At the county fair, Donna discovers an intriguing carnival game called the "Lucky Duck". The game features a pool of 100 rubber ducks, each hiding a random prize from $1 to $100 underneath. The rules are simple:

1. Donna can play as many rounds as she wants but each round costs $1
2. She looks at the number under the duck, and the duck is returned to the pool and well-mixed
3. She can either keep the amount she just saw, or pay another dollar to pick again
4. If she decides to stop, she wins the dollar amount under the last duck she picked