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You're actually in great shape for H. How badly do you want Y?

A third retake with a 173+ would look better than what you have now, even if your reviewers at Y disfavor retakers to some degree.

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Well, if you're consistently testing at 175+ under realistic conditions, I'd say go for it.

Like I said, even if one or more of your reviewers isn't crazy about retakers, that ship has already sailed. Adding a >172 to your list would be better than what you have now, both because it would give you a better highest score, and because it would dispell concerns that the scores in the 160s were more representative and the 172 anomalous.

Be forewarned that Yale dislikes retailers, and the admission process can be seemingly random.

Since you've already retaken, I don't see why not.

Maybe there's a way to mitigate retakes for Yale. I'm not sure.