The Multiplier Booth

At a night-market booth, you roll one fair six-sided die and draw one card from a well-shuffled standard 52-card deck. Cards carry their number value: ace counts as $1$, jack as $11$, queen as $12$, king as $13$. The booth pays you, in dollars, the product of the die's face and the card's value. What is the smallest entry fee the operator can charge without losing money on average?