Probability: What Is Expected Value?

You have two standard dice. On each, the sides with $1$ and $6$ are opposite, the sides with $2$ and $5$ are opposite, and the sides with $3$ and $4$ are opposite. You are playing a game with a friend, in which each of you takes a die, and rolls $20$ times. The highest score wins and your score is the product of the $20$ numbers you roll. What is your best strategy?