You're making the same mistake as the fallacy is talking about--you're thinking, deep in your heart, that probability must have some sort of memory and thus there is such a thing as having too much good luck. This is not the case. If you get heads 100 times while flipping a coin, the probability of the next coin being heads is still 50/50.

Casinos and other gambling establishments play on this--they set up the odds in such a way that you have a reasonable chance of winning, because not even the most foolish gambler will keep playing a game they never win at; however, the overall result will always be that the house takes more money from the gamblers than the gamblers win back from the house. In the simple heads/tails example, they might charge 50p for a coin flip and allow you to win 90p if you get heads but nothing for tails; on average, this still nets them £1 in income for every 90p they pay out, so they're happy, and the gamblers still win often enough to keep them playing.