to know what percentage of wheels in general are biased.

It may be though that there is something about the wheel that gives you extra hope. Perhaps it is more than ten years old. In that case if you were to obtain these extreme results you need only the statistics for ten year old wheels. If you somehow knew that those wheels are more likely to be biased your experimental results are more likely to have discovered one of them.

But -- on the other hand -- a roulette wheel is one of the finest examples of precision machining I've ever seen. They are expensive for a reason.

Fortunately, that doesn't eliminate bias that may occur over time.

Additionally, there are many historical accounts of biased wheel roulette coups. I am unaware of any recent development in design that would alter the fundamental vulnerability of the wheel.

Interestingly, when Ed Thorp looked into this fifty years ago he was asssured that roulette wheels were "Jewelled spheres of perfection" which could never produce a bias. Thorp notes this was false (then). I suspect it is now.