I will take up the role of bearer of not-so-great news. (And keep in mind that there is a "Chances" section for this sort of post.)
For starters, the set of schools in that acronym are some of the most selective extant. So your chances are generally under 20% to begin with.
Then keep in mind that the number of spaces per class falls off precipitously every year. So things get worse in terms of available slots.
When you factor in that you might need FA, which most schools state that they have limited resources for (I think Andover is the exception)...things aren't looking good at all.
That said, if you don't apply you have a 0% chance of getting in.
I would encourage you to broaden your scope of schools if attending a US boarding school is truly important to you.
I would also consider doing a repeat soph year (if you are currently a soph) to up your chances.