Racing to the first ace from unequal piles

A shuffled $52$-card deck is cut into a $13$-card pile and a $39$-card pile. You pick a pile and a friend gets the other. Each of you turns cards from the top of your own pile until reaching your first ace; whoever needs fewer cards wins. A pile with no ace loses to the other, and equal counts are a tie (no winner). Which pile should you pick? Answer $13$, $39$, or $-1$ if it makes no difference.

$39$. The small pile has no ace with probability about $0.30$, which outweighs its speed when it does contain one. Exact enumeration over the ace split gives a win probability of about $0.510$ for the $39$-card pile against $0.455$ for the $13$-card pile.