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.
But if the rule were to reset the game until the host doesn't make any more mistakes, it matters.
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.