Using the same logic you might think that within 100k tries you are definitely going to hit a 0.01% target at least once(because it "should" happen once in 10k tries). But this is not necessarily the case. Some gamblers lose big money relying on such wrong calculations.
Man, in fact, I absolutely agree with you ... Just recently, I decided to test the doubling strategy,
(if you can call it that) but it didn't end as I expected. I assumed that using a 47% chance, and doubling the rate in case of a loss will sooner or later pay for itself, but I could not imagine that with such a high probability I will have 10 losses in a row.
My personal record is 16 reds in a row betting with 50% win chance. But I also had 17 greens in a row once.
So from my experience I can say that not everything depends on statistics.
Statistics is a good thing when we are talking about millions or billions cases, but the less cases are being explored, the more wrong those statistical expectations can become. That's why so many people like the saying "There are three kinds of lies: lies, damned lies, and statistics."
One thing in defense of statistics I'd like to say here, though. If applied properly, statistics actually never lies: it never tells you that the probability of an event is 100%, when it's not the case. It's our own fault when we assume that if something happened in 99,999,998 cases out of 100 million, it will definitely, 100%, happen to us.
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