Setting aside all the math debate for just a second, the reason it’s hard to give advice about chances, when you’re talking about applying to just one top school or several, is that applying to several may change the quality of the applications. If the time required to apply to many top schools means the common app essay suffers, or the “why this school” essay to the one favorite school that actually did need an oboe player suffers, or the first semester senior year grades suffer as a result of too much time spent on extra applications, the probability of getting into each individual school could actually drop further than the already low odds the student had from submitting his/her best work, and the potentially increased probability of getting into at least one school out of the many applications may not overcome that. And for any one student, we can’t predict whether this will happen. For that one kid making the decision about whether to apply to two top schools, or ten, this needs to be considered.