Right, but as you said you have no idea when either a "winning streak" or a "losing streak" will occur. Nor, after winning or losing X hands in a row do you have any idea whether you're going to or lose the next one. Chance has "no memory". What happenned before with the spin if a roulette wheel (or with the deal of a BJ hand, shuffling after every deal) does not impact what will happen next.
Question: Who said otherwise? According to your first sentence I didn't.
As such if you're betting at a $1 - $500 "spread" table your chances of winning the $500 hands and losing the $1 hands are
exactly the same as winning the $1 hands and losing the $500.
OK. You're right. They are exactly the same.
Question: Who said otherwise?
Sure, if you could successfully
predict when a streak were more likely to occur you could certainly take advantage of the spread (that's what card counters do), but the sad fact is you can't. No one can.
OK. You're right. No one can.
Question: Who said otherwise?
According to your first sentence you know I can't successfully
predict when a streak is more likely to occur.
Therefore whether you play at a $1-$10,000 with a $5K average or at $4,901-$5,100 table with a $5K average bet, your expected loss is precisely the same in both cases.
Yes, You're right, expected loss is precisely the same in both cases.
Question: Who said otherwise? What does average betting have to do with limit betting?
I have to say, though, you all seem like really nice guys, which is all too rare on forums.

But you just happen to be 100% wrong here -- not 99% not 99.9%, not 99.999999% -- but 100%.

As I've said, it's called the Gambler's Fallacy, and you're hardly the first to have fallen for it, and certainly won't be the last. (But then again your $1.3MM win does provide a nice cushion.)
I have to say that your examples have nothing to do with the spread we are referring to and you just happen to be 100% Missing the Forest thru the Trees here -- not 99% not 99.9%, not 99.999999% -- but 100%.

As I've said, it's called Missing the Forest thru the Trees and you're hardly the first to miss it and certainly won't be the last.
(But then again your $1.3MM win does provide a nice cushion.)
I Tell you what. Give me a call before you intend to land and I'll provide a nice cushion.