||The Monty Hall Problem is a puzzle derived from the game show Let's Make a Deal, which first aired on American television during the 1960's and was for many years hosted by Monty Hall. Unlike most other philosophically interesting decision problems, the Monty Hall Problem has an uncontroversially correct solution, but this solution is easy to miss. The game show contestant is shown a series of closed doors and told that s/he may have what is behind exactly one of Door #1, Door #2, or Door #3. S/he is told that there is a new car behind exactly one of the three doors and nothing of much value behind either of the other two. The contestant selects exactly one of the three doors (say, Door #1), but this door is not opened. At this point the host opens one of the other doors (say, Door #2) revealing that the car is not behind that door. The host now asks whether the contestant would like to keep what is behind Door #1 or switch and take what is behind the unopened Door #3. Assuming that (1) the host must open a door that is not the contestant's initial choice and that does not have a car behind it, and (2) if the host has two non-car-concealing doors to choose from, the host will choose at random which of them to open, and (3) each door has an initial probability of 1/3 of concealing the car, it turns out that when the host opens Door #2, the probability of finding the car behind Door #3 increases from 1/3 to 2/3, which makes switching to Door #3 the correct decision. This result is surprising and counterintuitive, since, until the assumptions of the problem are taken into account, it may seem that the host has simply eliminated Door #2 and thereby given each of the remaining two doors a probability of 1/2 of concealing the car.