One thing you're missing: "The host of this game, who knows where the prize is, then opens one door without a prize" Does the host _always_ do this, or does th

One thing you're missing: "The host of this game, who knows where the prize is, then opens one door without a prize" Does the host _always_ do this, or does the host have discretion about _whether_or_not_ to do this? This has not been stated in any of the problem descriptions here, and I believe it's highly significant. If the host can choose whether or not to do this, then there is the potential for mindgames. If the host cannot choose whether or not to do this, that must be stated.