| >> But it doesn’t depend on Monty knowing ahead of time. Monty can learn after you pick, but before he reveals (to be sure he doesn’t reveal a car). Right, of course. I just meant he knows ahead of opening his door, it doesn't matter if he knows when you pick your door. The scouts did not know that the herds are not in the mountain when they chose to scout the mountains. Monty, on the other hand, does know that the car is not behind door C, when he chooses to open door C. The difference is that Monty will never pick the door where the car is, whereas your scouts will sometime recon a region and find the herds there. (Unless you assume that your scouts know where the herds are, and are purposefully not telling you and scouting empty areas, which would make them terrible scouts. We can expect this sort of crafty behaviour from a game show host, sure, but not from your own scouts.) This results in different odds. With the scouts, switching makes no difference. You can run simulations or draw a full probability tree to convince yourself of it. |