 There, the possibility exists that the show master plays deceitfully by opening other doors only if a door with the car was initially chosen.A show master playing deceitfully half of the times modifies the winning chances in case one is offered to switch to "equal probability".As already remarked, most sources in the field of probability, including many introductory probability textbooks, solve the problem by showing the conditional probabilities that the car is behind door 1 and door 2 are and (not and ) given that the contestant initially picks door 1 and the host opens door 3; various ways to derive and understand this result were given in the previous subsections.