Yes, the whole point is that the car doesn't move. When you initially chose, you had a 1-in-3 chance of correctly choosing the door with the car. The host is now offering you to switch over to, essentially, "all the doors you didn't choose", which means 1-(1/3). As you state, you've only got one opportunity to play, and the car itself hasn't moved, but you can switch your choice. Stick with the initial 1-in-3 chance, or go to the other side, i.e. 2-in-3 chance?

> But you’re not improving this game’s chances.

You’re quite wrong. That is precisely what you are doing.

> You’re improving your average chances. But you’re not improving this game’s chances.

If the strategy won't improve your chances in any single game in a series of games - how can it improve the average chances?

Unless you are arguing that you don't really have a choice because your actions are predetermined you are absolutely increasing your chances of winning this game.

What do you think “this game’s “ chance of winning is by following the strategy vs not following the strategy?

I don't get what you're trying to say.

The car doesn't move, but your pick moves, even in this single game.