The problem comes down to this: At a gameshow there are three doors. Behind two of them there is a goat, and behind one is a car. You pick a door. The gameshow host, who knows where the car is, then opens one door that you didn't pick, but contains a goat. You are then allowed to change your pick to the other door that is left unopened. Does this increase your chance of winning? For a more detailed description plus solution, read here: http://en.wikipedia.org/wiki/Monty_Hall_problem I've read it and the solution makes sense when you look at the possibilities and write them out, but i don't really get it on an intuitive level. There is this bit to understand it better: "It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens 999,998 of the other doors revealing 999,998 goats—imagine the host starting with the first door and going down a line of 1,000,000 doors, opening each one, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat. A rational player should switch. Intuitively speaking, the player should ask how likely is it, that given a million doors, he or she managed to pick the right one." This does explain on how you have a 1/3 chance of selecting the right one from the start, and how the probability of the car being behind the other one is 1 - 1/3 = 2/3, just like it is 1 - 1/1.000.000 in the other case. Okay. I kind of understand the solution of the problem. But i still can't get my head around the fact that one door is shown to contain a goat, let's say, door 3, the car is either behind door 1 or door 2, i.e. a 50% chance. Why is this not true? Is it because our mind tends to ignore additional information that makes it less than 50%, as the 1.000.000 goats example shows?