> I don't want to argue which rule would be more natural or make a more interesting show. But without a clear rule, I cannot decide on a playing strategy.
It doesn't make any difference to your strategy! You don't get any choice if the host opens the door and reveals the prize, so your strategy can't possibly be affected by what the payoff for that scenario is - even if you win 10x the prize if that happens, or get executed if that happens, it makes no difference to whether you should switch or not in the scenario where you actually do get given a choice.
I agree you do not need a strategy if the rule is insta win/loss.
But if the rule were to reset the game until the host doesn't make any more mistakes, it matters.
I don't want to argue which rule would be more natural or make a more interesting show. But without a clear rule, I cannot decide on a playing strategy.
> Why "provided he gets into the gameshow final"?
Because I assumed that the host always has to open a door and give a choice to switch.