<p>For any school with admit rates below 10%, you might as well regard your chances of getting in as infinitesimally distant from zero. </p>
<p>You are absolutely a highly competitive candidate for every Ivy and every top LAC, but that doesn’t mean you won’t be denied by all of them just because you didn’t win the admissions lottery.</p>
<p>Frankly, your chances depend most on none of the things you told us here. They depend on you.</p>
<p>Do research on all the top schools for your major. Learn what they say about themselves and their values as an institution. Read college guidebooks by students and see what <em>they</em> say about those schools. Do your best to find what uniquely draws you in at each school, what connects you to it and makes you want to be a part of the community.</p>
<p>Then communicate that personal connection effectively. Demonstrate in words and deeds that you belong there. </p>
<p>Right now, you seem to be evaluating schools on a single-axis system: Prestige. I encourage you to incorporate more variables into your value system. Have a reason, for example, why Harvard is #1 other than “Because a ranking list said so.”</p>
<p>As an example, someone applying to Oxford in the UK might value it highly not only because of prestige, but because of the residential college system, the intimate tutorial method of instruction, the specific reputation of its faculty in PP&E (Politics, Philosophy & Economics), and the community of the city of Oxford. </p>
<p>On the other hand, someone else might value the London School of Economics not only because of prestige but because they prefer to live in a big city with ample internship opportunities, prefer larger classes than the tutorial system provides, revere the reputation of its faculty, and think a residential college system is for ninnies who want to pretend they’re at Hogwarts.</p>
<p>The devil is in the details. Prestige matters, but fit matters more. Find what fits for you, and I like your chances very much. Your stats on paper look very fine, but it’s the man - not the paper - who gets admitted to any school.</p>
<p>As T26E4 said with more brevity, “You should thoughtfully investigate schools on what they have to offer you (and what you have to offer them).” This. This, times 1000.</p>