Switching doesn't change where the prize is more likely to be. That's not how the Monty Hall Problem works. It's the host giving you information about what's happening behind the scenes, by choosing a door to open and you knowing how the host operates.

Whether you end up switching or not, the other opened door is 2/3 likely to contain the prize and the door you picked originally has a 1/3. Whether you switch or not, doesn't change the odds.