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I wish everyone is doing well.

I’m an international student and just received my score in June-Flex, which is a 166. Due to some technical issues, I was informed at 0:01 am suddenly that I had to take the rescheduled exam at 3:20 am, which was quite horrible and my brain wasn’t really working. I usually get a 168-169 when testing myself, well, not a great score either.

In April-Flex I forgot to bring my passport and showed only my Chinese ID(I know it’s stupid) so I was labeled ‘Cancel/Other test Violation’. Is that going to damage or destroy my application?

I have decent softs so no worries on that. I also think that I have good chances to get an S on GPA for my university ranks high and my average is over 91/100.

I’m surely to retake lsat, and my only chance this year is in October, hopefully I would get a 170+.

And I’m just wondering my chances right now to make sure I understand my situation, basically like whether I would have any chance concerning T20 or T21-25(I’m not sure), for it seems that everyone has a 170+ with high GPA and decent softs already…

Hey, welcome to the forum!
So, I'll do my best to tackle a few of these.
1) I'm not sure what a violation means or how schools will view it. I would retake the LSAT anyways if you feel you have more room to go. A 166 is a good but not great score. Being an international, you are relying on the LSAT for substantial part of your application (think normally it is like 70% of your application, now it is 95%...) because your GPA just won't count toward their rankings.
2) You have the scores for a T20, but, do you plan on staying in the USA? If you do, T20s don't guarantee biglaw, and you'll need biglaw to get a visa. You really need to get into a T14, which, you don't have the scores for. Yes, Vandy, WashU, UCLA, UT, and even to some extent USC/BU/BC, have 50/50 chances at biglaw, but you are rolling the dice on your future. Going to a T20 on a full scholarship is a great option (and I often recommend it over T14 at sticker, but for you, it may make sense to get a T14 so that you secure biglaw).
3) I don't mean to sound rude, but your English skills may need some work (not that mine are amazing and my grammar blows and this is an online forum). Your scores in law school may suffer regardless of your intellect if it is hard for the grader to understand what you are jotting down on that torts exam. I would just recommend reading more and watching some more American/Anglo tv.
Best of luck!