The article gets the 50/50 case subtly wrong. The really naive analysis is that you have two doors so it's 50/50. A less naive, more interesting analysis, is th

The article gets the 50/50 case subtly wrong. The really naive analysis is that you have two doors so it's 50/50. A less naive, more interesting analysis, is that there are twelve possible outcomes, of which six are favourable (if the correct option is A, pick A -> presenter picks B is different from pick A -> presenter picks C). The article hides this away by lumping those two under "Host opens B or C" without further justification, but it's important to notice that this only works because those twelve outcomes have different probabilities. Edit: In table form, Car Guest Monty Swap? Probability A A B No 1/3 * 1/3 * 1/2 = 1/18 A A C No 1/3 * 1/3 * 1/2 = 1/18 A B C Yes 1/3 * 1/3 = 1/9 A C B Yes 1/3 * 1/3 = 1/9 B A C Yes 1/3 * 1/3 = 1/9 B B A No 1/3 * 1/3 * 1/2 = 1/18 B B C No 1/3 * 1/3 * 1/2 = 1/18 B C A Yes 1/3 * 1/3 = 1/9 C A B Yes 1/3 * 1/3 = 1/9 C B A Yes 1/3 * 1/3 = 1/9 C C A No 1/3 * 1/3 * 1/2 = 1/18 C C B No 1/3 * 1/3 * 1/2 = 1/18 Total Yes = 6 * 1/9 = 6/9 = 2/3 Total No = 6 * 1/18 = 6/18 = 1/3