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You are correct in saying that my writing was not precise enough. I did switch between perception of the player and reality in mid sentence without identifying it; that is sloppy writing.
It is obvious that the player had a 1/3 chance of picking the grand prize when he made his original selection. That remains constant if he doesn't change that selection. The other two doors equally split the remaining 2/3 probability since the sum must always equal one as you stated.
Monte's action in stage 2 of the game always changes the odds of the remaining door, even if he selects the winning door which he never does. Since the player's odds are invariant before he chooses to act or not to act, the remaining unopened door must have a 2/3 probability as the game usually proceeds. If Monte elects to violate his usual practice and exposes the grand prize, the odds of the unopened door containing the grand prize obviously drop to zero.
Regardless of Monte.'s actions, the odds assigned to each of the unopened doors always change as the result of Monte's second stage actions.
Your effort in this exchange is very impressive. There is no doubt that your probability skills (familiarity with Bayes application) and sophistication exceed most of us. That should help your investing decisions.
Comments
You are correct in saying that my writing was not precise enough. I did switch between perception of the player and reality in mid sentence without identifying it; that is sloppy writing.
It is obvious that the player had a 1/3 chance of picking the grand prize when he made his original selection. That remains constant if he doesn't change that selection. The other two doors equally split the remaining 2/3 probability since the sum must always equal one as you stated.
Monte's action in stage 2 of the game always changes the odds of the remaining door, even if he selects the winning door which he never does. Since the player's odds are invariant before he chooses to act or not to act, the remaining unopened door must have a 2/3 probability as the game usually proceeds. If Monte elects to violate his usual practice and exposes the grand prize, the odds of the unopened door containing the grand prize obviously drop to zero.
Regardless of Monte.'s actions, the odds assigned to each of the unopened doors always change as the result of Monte's second stage actions.
Your effort in this exchange is very impressive. There is no doubt that your probability skills (familiarity with Bayes application) and sophistication exceed most of us. That should help your investing decisions.
Best Wishes.