The Wikipedia gives a nice brief summary which hopefully will convince you (EFLI) that the 'two-thirds when switching' probability has been far from readily/easily 'accepted':[in response to EFLI]I fear you have missed the 'issue' The countless thousands (or millions) of (wo)man-hours that have gone into the discussions, debates and arguments over the years about the MH problem have all been about the probability of winning if one switches (or doesn't switch). In other words, "If it is accepted that it is two thirds when switching..." is very far from 'being accepted' without a big fight!!
Vos Savant's response was that the contestant should switch to the other door. (vos Savant 1990a) ... Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. ... Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999).
Kind Regards, John