Chance me for Chicago/Stanford/Ivies?

<p>I am applying to Chicago, Stanford, Harvard, and Princeton, and I was hoping that I might be able to get some rough estimates on my odds for those schools.</p>

<p>This past year I transferred, for reasons I won't get into here, from one of the strongest schools in my area (average SAT of about 1800) to one of the weaker schools (average SAT of high 1600s). As a result my class rank is difficult to calculate as my previous school did not give me a class rank and many of my classes do not transfer over to my new school's GPA.</p>

<p>UW GPA: 3.7
W GPA: 4.48
SAT: 2190
Math: 760
CR: 800
Writing: 630</p>

<p>APs:
Freshman: Comp Sci-4
Sophomore: Calc BC-5, Stats-5, Physics C Mech-4, Euro History-5
Junior: Chem-4, Eng Lang-5, US History-5
Senior: Econ, Eng Lit, US Gov</p>

<p>Extracurriculars:
Varsity Track and Field / Cross Country: Varsity letter as freshman on very competitive team, several coaches awards, multiple time indoor state championship qualifier, world youth trials qualifier, sub-15 3-miler in cross country. Unfortunately my track times are not quite fast enough to be recruited to a top D1 school, as I took some time off from competition in sophomore/junior years.
Mathematics: Several colleges courses outside of regular curriculum. Pass (on P/NP basis) in Multivariable Calc, A in Linear Algebra, and taking Real Analysis next semester at Stanford OHS. A- in UCLA upper division Game Theory, and getting a letter of recommendation from professor there. Wrote some of my supplementary essays on self-studying Rudin's "Principles of Mathematical Analysis" which is taught in many universities' advanced undergraduate coursework.
Little volunteer work, worked at city's library in sophomore/junior year and as "team manager" for school's swim team but otherwise very little.</p>

<p>Essays:
I believe that my essays are very unique and strong (although that may just be bias). Personal statement written about how mathematics is a world of it's own, and seeing through this world gives me a unique perspective on life. Supplementary essays have also been for the most part about how I have developed as a thinker (in many cases from exploring abstract concepts in mathematics), and I think that they are very individual as they cover my experience with topics that most students will not explore until junior/senior year in college. While the personal statement and supplementaries may sound similar, I assure you, they are written very differently with dissimilar focuses and information.</p>

<p>Thank you for your help, and I appreciate your opinions!</p>

<p>SAT and GPA are on the low side…</p>

<p>GPA is rather low, any idea what your class rank is, also where the Bs mainly in core subjects or electives?</p>