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.