Oy, false as stated, as so much about the Monty Hall Problem is. While the importance of "standard assumptions" are noted, the key standard (and almost always u

Oy, false as stated, as so much about the Monty Hall Problem is. While the importance of "standard assumptions" are noted, the key standard (and almost always unstated) assumption is not: that all contestants get the offer to rechoose. This wasn't true in the actual show, which was using the rechoose option sparingly, and employing it to take back prizes. I'm old, before anyone wrote about the problem I noticed the show rarely offered a rechoice unless the contestant had guessed right. Why not? They had a chance to save some money by preying on naive contestants. In such a case (where the host either knows the sequence of doors in advance or is signaled) there is no probability, or if you like, the probability is whatever the show's producer or executives decide it will be. In the event, way back, it seemed to me that that probability was very low.