No, just a mismatch with understanding your wording. With your original wording, it didn't make sense, since each roll would have the same prob, no matter how many times you rolled. That's why I figured you meant that rolls weren't independent from each other.
But it seems that you mean, what's the chance that given x number of rolls, the very last one is a "1" (assuming you only need/want to get rich once). As the number of rolls increase, the chance of that scenerio (a string of non-1s with the last one being 1) becomes smaller and smaller when taken as a whole.
How else could I possibly mean "keep trying for 10-15 years"? One can't take 2-5 year increments of your life in isolation, since, as you've noted, you only need to get rich once to be rich.
So, no matter how many times you roll a die, you've only got one in six chance of rolling a 1 in all of the rolls?
Somehow, I think your math is slightly off.