A new monty hall problem

Question

could someone help me to solve this question with the use of bayes theorem?

What would be the optimal strategy and its probability to win an item of the greatest value if the Monty Hall problem was changed such that:

1. The host will always open a door without the car (He knows where the car is at) a. The player will be able to ask the host to open a maximum of 3 doors, the however, he is not allowed to switch to the opened door(s).
2. The gameshow will include 10 doors
3. Each door contains an item of value, an increasing value, from a $1 coin to a car
4. The player will be given an opportunity to switch to an unopened door

If required (in the event the question does not work), can someone include a way to make it work? Thanks!

EDIT 1: Monty does not know the value of each door, only the door that contains the car. The contestant aims to walk away with the highest possible value, hence does not necessarily mean he has to walk away with the car prize (IE highest possible prize value)