<p>There is no need to fret over something like this for now. Visit both campuses and decide if you should apply to both schools. If you apply to both, you will four possible results, 1. you will get rejected by both schools; 2. you get accepted to Stanford “only”; 3. you get accepted by Caltech “only”; 4. you get accepted by both schools. Your good problem will occur only with Scenario #4. When that happens, come back and post the question again and I am quite sure a lot of good people in the forum will try to help you from there, I promise.</p>