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His ideal adversarial strategy becomes non-trivial when you know about it.

It is very likely “just flip a coin to turn it back to 50/50” but may be something statistically sophisticated.




If his desire is for the contestant to lose, then he can't really do better (formally) than winning 2/3 of the time by simply opening the door that they choose. In practice, always opening a goat-door and always asking to switch for a car-door can do slightly better than 2/3 because some contestants, unaware of his strategy and objectives, might choose to switch.

If his objective is more subtle -- increasing suspense or entertainment value or getting a kick out of people making a self-destructive choice or just deciding whether he likes a contestant -- then I'm not sure what the metrics are or what an optimal strategy would be in those cases.

Given that his motives are opaque and given no history of games upon which to even inductively reason, I don't think you can reach any conclusion about whether switching is preferable. Given the spread of possibilities I would tend to default to 50/50 for switch/no-switch, but I don't have a formal justification for this.




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