a group of spins (cycle/session, etc) gives predictable results even though each spin is random and independent

You are confusing plain statistics with predictability.

For example, the law of a third. In 37 spins, about a third of numbers will be repeated.

It sounds predictable and usable. The reality is:

* You don't know which numbers will repeat, with better than 1 in 37 accuracy.

* Even if you knew some recent repeaters, you don't know which will repeat again, with better than 1 in 37 accuracy.

You are trying to say one sequence of spins has a different probability of another sequence. Like 33,33,33 is any different to 32,4,15. Anyone who tested enough would know this. You're just talking about plain statistics.

The fallacy is just like saying after 10,000,000 spins, there will be around even reds and blacks. It doesnt help, at all.

That means that any number on average will show up once per 37 spins.... we can all agree with this right ?

Sure, we agree on that.

But no.. as you can test and prove to yourself - 24 numbers appear on average every 37 spins, not 37.

You appear to be forgetting that a number can hit perhaps 3 times in 37 spins. Or it can not hit at all for 100 or so spins. The average is still 1 in 37.

Another thing to test is see how often this combination of numbers will spin in trillions and trillions of spins:

0,1,2,3,4,5,6,7,8,9,10,11,12, ... etc to 36

Then see how often any other combination of numbers spins. What you'll find is in the long term, it's exactly the same!

The point is the wheel doesn't give a crap about what you think. Patterns in your head, hot numbers and trends, are just in your head.

there will never be 37 numbers that show once and no repeats.

Completely wrong. If you test my point above you'll see you've made a mistake.

I said it until I'm blue in other posts. A number can't show twice unless it's shown once, it can't show 3 times unless it's shown twice, etc.. And most importantly - you can never lose a single unit on any number that doesn't appear because you never bet on it.

If you agree the odds of the next number are 1 in 37, then this is true for every spin. You cannot put a chain of 1 in 37's together to change odds. And if you claim you arent changing the odds, then what are you changing? You certainly cant change the payouts.

In roulette the two main parts are odds and payouts. You can only ever change the odds. If you claim to not be changing the odds, but that you have a long term winning system, then you dont understand what you're saying.

This is not about anyone being a "naysayer". This is plain and simple mathematics and simple logic. If a mathematician saw your claims, they would immediately recognize your mistakes. This is not complicated stuff.