Well if we frame the question as “what is the probability of winning by always switching” then this doesn’t play into it and the answer is indeed 2/3. Hence as

Well if we frame the question as “what is the probability of winning by always switching” then this doesn’t play into it and the answer is indeed 2/3. Hence as a question about general strategy the standard answer is correct. You’re right if we are asking about a specific case though.