<p>The OP says that he knows Stanford really well, has not visited Yale, but likes their residential system.</p>
<p>He is very vague about what else he cares about.</p>
<p>In terms of strategy, I agree that a person with a strong math background might have slightly more of an edge at Yale than Stanford, since Stanford tends on average to attract more math people.</p>
<p>However, the real issue is which place is preferred by the OP. He really needs to clarify his interests more (including considering visiting Yale) before making this choice.</p>