Ann has a choice of two babysitting payment options:

1. She can accept a flat rate of $15 for a night's work, or:
2. She can choose two of six sealed envelopes containing $1, $1, $5, $5, $10 and a $20 bill.

(For example, the second option could leave Ann with as little as $2 or as much as $30 for a night's work.)

Assuming that Ann will have to babysit for a very long period of time, which is the better payment option for her?