==> decision/monty.hall.s <== Under reasonable assumptions about Monty Hall's motivation, your chance of picking the car doubles when you switch. The problem is confusing for two reasons: first, there are hidden assumptions about Monty's motivation that cloud the issue; and second, novice probability students do not see that the opening of the door gave them any new information. Monty can have one of three basic motives: 1. He randomly opens doors. 2. He always opens the door he knows contains nothing. 3. He only opens a door when the contestant has picked the grand prize. These result in very different strategies: 1. No improvement when switching. 2. Double your odds by switching. 3. Don't switch! Most people, myself included, think that (2) is the intended interpretation of Monty's motive. Interviews with Monty Hall indicate that he did indeed try to lure the contestant who had picked the car with cash incentives to switch. However, if Monty always adopted this strategy, contestants would soon learn never to switch, so one presumes that occasionally Monty offered another door even when the contestant had picked a goat. At any rate, analyzing the problem with this strategy is difficult, since it requires knowing something about Monty's probability of bluffing. A good way to see that Monty is giving you information by opening doors that he knows are valueless is to increase the number of doors from three to 100. If there are 100 doors, and Monty shows that 98 of them are valueless, isn't it pretty clear that the chance the prize is behind the remaining door is 99/100? The original Monty Hall problem (and solution) appears to be due to Steve Selvin, and appears in American Statistician, Feb 1975, V. 29, No. 1, p. 67 under the title ``A Problem in Probability.'' It should be of no surprise to readers of this group that he received several letters contesting the accuracy of his solution, so he responded two issues later (American Statistician, Aug 1975, V. 29, No. 3, p. 134). However, the principles that underlie the problem date back at least to the fifties, and probably are timeless. See the references below for details. Reference (too numerous to mention, but these contain bibliographies): Leonard Gillman, "The Car and the Goats", AMM 99:1 (Jan 1992), p. 3 Ed Barbeau, "The Problem of the Car and Goats", CMJ 24:2 (Mar 1993), p. 149 The second reference contains a list of equivalent or related problems.