Correct me if my understanding is invalid: Penn has early decision (binding) and Princeton has early action (restrictive). The restrictive early action prohibits applying to other early to other private institutions, but not public institutions.
My scenario: I am a strong student looking to apply to Princeton, Penn, Chicago, and WashU (as reach/first/un-guaranteed choices, if accepted to all/some then I choose which to attend based on that order) in the fall of 2019. I believe that I have a higher chance of getting into Penn than Princeton, which is further reconfirmed to me in the fact that Penn also has a higher acceptance rate than Princeton. Penn, with regular about 9% acceptance, admits more students than Princeton (nearly 3x as many), and Princeton's acceptance rate is about 6.5%. However, with early decision at Penn, the acceptance rate jumps to roughly 23%. To be clear, I do recognize that Penn has a larger student body than Princeton, that more people apply to Penn than Princeton, and that most of Penn's class applies early. I believe I can get into Penn (especially with early decision), however I do like Princeton more than Penn. I'm just unsure as to whether I'd be willing to sacrifice applying early to other schools by applying restrictive early action to Princeton. I don't think my chances will be as high getting into Princeton and I don't want to not get into Penn because I applied regular decision. On the other hand, I also don't want to apply early decision to Penn and then get accepted into both Penn (ED) and then Princeton (regular), and be regretful that I can't attend Princeton due to choosing to apply early decision to Penn. Would it be worth applying early action to Princeton even if I'm questioning whether I'll get in? Princeton is undoubtedly my number one school, between the campus, and the city, and the college, I love it all, yet I don't want to cost myself getting into another quality school. My safety schools are UMich, UVA, and OSU (all public schools), so the restrictive early action wouldn't affect them correct? For WashU and Chicago don't have (or in Chicago's case, have, but also have ED) EA, so I didn't plan on applying EA/ED to them anyways. I don't expect to get into Chicago, and Penn and Princeton are Ivies so they are obviously reach schools, yet I don't know just where my chances lie. I have a few months, but any help/direction/opinions on which school to apply early to would be incredibly appreciated.
Condensed Version / Main Question: I like both Penn and Princeton (Princeton the most), and am having trouble deciding which school I should apply early to. I believe I have a higher chance of getting into Penn (especially should I apply ED), yet I am confident if I apply ED to Penn I will get in, but because of my luck Im sure if I got into Penn ED then I would also get into Princeton regular, and on the flip side I don't want to chance applying to Princeton EA and then not getting into Penn (possibly due to the disparity of ED versus regular at Penn). Which school should I apply early to?