I don't get how you're guaranteed to be rich in 10-15 years. If it's a 1/4 chance of being rich every x years, it's still just 1/4 chance over the span of 10-15 years, right?
However, I'm going to guess that you mean every time you try is going to influence the next time you try for the better (as evidenced by some paper about higher success rates for 2nd+ time entrepreneurs I remember on here), which makes sense. You learn from your mistakes, you make contacts, you have a better view of the market--so it shouldn't stay one in four every time you try.
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.
However, I'm going to guess that you mean every time you try is going to influence the next time you try for the better (as evidenced by some paper about higher success rates for 2nd+ time entrepreneurs I remember on here), which makes sense. You learn from your mistakes, you make contacts, you have a better view of the market--so it shouldn't stay one in four every time you try.