I think you are confusing the likelihood of something happening with the estimate based on a given set of facts. The man doesn't have quantum children that are 1/3 boy or girl. So trivially P(the gender of the man's children is the gender of the man's children) = 1. They don't change gender depending on your guess. The only thing that changes is the trueness of your guess of the other child's gender (it changes when you change the guess)
The way to get clear hear is to simulate meeting the man 1000 times, and counting how many times you would have guessed right if you said he has two boys. This yields 1/3 because you don't even guess when he has 2 girls.
The way to get clear hear is to simulate meeting the man 1000 times, and counting how many times you would have guessed right if you said he has two boys. This yields 1/3 because you don't even guess when he has 2 girls.