Oh Oh Oh I GET IT!!!!
That’s kind of a cool way of looking at it.
It easy to see that your strategy should be switching if you look at this way. If you don’t get the prize on the first pick (with a probability of 2/3) you automatically get it after you switch, but you don’t get after you switch if your first pick was the prize (with a probability of 1/3). Thus by switching, your conditional probability of getting the prize is being weighted towards the greater probability on the first pick, that is the probability of not picking the prize in the first place.
Err...
Allowing that Monty is constrained to NOT opening the Door with the prize.
If the Prize were behind “A” - he could have opened either “B” or “C”. Thus, he was not “forced” to open “B” - “B” is simply a valid choice of available options.
The author concedes this when he states:
“Now suppose you had first picked C. Which doors could Monty have opened? Right: A or B. And in this case you should stay.”
The problem with the hypothesis is that the author, in his conclusions includes assumptions as evidence!
He asks - assume the prize is behind “C”, then “A” = 1/3, “C” = 2/3.
The problem is - at the time you need to make the decision, you have no evidence that the prize is behind “C” - you only know that it “could” be behind it, but that was a given from the beginning.
I remember this was a question somebody asked Marilyn and her (correct) answer was a topic of debate in Parade Magazine for weeks. This was many, mnay years ago.
Idiotic, but good to generate hits.